Copyright is owned by the Author of the thesis. Permission is given for a copy to be downloaded by an individual for the purpose of research and private study only. The thesis may not be reproduced elsewhere without the permission of the Author. THE DETERMINATION OF KINETIC PARAMETERS IN HEAT PROCESSING OF BABY FOOD A thesis presented in partial fulfilment of the requirements for the degree of Ph.D. in Biotechnology at Massey University Kalaya Taimmanenate 1980 . ","lO_l ABSTRACT Two methods of heat processing kinetic parameter determination by steady-state and unsteady-state heating procedures were studied. The unsteady-state procedure was used for colour and viscosity where large amounts of samples were required for measurement, and both were used in considering the destruction of ascorbic acid and riboflavin in a baby food . To obtain accurate determination of the kinetic parameters, standard k and Ea, experimental methods had to be developed to measure the quality factors within narrow limits of accuracy. Determination of the kinetic parameters by unsteady-state procedure involved the development of a computer method for the can temperature distribution calculation, the quality retention calculation, and finally determination of the empirical relationships of the standard parameters,k and Ea,to the residuals (differences between experimental and predicted concentrations) . Temperature distribution in a can was predicted by a modified computer program based on an analytical solution to obtain a form fitting of the experimental heat penetration curve . From this, the quality retention was calculated by numerical integration. The standard k and Ea were roughly estimated from the literature either on the studied quality or on a similar quality . Then the ranges of standard k :and Ea were assigned in an orthogonal composite design and used to calculate the retained quality which then was compared with the experi? mental result to obtain the absolute residual at each standard k and Ea . The average residual at each processing temperature was used in multiple linear regression to determine the relationships between the standard k and Ea, and the residual. By optimising the empirical equation the best values for the standard k and Ea were determined. The standard k and Ea for ascorbic acid and riboflavin were also determined by the steady-state procedure. In this, small tubes of the baby food were heated in a constant temperature , oil bath. Nearly identical results obtained for ascorbic acid by both methods indicated that the method used was feasible and the degradation of ascorbic acid 0 was best described by a f irst order reaction . For riboflavin , d ifferent results were found from the two methods but these could be explained as the results of the low destruction rate of riboflavin on heating , the analytical error and the change in physical conditions from cans to tubes . So , use of the steady-state kinetic parameters for qual ity retention calculat ion in unsteady-state was conf irmed experimentally . For colour and viscosity.changes in processing , the method of kinetic parameter determination in unsteady-s tate heating procedure .was used assuming firs t order kinetics . It was concluded 0 60-139 c, the kinetic were 0 . 4 2-0 . 44 x 1 0-4 -1 and 84-105 kJ mole , in this food system for the temperature ranges of reaction rate at 1 29?C and the activation energy -1 -1 -4 -1 s and 77-85 kJ mole , 0 . 1 1-0 . 25 x 10 s -4 -1 -1 -4 1 . 20 x 1 0 s and 1 22 kJ mole and 1 . 65 x W - 1 -1 s and 1 51 kJ mole for ascorbic acid , riboflavin , colour and viscosity respect ively . ACKNOWLEDGEMENTS The success of this research was due to the experience and confidence of my supervisors , Professor R . L . Earle and Dr Mary D . Earle , whom I shall always be grateful . Their untiring interest , patience and encouragement are deeply appreciated . This work would not have been possible without the support of Chulalongkorn University to whom I am indeb ted . This scholarship would not have been possible to obtain without the help of Dr Mary D. Earle and the Chemical Technology Department , in particular , Dr K. Santiyanont , Dr C . Thanyapit tayakul , Mr V . Premyothin and Dr P . Chittaporn . I also wish to express my appreciation to various people who assis ted this research in many ways . In particular I would like to thank : Dr A . C . Cleland for his valuable discussions and criticisms and also his willing assis tance . Food Technology Research Centre , Department of Food Technology for financing the experimental work . Professor R . Richards for providing the facilities and funding the computer expenses . Mr T . Gracie for his assis tance in experimental work . Miss S .A . Wilkinson for helpful guidance in setting up s teady-state heating experiments . All tas te panelists for taking part in the preliminary work and all those in the Faculty of Food Science and Biotechnology for making such a happy working environment . Also to my typist , Vivienne Mair , for her efficiency and patience , and Nuch for taking part in the final preparation . Finally to my mother , sis ter and brothers for their continual moral support during the study . Kalaya Taimmanenate October , 1980 1 . 2 . 2 . 1 2 . 2 CONTENTS List of Tables List of Figures INTRODUCTION LITERATURE REVIEW Introduction Kinetic Theory of the Changes in Food During Heat Processing 2 . 2 . 1 Theory of kinetic reaction rate 2 . 2 . 2 Temperature dependence of the reaction rate 2 . 2 . 3 Effect of other variables on the reaction rate 1 3 3 4 4 6 9 2 . 3 Quantitative Estimation of the Changes in Food During Heat 2 . 4 2 . 5 3 . 3 . 1 3 . 2 Processing 2 . 3 . 1 Analysis of concentration 2 . 3 . 2 Determination of temperature distribution 2 . 3 . 2 . 1 Determination of thermal lag in steady-state heating -- 10 1 0 10 1 1 2 . 3 . 2 . 2 Experimental heat penetration measurement 1 2 2 . 3 . 2 . 3 Theoretical determination 1 3 2 . 3 . 3 Calculation o f kinetic parameters Changes of Food During Heat Processing 2 . 4 . 1 Ascorbic acid 2 . 4 . 2 Riboflavin 2 . 4 . 3 Colour 2 . 4 . 3 . 1 Browning reaction 2 . 4 . 3 . 2 Pigment/chlorophyll destruction 2 . 4 . 3 . 3 Total colour change 2 . 4 . 4 Viscosity Conclusion INVESTIGATION OF TESTING METHODS AND DEVELOPMENT OF PROCESS Introduction Investigation of Testing Methods 3 . 2 . 1 Ascorbic acid 3 . 2 . 2 Riboflavin 3 . 2 . 3 Colour 3 . 2 4 Viscosity 1 4 1 7 18 22 2 5 25 28 29 32 33 35 35 36 36 37 37 38 3 . 3 3.4 3.5 4. 4 . 1 4.2 4.3 4.4 Development of Process 3.3.1 Preparation of baby foods 3. 3 . 2 Preprocessing 3 . 3 . 2.1 Thawing 3.3. 2 . 2 Preheating 3 . 3 . 3 Processing 3.3 . 3 . 1 Temperature measurement 3.3.3.2 Retort operation 3 . 3 . 3 . 3 Processing conditions Adjustment of Process 3 . 4 . 1 Formulation 3.4.2 Preprocessing conditions Final Process TEMPERATURE DISTRIBUTION IN A CAN DURING PROCESSING Introduction Experimental Determination of Temperature Distribution Computer Programs for Temperature Dis tribution Calculation 4.3 . 1 Analytical sqlution method 4.3.2 Numerical .finite dif ference method Thermal Property Determination 38 38 40 40 40 41 41 42 42 44 44 46 47 51 51 52 54 54 57 60 4 . 5 Comparison between Predicted Temperatures from the Two Computer Programs - Analytical Solution and Numerical Finite Difference 63 4.6 Comparison of the Predicted Temperatures from the Analytical 4.7 Solution Program and the Experimental Temperatures 4 . 6 . 1 Comparison of temperatures in the heating 4 . 6 . 2 Comparison of temperatures in the cooling 4.6. 3 Comparison of temperatures in the overall Modification of the Analytical Solution Program 4.7.1 The beginning of the cooling 4.7 . 2 The later cooling s tage 4 . 7 . 3 Conclusion s tage phase phase process 4.8 Comparison of the Experimental Temperatures and the Predicted 68 68 71 75 75 75 79 80 Temperatures from the Modified Analytical Solution Program 82 4.9 Conclusion 86 5 . DETERMINATION OF KINETIC PARAMETERS BY UNSTEADY-STATE PROCEDURE 88 5 . 1 5 . 2 5 . 3 5 . 4 Introduction Experimental Analysis of Quality Retention Quality Retention Calculation 5 . 3 . 1 Theory of quality retention calculation 88 88 89 89 5 . 3 . 2 Computer program for quality retention calculation 9 2 5 . 3 . 3 Size o f time increment and dimension increment 93 Determination of Kinetic Parameters 5 . 4 . 1 The design 5 . 4 . 2 The analysis 95 96 96 5 . 5 Determination of Kinetic Parameters for Ascorbic Acid 100 5 . 5 . 1 Determination of the range of k1 29 oc and Ea 100 5 . 5 . 2 A model for ascorbic acid for determination of kinetic parameters 1 0 1 5 . 6 Determination o f Kinetic Parameters for Riboflavin 105 5 . 7 Determination of Kinetic Parameters for Colour 1 10 5 . 8 Determination of Kinetic Parameters for Viscosi ty 1 1 1 5 . 9 Conclusion 1 14 6 . 6 . 1 6 . 2 6 . 3 6 . 4 6 . 5 6 . 6 KINETIC PARAMETER DETERMINATION BY STEADY-STATE PROCEDURE Introduction Experimentation 6 . 2 . 1 Sample preparation 6 . 2 . 2 Thermal processing sys tem 6 . 2 . 3 Determination of ascorbic acid and riboflavin Des truction of Ascorbic Acid and Riboflavin on Heating Determination of the Order of Reaction Kinetic Parameters Determination 6 . 5 . 1 Calculation of kinetic parameters for f irs t order reaction 6 . 5 . 2 Calculation of kinetic parameters for second order reaction 6 . 5 . 3 Determination of kinetic parameters for ascorbic acid 6 . 5 . 4 Determination of kinetic parameters for riboflavin Comparison of Kinetic Parameters Determined by Steady-State and Unsteady-State Procedures 1 1 7 1 1 7 1 1 7 1 1 7 1 1 8 1 19 1 19 1 2 1 1 26 1 26 1 2 7 1 29 133 1 38 6 . 7 7 . 7 . 1 7 . 2 7 . 3 7 . 4 7 . 5 8 . 3 . 1 3 . 2 3 . 3 4 . 1 4 . 2 4 . 3 4 . 4 4 . 5 6 . 6 . 1 Ascorbic acid 6 . 6 . 2 Riboflavin Conclusion DISCUSSION Temperature Prediction in the Can Use of Steady-State Kinetics Data to Predict Quality Changes in Uns teady-State Heat Processing Kinetic Analysis Us ing Unsteady-State Heating Procedure Kinetic Parameters for Ascorbic Acid, Riboflavin, Colour and Viscosity in Heat Processing of Baby Food Application to Processing CONCLUSION REFERENCES APPENDICES Analysis of Ascorbic Acid and Riboflavin Analytical Method x, y and Y of Control and Heated Samples Analytical Solution Program Numerical Finite Dif ference Method Program Thermal Diffusivity De termination Results Dis tribution of Residuals for Determining Accuracy of the Analyti'cal Solution for Calculating Temperatures Modified Analytical Solution Program 4 . 6 Comparison o f Experimental Temperatures and Predic ted 1 38 1 39 142 144 144 145 145 146 148 149 1 50 1 75 176 1 80 1 8 1 1 86 1 89 190 193 Temperatures from the Modified Analytical Solution Program 199 4 . 7 Method of Quality Retention Calculation for Micro-organisms and Ascorbic Acid 4 . 8 An Example of Lethality Calculation 4 . 9 Dis tribution o f Residuals for Determining Accuracy o f the Modified Analytical Solution Program for Calculating Temperatures 5 . 1 Analytical Results 5 . 2 Quali ty Retention Calculation Prog?am 201 203 205 207 2 1 1 5 . 3 5 . 4 5 . 5 An Example of Kinetic Parameters Calculation Estimation of k 129oC for the Design for Ascorbic Acid Determination of k 1 29oc and Ea for Riboflavin , Colour Y , and Viscosi ty Using Equivalent Processing Time 6 . 1 Quality Retention Calculation Program Based on Second Order Kinetics 2 1 7 224 226 230 LIST OF TABLES 2 . 1 Reac tion Rate Constants and Ac tivation Energies for Ascorbic Acid 2 . 2 Reaction Rate Constants for Riboflavin 2 . 3 Reaction Rate Constants and Activation Energies for Non-Enzymic Browning Reac tion 2 . 4 Reaction Rate Cons tants and Activation Energies for Chlorophyll Des truction 2 . 5 Reaction Rate Cons tants and Activati'on Energies for Colour Change 3 . 1 Dis tance from the Centre to the Measured Points 4 . 1 Experimental Run Number and Processing Conditions 4 . 2 Comparison of the Calculated Temperatures at the Centre of the Can 4 . 3 Diffusivities o f Baby Food a t Variuos Temperatures 4 . 4 Comparison of Temperatures Predicted by the Analytical Solution and the Numerical Fini te Dif ference Programs 5 . 1 The Mean Initial and Final Quality on Heat Processing 5 . 2 Effect of Size of Increment on Quality Retention Calculation 5 . 3 Level of the k 129oC and the Ea in the Orthogonal Composite Design for Ascorbic Acid 5 . 4 Orthogonal Composite Design for Riboflavin 5 . 5 Average Absolute Residuals and their Standard Deviations Resulting from Different Levels of k129oC and Ea 6 . 1 Heating Temperatures and Times for Steady-State Heating Method 6 . 2 Concentration of Ascorbic Acid and Riboflavin Before and Af ter Heating 6 . 3 Correlation Coefficients of Regression Analysis of Concentration of Ascorbic Acid and Riboflavin with Time of Heating 2 1 24 27 30 3 1 43 53 57 62 64 90 93 103 106 107 1 19 1 20 1 23 6 . 4 Kinetic Reaction Rate Constants at Various Temperatures for Ascorbic Acid 6 . 5 Activation Energy , Frequency Factor and Kinetic Reaction Rate at 129?C for Ascorbic Acid 6 . 6 Kinetic Reaction Rate Constants at Various Temperatures for Riboflavin 6 . 7 Activation Energy , Frequency Factor and Kinetic Reaction Rate at 1 29?C for Riboflavin 6 . 8 Second Order Kinetic Reaction Rate Constants at Various 6 . 9 Temperatures for Riboflavin Activation Energy , Frequency Factor , Kinetic Reaction Rate at 129?C for Second Order Kinetics for Riboflavin 6 . 10 Comparison of Ea and k 129oc for Ascorbic Acid Determined by Steady- and Unsteady-State Procedures 6 . 1 1 Comparison of Ea and k 1 29oC for Riboflavin Determined by Steady- and Unsteady-State Procedures 6 . 12 Average Residuals at Various k 129oc and Ea for Riboflavin in Unsteady-State Heating in Can 1? 1 30 1 34 1 34 1 36 1 36 1 38 1 39 1 4 1 3 . 1 3 . 2 4 . 1 4 . 2 LIST OF FIGURES Thermocouple Arrrangement in a Can Time , Temperature and Viscosity Relationships During Preprocessing of Baby Food Comparison of Predicted Temperatures from the Computer Programs at (r/a , x/h) of (0 . 0 , 0 . 0) Comparison of Predicted Temperatures from the Computer Programs at ( r/a , x/b) of ( 2 / 3 , 2 /3) 4 . 3 Distribution of Residuals for Comparison of the Analytical Solution and the Numerical Finite Difference Method for ? Run no . 6 4 . 4 Comparison of Experimental Temperatures and Predicted Temperatures from the Analytical Solution Computer Program for Run no . 6 4 . 5 Comparison of Experimental Temperatures and Predicted Temperatures from the Analytical Solution Computer Program for 43 48 65 66 67 69 Run no . 7 70 4 . 6 Heat Penetration Curves for Different Can Contents and Different 4 . 7 4 . 8 Head spaces Diagram Showing Different Parts in Heat Processing Variance versus Thermal Diffusivity 4 . 9 Comparison o f Experimental Temperatures and Predicted Temperatures from the Modified Analytical Computer Program for Run no . 6 4 . 10 Comparison o f Experimental Temperatures and Predicted Temperatures from the Modified Analytical Computer Program for Run no . 7 5 . 1 5 . 2 Flow Chart for Quality Retention Calculation Program An Orthogonal Central Composite Design to Fit a Second Order Response Surface 7 3 76 78 83 84 94 9 7 5 . 3 First Design for Ascorbic Acid with Calculated Average Absolute Residuals and their Standard Deviations 5 . 4 Orthogonal Design for Ascorbic Acid with Calculated Average Residuals and their Standard Deviations 5 . 5 Second Orthogonal Composite Design for Riboflavin with Average Absolute Residuals and their Standard Deviations 5 . 6 First Orthogonal Composite De sign for Colour, Y,with Average Absolute Residuals and their Standard Deviations 5 . 7 Second Orthogonal Composite Design for ' colour, Y, with Average Absolute Residuals and their Standard Deviations 5 . 8 First Orthogonal Composite Design for Viscosity with Average Absolute Residuals and their Standard Deviations 5 . 9 Second Orthogonal Composite Design for Viscosity with Average Absolute Residuals and their Standard Deviations 6 . 1 Degradation Rate for Ascorbic Acid in Baby Food on Heating Described by First Order Kinetics 6 . 2 Degradation Rate for Riboflavin in Baby Food on Heating Described by First Order Kinetics 6 . 3 Degradation Rate for Riboflavin in Baby Food on Heating Described by Second Order Kinetics 6 . 4 Arrhenius Plot for Degradation of Ascorbic Acid and Riboflavin in Baby Food on Heating 6 . 5 6 . 6 Probability Plot of Calculated % Residual for Ascorbic Acid Probability Plot of Calculated % Residual for Riboflavin 6 . 7 Arrhenius Plot for Degradation of Riboflavin in Baby Food on Heating Described by Second Order Kinetics 102 104 108 1 10 1 12 1 1 3 1 15 1 24 1 25 125 1 3 1 132 1 35 1 37 1 1 . INTRODUCTION Although the heating process has been known for a long time to affect both the nutritional and the sensory qualities of food products , there i s a lack of quantitative data on the destruction of nutrients and on the changes in eating qualities by the heating process (Lund , 1975a , b ; Lund , 1 9 7 7) . Thiamine is the only vitamin which is at all well documented (Farrer , 1 955; Feliciotti and Esselen , 1957) . There is some data available for other vitamins (Chittaporn , 1 9 77) but they were determined under restricted conditions . Reliable kinetic infor? mation on other quality changes occurring in heat processing is practically non-existent . At the present time , the nutrient value of a food after heat processing can only be determined empirically . Es tablishing the kinetics of changes in vitamins and food qualities during processing is necessary to provide general relationships which can be used for predictions of nutritional losses and food quality changes . Ascorb ic acid , riboflavin , colour and viscosity were the qualities selected for this study , the heat process used was can retorting ( sterilisation) and the food was homogenised , baby food made from strained beef and mixed vegetables . Ascorbic acid and riboflavin were chosen as they are important constituents , there was no reliable information on the kinetic parameters and the analytical methods were simpler than the other vitamin assays . Can sterilisation was used because this data would be useful for the design of canning processes and because large samples were required for colour and viscos ity measurements . Homogenised baby food was used because the heat transfer into the can was only by conduction , the food throughout the can was homogeneous and it was a mixed food sys tem of commercial significance . Being heated in a can, the food was subjected to a variation of temperature with time and position in the can . It was necessary for the quality retention calculation to determine the temperature d istri? bution in the can , and this was ob tained from a computer program based on unsteady-state heat transfer theory . 2 A method to determine the kinetic parameters was developed working from the processing time and temperature, and from the initial and final qualities, which were measured . This involved a computer program con? structed for temperature distribution and quality retention prediction . The kinetic parameters for ascorbic acid and riboflavin were also determined by a steady-state procedure where food was heated in a small tube in which instantaneous heating and cooling could be assumed . These kinetic parameters were compared wi th the ones ob tained from the unsteady- s tate procedure to tes t the feasibility and accuracy of the computer model for the can . 2 . LITERATURE REVIEW 2 . 1 INTRODUCTION Canning, as a method of food preservation, has its origin in the work of Nicholas Appert ( 1 750- 184 1 ) who was the first to use heat as a means of preserving food in hermetically sealed containers . Initially boiling water baths were used as heating medium but, sometime before 1830, the autoclave was introduced as a means of cooking canned foods under pressure . Further developments in processing equipment came with the introduction of agitating cookers and continuous s terilisers which helped to reduce processing time . The first spiral continuous cooker 3 was patented in 1 899 . In recent years, there have been the introduction of hydrostatic pressure cookers ( 1 936 ) , high speed spinning cookers ( 1952 ) , f lame sterilisation ( 1957 ) , high velocity air s terilisation ( 1974) , and aseptic canning ( 19 38) . Th? aim of all these changes was to shorten the processing time and so reduce the quality changes during the heat processing . The value of high temperature short-time s terilisation lies in exploiting the principle that higher temperatures have less effect on quality in proportion to the lethal effects than lower temper? atures . However, it has been found that the high temperature short time processes are not always beneficial in retaining the quality of canned food (Teixeira et al, 1969 ; Lund, 1977 ) . Although the canning process was int:;:-oduced i.n 1800 and there have been many developments, very lit tle is known on the optimisation of thermal processing for maximum quality retention . There is a lack of kinetic parameters showing the rate of quality destruction and the effect of temperature on the rate (Lund, 1977 ) . This chapter studies the quantitative estimation methods of the changes in food and reviews the literature on the kinetics of food quality changes during heat processing . 2 . 2 KINETIC THEORY OF THE CHANGES IN FOOD DURING HEAT PROCESSING There are several types of changes occurring in heat processing - destruction of micro-organisms , enzymes , nutrients and changes in 4 quality factors such as flavour , colour , texture . With micro-organisms and enzymes , the obj ective of the heat processing generally is inacti? vation , whereas with nutrients and other quality attributes , the obj ective is maximum retention . There are many factors affecting the extent of these changes . Lund ( 1 975a) reviewed the factors affecting the thermal resistance of micro-organisms . Whi taker ( 197 2) discussed the dependence of enzyme stability on many factors . Harris. and van Loesecke ( 1960) reviewed the effect of heat processing on nutrients . Other chemical changes - browning reaction , hydrolysis , oxidation-reduction reactions also occ?r and these may change food qualities e . g . colour and flavour changed by the browning reaction (Tannenbaum, 19 76b) . To follow the effect of heat on the food components including micro-organisms , two types of information are needed ; ( 1 ) the kinetic reaction rate of destruction and (2 ) the dependence of the rate constant on temperature . -- 2 . 2 . 1 Theory of Kine tic Reaction Rate According to the law of mass action , the velocity of reaction at a given temperature is proportional to the product of concentrations of the reacting substances . The rate of the disappearance of reactant , A , can be where a b -kcA cB dcA/dt is the rate of disappearance of reactant , A cA , cB . ? ? cN are the concentrations of reactant A , B , ? . ? N k is the reaction rate constant t is time. ( 2 . 1 ) The order of the reaction is defined as the sum of the powers to which the concentration of all reactants are raised , this can be a fractional value or an interger . 5 Considering the destruct ion of nutrients or a specified food quality , the concentrations of water , oxygen , acid , alkali and reducing sugar are of ten important , as are the concentrations of metal catalysts and enzymes . However , the most important factor is the concentration of the reacting substance cA . The destruction of nutrient or quality , A , at a given temperature is where cA is the concentration of the nutrient or quality , A n is the order of the reaction . This equation can be separated and on integration gives: where c A 0 CA -kt where n 1 1-n and cA (n- 1 ) kt where n # 1 is the concentration of A at zero time is the concentration of A at time t . ( 2 . 2 ) ( 2 . 3) ( 2 . 4 ) The order , n , cannot be found explicitly from the above equations so a trial-and-error solution must be used . This is not difficult as different values of n can be used in the equation to find the order , n , which most closely explains the experimental results . If the reaction of nutrient or quality A destruction is a first order reaction , it will be described by equation (2.3). The plot of the logarithms of the reaction against time yields a straight line with slope "-k" . So the reaction rate constant at a given temperature can be determined . In a second order reaction , the destruction of A can be described as : kt ( 2 . 5 ) That is , the plot of 1 /cA against time will give a straight line with the slope k and the intercept 1 / cA . 0 6 For zero reaction rate , the change in concentration of the reactant A is not dependent on the concentration , a p'lot of concentration versus time will yield a straight line of slope "-k" as cA - cA = kt . However , usually reactions are o f zero order only a t high concent?ations of reac? tant . When the concentration is lowered the reaction rate becomes con- centration dependent , that is the order of reaction rises from zero (Garret? 19 59? The order of ascorbic acid destruction was found to follow a zero order at high initial concentration and then the order changed to first order where concentration of ascorbic acid was lower . For micro-organisms , the thermal destruction generally follows first order kinetics , the time required for the survivor curve to trans? verse one log cycle corresponds to a 90% reduction in the number of survivors (Lund , .1 975a) . The "decimal reduction time" or D value , which is the time required to reduce the population by 90% , can also be used to characterize the reaction rate constant of micro-organism destruction . The relationships.between k and D can be expressed as : D 2 . 303 k 2 . 2 . 2 Temperature Dependence of the Reaction Rate ( 2 . 6) The effect of temperature on the reaction rate has long been known and the temperature - dependent term of a rate equation can be written in many forms according to various theories, The f irst quantitative formulation of the dependence of reaction rates on temperature was given by Arrhenius ( 1889) and this is still extensively used as : k Ae-Ea/RT where A is the frequency factor Ea is the activation energy R is the gas constant T is an absolute temperature. ( 2 . 7) This equation is found to fit many of the available experimental kinetic data (Aiba et a l , 1 9 65) . Taking lo.garithms of the above equation gives : ln k Ea ln A -?RT ( 2 . 8) The plot of ln k against 1 /T yields a straight line with slope equal to -Ea/R . The influence of temperature on k is then expressed in terms of Ea , activation energy . For micro-organisms , the thermal death time (TDT) method for describing the temperature dependence of the destruction rate was introduced by Bigelow ( 1 9 2 1 ) . The slope of the plot of log (TDT) against temperature , - 1 /z , is used to characterize the dependence of 7 the react ion rate constant on temperature . In 1 957 , Ball and Olson pointed out that the use of " z " is equivalent to the use of the Q10 concept which is the rate quot ient for a temperature interval of 10?C . Since the use of thermal death time was adapted to the decimal reduc? tion time (Stumbo , 1 948a) , the log D against linear temperature , has remained as a basis for process calculation and is still used to explain the effect of temperature on the destruction rate in term of "z" . Over wide temperature ranges , Gillespy ( 1 948) as well as Pflug and Esselen ( 1 953) reported that the plot of log D against the reciprocal of absolute temperature was more nearly linear . This is the form of the relationship predicted by the Arrhenius equation . Gillespy ( 1948) also pointed out that over small ranges of temperature , the linear plot gave a good approximation to the Arrhenius plo t . He also gave the relation? ship between Ea and z as : at a given temperature , T z = ( 2 . 9 ) over a range of temperature , T1 to T2 z = ( 2 . 10) Aiba et al ( 1 965) discussed the types of relationships between reaction rate and temperature , and included Erying ' s theory of absolute reaction rate with the Q 10 (or z ) approach and the Arrhenius equation. According to Eyring: -ilH*fRT ilS*/R gTe e where ilH* is the heat of reaction of activation ilS* is the entropy change of activation (2 . 1 1 ) g is a factor including Planck ' s and Boltzmann ' s constants T is absolute temperature . The Arrhenius and Eyring theories were found to be not signi? ficantly different . When used to extrapolate data , the Q10 (or z ) basis of calculation gave values of D significantly less than the other theories . The Arrhenius equation also seemed to be applicable over a 8 broader temperature range . Aiba et al stated that where an activation energy -1 was less than 126 kJ mole , the Arrhenius equation more accurately described the temperature dependence over a wide temperature range than the more corrnnonly used TDT?. equation . But where an activation energy was higher than 126 kJ mole -1 both equations were comparable . Another advantage of the Arrhenius equation over the TDT equation was that it could be extrapolated safely while the " z" equation is known to become non-linear at high temperatures (Hayakawa , 1978) . The TDT equation was found to be easier to apply in industry because of its simplicity (Hayawaka , 1978) ; the Arrhenius equation was a more complicated computation . He also stated that the Ea value is more strongly influenced by errors in k values than the s lope o f z . 9 There have been a number of other variations of the rate of reaction versus temperature equations . Moore ( 195 7) discussed some of these equations and stated that it was worthwhile making a correction of ac tivation energy by E = Ea + ?RT . Fennema ( 1975) described the temper? ature dependence of the destruction rate , k? by an exponential function for enzymes and micro-organisms: k exp (aiT) i , o ( 2 . 1 2) where k. is a value of k i when the absolute temperature , T , is zero 1,0 T is absolute temperature a. is a constant . 1 For a range of t emperature , equation (2 . 1 2) was used for process calculation (Thij ssen et al , 1978) . where k i , Tr k. 1 k exp (ai (Ti - Tr) ) i , Tr is -a value of k. at reference temperature , Tr . 1 ( 2 . 1 3) These equations , ( 2 . 1 1 ) and (2 . 12 ) , are just another way of expressing the Q10 concept . 2 . 2 . 3 Effect o f Other Variables on the Reaction Rate Besides depending on the temperature , the rates of the reaction are also affected by other variables , namely , pH , water activity , concentration of oxygen and concentration of minor components such as trace metals and enzymes (Labuza , 1972 ; Wanninger , 1972 ) . Wanninger ( 19 72 ) postulated a mathematical model for the effect of moisture content on the rate of reaction. Lee et al ( 19 7 7 ) used the least squares technique in establishing 10 an equation showing the effect of pH and moisture content on the kinetic reaction rate of ascorbic acid in tomato juice . 2 . 3 QUANTITATIVE ESTIMATION OF THE CHANGES IN FOOD DURING HEAT PROCESSING The changes in food during heat processing can be expressed quanti? tatively by kinetic parameters . To determine these parameters , the initial concentration of reactant e . g . nutrients , quality factors , the concentration of reactant af ter certain heating time , and the temperature of heating either by measurement or calculation mus t be known . 2 . 3 . 1 Analysis of Concentration As the accuracy of the kinetic parameters determined depends on the accuracy of the concentration measurement , reliable analytical techniques for the sys tem under s tudy must be used . Any assumptions made should be verified experimentally (Hill and Grieger-Block , 1 980) . Benson ( 1 960) has presented a useful table 'vhich summarizes the errors in calculated rate cons tants caused by analytical errors for orders of reaction from zero to four . Inspection of the table illustrates the dilemma the kineticist faces in planning experiments (Hill and Grieger-Block , 1 980) . 2 . 3 . 2 Determination of Temperature Distribution To determine the kinetic model for des truction of food components during heat processing, two procedures can be used : a steady-state procedure where thermal death time cans or tubes are commonly used and an unsteady-state procedure where food is heated in any container (Lenz and Lund, 1980) . Theoretically , the heating and cooling to and from the desired temperature should be instantaneous so that no signi? ficant des truction occurs during the coming-up and coming-down periods but this is practically impossible . The problem of thermal lag in the steady-state has been tackled in different ways . In unsteady-s tate procedure , the temperature of food in a container (usually a can) changes with time and position . The temperature distribution in the container at any given process time mus t be determined as the calcu? lation of the kinetic parameters is based on an average retention con? centration . To determine the temperature dis tribution , two methods can 1 1 be used - experimental measurement and theoretical prediction . 2 . 3 . 2 . 1 Determination of Thermal Lag in S teady-State Heating Firstly , the thermal lag periods can be ignored if they are small and considered insignificant to the processing effect or they can be reduced by methods such as reducing the sample size (Lyster , 1970 ; Mulley et al , 1975) , preheating the heating medium (Paulus et al , 197 8 ; Saguy e t al , 1978a) , and/or using relatively long heating periods (Eagerman and Rouse , 1976 ; Navankasattusas , 1978) where the thermal lag period effect can be considered negligible ? . Procedures for correcting thermal lag have been proposed and fell into three general categories - graphical method , numerical method and experimental manipulation . Farkas and Goldblith ( 1962) studying the kinetics of lipoxidase inactivation using thin walled , melting point) capillary tubes , estimated the thermal lag by extrapolating the first order reaction rate of destruction curve . Saper and Nickerson ( 1 962) and Gupte et al ( 1964) also used a graphical method . By the numerical method , the thermal lag was determined by two different methods. Firstly, a "z" value or a rate of reaction was assumed and used for calculating an equivalent time at a specified temperature ( Sognefest and Benjamin , 1944 ; Tan and Francis , 1 962) . Secondly , iterative procedures were used (Resende et al , 1 969 ; Hayakawa et al , 1 9 7 7 ) . This method was based on the assumption that the rate of reaction was first order . A "z" value was assumed , equiva? lent heating times calculated and graphed with the measured quality to determine a new "z" value . If there was a significant difference between the calculated and the assumed "z" value , calculation were repeated using the determined "z" value . In the experimental manipulation method , the coming-up time is determined and then actual timing started from this period . The method was used by Feliciotti and Esselen ( 1 957 ) , Hamm and Lund ( 1 978) . 2 . 3 . 2 . 2 Experimental Heat Penetration Measurement The measurement of heat penetration in a can was first done by Prescott and Underwood ( 1897) using a maximum recording thermometer . Because the metal mounting tube of the thermome?er , or the s tem of 1 2 the thermometer itself , if no mounting tube was used , could conduct heat to the bulb and thus distort the temperature record , this method was criticised by Bigelow et al ( 1 920) . The use of a chemical thermo? meter first described by Bitting ( 1 9 12) was also criticised by Bigelow et al ( 1920) for the same reason . However a mercury in s teel recording thermometer described by Bigelow et al ( 192?) also had the same heat conduction errors . The use of thermocouples in cans was first described by Bitting and Bitting ( 19 1 7 ) . The thermocouple probe in glass was described and used extensively by Thompson ( 19 19 ) and Bigelow et al ( 1920) . In 1927 , Ford and Osborne s tated that a thin wall copper tube used as part of the probe could probably be subjected to greater conduction errors in con? duction heated food than the glass thermometer . Various improvements of a mechanical nature have been made on heat penetration thermocouple probes (Benjamin , 1938 ; Ecklund , 1949 ) . Conduction errors had been shown to be negligible except for small cans of conduction heated product ; the correlation factor for this error has been proposed also by Ball ( 1923) and Ecklund ( 1 949 , 1956) . In 1965 , Board introduced the method of mounting thermocouples in cans without the use of support . The two wires pass through diametrically opposed holes in the can walls or through holes in the can ends and are sealed with a heat resistant epoxy resin adhesive . This method is probably the least susceptible to con? duction errors . As the can must be fitted with thermocouples before filling by this method ? Board and S tekly ( 1978) designed a simple new thermocouple assembly which allowed the hot junction to be placed at the desired measuring point af ter the can was filled and closed . 1 3 Sensitive galvanometers have been used to indicate the potential produced by the thermocouple junction (Thompson , 19 19) . Potentiometric devices ( zero current at balance) had become to be preferred later on as the voltage indicated was independent of the resistance of the lead wires ( Ecklund , 1949) . Automatic or manual cold j unction compensation have both been used , as well as ice-flask reference j unctions . Various types of recording potentiometer have been introduced and used (Clifcorn et al , 1950 ; Hoare and Warrington , 1963) . There are other errors in using thermocouples caused by the break? down of insulation at a point distant from?the j unction or/and the breakdown of insulation or earthing of thermocouple leads outside the can . These breakdowns could cause dropping in potential difference by the current flowing between the points of contact of the wire and electrotytes which could be food products , cooling water etc . These effects have been discussed by Middlehurs t et al ( 1964) who demonstrated that very high emf (up to 4mV) could be generated in unfavorable condition . Even though the methods of measurement have been developed from the use of thermometers to thermocouples where more points in the can can be followed by continuous recording potentiometric devices , there is a limitation on the number of points that can be followed and on the time interval of recorded temperature . Therefore , a theoretical determination is needed for calculating temperature distribution in the can. 2 . 3 . 2 . 3 Theoretical Determination A number of attempts to use basic heat transfer theory in the calculation of heat penetration have been made (Olson and Schult z , 194 2 ; Hicks , 195 1 ; Gillespy , 1953; Ball and Olson , 1957 ; Board e t al , 1960 ; Charm, 196 1 ; S tumbo , 1964) . Various forms of the heat conduc? tion equations (Thompson , 19 19 ; Carslaw and Jaeger , 1959) were used for determining the temperature of food during heating and cooling . Thompson ( 19 19) gave the fundamental equation describing heat penetra? tion in uniform conduction heating finite cylinders and used these formulae to calculate values of thermal diffusivity from various 1 4 experimental heating curves . For practical purposes , simplifications were made in the equation by neglecting terms which were important only at the beginning of heating . The prediction of the cooling curve was not as satisfactory as prediction of the heating curve . Hicks ( 19 5 1 ) proposed the method of prediction of heating and cooling curves based on the heat transfer equations (Carslaw and Jaeger , 1959) using only the first term in the series for the heating phase and a number of terms in series for cooling phase . Gillespy ( 1953) had also outlined a method of calculation for centre temperature in conduction heating can based on the fundamental heat conduction equation of Carslaw and Jaeger and Duhamel ' s theorem . Complex heating and cooling cycles could be calculated . As the technology of the computer has been improved and become more advanced , computer programs have been written and used for calculating the temperature distribution in the cans during conduction heating based on the heat transfer equations (Carslaw and Jaeger , 1959 ) by many workers (Hawakawa and Ball , 1969 ; Flambert and Deltour , 1972b ; Lenz and Lund , 1 9 7 7a) . The finite difference method has been also used for solving the heat transfer equations using the computer program by Teixeira et al ( 1969) and Flambert and Deltour ( 19 7 2b) . The later technique could also be applied where the thermal properties of the foods were changed with temperature . 2 . 3 . 3 Calculation of Kinetic Parameters In a steady-state procedure , the raw data of concentration of the desired factor versus heating conditions ( temperature and time) can be analysed by various methods reviewed by Hill and Grieger-Block ( 1980) . The data at each temperature are compared to a model of the kinetics ( zero- , first- , or second-order model) ; a rate cons tant can be calcu? lated for that heating temperature when the data sufficiently match the model (Lenz and Lund , 1980) . Then the temperature dependence of the rate can be determined . 1 5 In an unsteady-state procedure , the calculation o f kinetics is based on mass average prediction . This method firstly developed for estimating mass average s terilizing values . Gillespy ( 19 5 1 ) used only the first term in the series of analytical formulae for heat conduction in a cylinder in estimating the temperature distribution and developing parametric tables for determining mass average s terilizing values . Stumbo ( 1953) developed a mathematical procedure to evaluate the capacity of a heat process to reduce the number of bacteria in a container of food by considering the heat treatments received by all points through? out the container rather than that received at any one point . Ball and Olson ( 1957 ) developed a similar method based on S tumbo ' s original work , which they applied to the evaluation of thiamine retentions in conduction-heated foods . Hicks ( 195 1 ) used the fundamental heat con? duction equation , exponential integral functions and graphical integra? tions to evaluate survival probabilities for the whole container . He introduced the very useful concept of an equivalent volume , which , when multiplied by the residual number of spores per unit volume , at the centre point would give the total number of viable spores to be expected in the container . In 1952 , he had also reviewed the similarity and the implication of the methods of Stumbo ( 1948a , 1949a) , Gillespy ( 195 1 ) and Hicks ( 19 5 1 ) . Hayakawa and Timbers ( 1967 ) observed that S tumbo ' s formula did not give reliable answers when it was applied to the z and D values of organ? oleptic or nutritional factors which are considerably greater than those . of micro-organisms . In 197 1 , Jen e t al removed this limitation by deriving another formula which also does not require complicated calcu? lations for evaluating mass average s terilizing values . This formula is based on and similar to S tumbo ( 1953) . Hayakawa ( 1969) used dimen? sional analysis and found that six dimensionless groups , which are not included in both S tumbo and Jen ' s formula , are required for the unique mathematical es timation of a mass average s terilizing values . The reliability of the formula derived by Jen e t al should be investigated in the future, s tated Hayakawa ( 19 77 ) . He also derived new tables of dimensionless groups for calculating the lethality or quality retention of processed foods . In 197 7 , Downes and Hayakawa developed the table based on a new parameter , Ks , developed by Hayakawa using the combina- .tion of the major theoretical advances of S tumbo ( 1973) , Jen e t al ( 19 7 1 ) and Hayakawa ( 19 70) for mass average s terilizing value calcu? lation . 1 6 Recent advances in computer technology have also led to computer? ization of ther?l process calculations . Manson and Zahradnik ' s ( 1967 ) program was based on S tumbo ' s method . Hayakawa and Timbers ( 1967 ) calculated the mass average sterilizing value of a thermal process based on a first term approximation of the Fourier-Bessel series for heat conduction in a finite cylinder . Hayakawa ( 1969) applied his method to the evaluation of thiamine retention . Teixeira et al ( 1969 ) deve? loped a numerical solution of a finite difference approximation applied to both lethality and thiamine retention calculation . Flambert and Deltour ( 19 72a) used the same method as Teixeira ( 1967 ) with 10 incre? ments on the radius and on the half height and 0 . 125 minute time incre? ments with the first order reaction rate as D and z and calculated the mean temperature and the mean residual concentration of the entire process . Manson e t al ( 19 70) used the same method as Teixeira applied to a rectangular can of solid food . Sasseen ' s program ( 1969) is for es timating sterilizing values by Ball ' s method ( 1923) . Lenz and Lund ( 19 7 7 ) proposed a Lethality - Fourier number method for process eval? uation , which is also used for predicting the quality retention , based on the theoretical heat transfer equation of the analytical method in combination with the kinetic reaction rate constants , k and Ea . This method was shown to be as accurate as other available methods for pre?icting the mass average retention of thermally vulnerable components in conduction he?ting of a food . Thijssen et al ( 19 78) proposed a short? cut method for the calculation of s terilisation conditions yielding optimum quality retention for conduction-type heating based on the use of the computer in analyzing the temperature distribution in the can and the overall quality retention . 1 7 2 . 4 CHANGES OF FOOD DURING HEAT PROCESSING There are a number of s tudies on the change of nutrients during heat processing reviewed in Bender ( 1966) , Cain ( 1967 ) , Schroeder ( 19 7 1 ) , Harris and Karmas ( 1973) , Pries tley ( 1979) . Unfortunately , the majority of the data is the result of end point analysis , that is , the measurement of concentration at the beginning and at the conclusion of a given process or s torage period . These data were generally not subjected to kinetic analysis . However , Lund ( 1975) and Chit taporn ( 19 7 7 ) have reviewed the kinetic parameters for various nutrients by ei ther collection or calculation of the exi?ting data . Lund ( 1975 ) had also included some kinetic parameters for enzymatic inactivation , chlorophyll destruction , browning reaction , colour , texture and flavour . Inspection of Lund ' s table shows that only one determination of "k" and "Ea" was found for both ascorbic acid and riboflavin . Thiamine was the only vitamin that seemed to be well characterized . Although there were a number of "k" and "Ea" reported for chlorophyll des truction and browning reac tion , only one "k" and "Ea" was reported for colour . However , there are a number of s tudies on the kinetics of the nutri tional and quality changes of food during processing af ter 1975 - Hamn and Lund ( 19 78) on pantothenic acid , Navankasattusas ( 19 78) on vitamin B6 , Saguy et al ( 19 78a) on betanin and betalamic acid , Chen and Cooper ( 19 79 ) and Paine-Wilson and Chen ( 19 79) on folacin , Slater et al ( 19 79) on vitamin A and Widicus et al ( 1980) on a- tocopherol . There were , also , a number of s tudies on ascorbic acid, but most of them were on dehydrated foods . The kinetic reaction rate and the activation energy were found to be in a wide range (section 2 . 3 . 1 ) . For riboflavin , the kinetic s tudies were mostly on the photodegradation . Only one study,of Ohlsson ( 1980 ),was found for the changes in sensory quality on heating . Therefore , because of the lack of kinetic data, ascorbic acid and riboflavin were chosen in this s tudy . Colour and viscosity were the two sensory qualities chosen as flavour analysis involved subjective measurement which was difficult to measure accurately . The details of the kinetic s tudies on these chosen qualities were reviewed . 2 . 4 . 1 Ascorbic Acid Ascorbic acid is known as one of the most heat labile vitamins as reviewed up to 1 960 by Harris and Von Loesecke and thereafter by Lang in 1970 and de Ritter in 1976 . The destruction of ascorbic acid 1 8 in food can follow either an aerobic oxidation reaction or an anaerobic pathway (Tannenbaum , 1976a) . Both of these reactions have common inter? mediates and are hardly distinguishable . The specific pathways and the degradation rate are determined by factors such as oxidation-reduction potential of the system , temperature , oxygen , pH , moisture content , trace metals especially copper and iron , enzymes , sugar concentration and amino acid . (Joslyn , 1 949a , b ; Kurata and Sakurai , 1967a , b , c ; Bauernfeind and Pinkert , 1970 ; Huelin et al , 197 1 ) . Iron was found to be effective to a lesser extent than copper (Bauernfeind and Pinkert , 1970) . Khan and Martell ( 1967) found that in the pH range of 2-5 , the destruction of ascorbic acid increased with increasing pH and the decomposition rate was strongly accelerated by temperature . The rate of ascorbic acid destruction was found to reach a maximum at the pH near to pKa (Lee et al , 1 9 7 7 ) . I t was also found that alcohol and sugar might be either pro- or anti-oxidant depending on their concentration and on the presence of natural substances in food such as anthocyanin or other phenolic compound . Huelin ( 1 953) studying the anaerobic decomposition of ascorbic acid found that the destruction rate was accelerated by both sucrose and - fructose . Moisture content and water activity are important factors especially in dried products and they were extensively studied (Gooding , 1962 ; Karel and Nickerson , 1 964 ; Jensen , 1967 ; Vojnovich and Pfeifer , 1970 ; Lee and Labuza , 1 975 ; Kirk et al , 1 9 7 7 ; Reimer and Karel , 1 9 7 7 ; Dennison and Kirk , 1978 ; Laing et al , 1978 ; and Papanicolaou and Sauvageot , 1 979 ) . The destruction rate was found to increase with increase in total moisture content and water activity . This was explained as the result of dilution of the aqueous phase causing a decrease in viscosity which led to increase in mobility (Lee and Labuza , 1975 ) . The activation energy was found to increase with moisture content (Jensen , 1967 ; Voj novich and Pfeifer , 19 70) , but Lee and Labuza ( 1 975) found that there was no effect of water activity on the activation energy . The reason for this variation was stated to be unknown by Kirk et al ( 1 9 7 7 ) . 1 9 Oxygen or air , as shown by Clifcorn ( 1948) , Mapson ( 1956) , Bender ( 1958a) and Chichester ( 1973) , did effect the des truction rate of ascorbic acid in canned foods . The effect of oxygen on the rate of ascorbic acid des truction in liquid foods was also reported (Joslyn and Miller , 1949a , b ; Bayes , 1950 ; Khan and Martell , 196 7 ; Ford et al , 1969) . In a dehydrated food system, Kirk et al ( 1977 ) found that the rate of ascorbic acid des truction was dramatically increased with the presence of oxygen , as did Dennison and Kirk ( 1978) . The anaerobic mechanism of ascorbic acid des truction in a canned food was reported by Huelin ( 1953) and Huelin e t al ( t967) . In 1978 , Reimer and Karel found that ascorbic acid des truction in dehydrated tomato j uice was largely an anaerobic reaction . Papanicolaou and Sauvageot ( 19 79 ) also found that vitamin C des truction differed j us t a little between samples of freeze-dried orange j uice stored under vacuum, nitrogen or air . Therefore , it is likely that both aerobic and anaerobic mechanisms could be involved depending on o ther factors such as pH and compositional factors . In heat processing , especially , in the canning process , the reten? tion of ascorbic acid has been s tudied by many workers on various food products (Guerrant et al , 1 947 ; Lamb et al , 1 947 ; Wagner et . al , 1 947 ; Cameron et al , 1 949 ; Watt and Merrill , 1963 ; Marchesini et al , 1 9 7 5 ; Lee e. c al , 1 976) . The percentage of ascorbic acid retention varied with types of products as the processing conditions were differen t , the reten? tion was found to vary from 26-90% . Unfortunately the kinetic parameters cannot be determined as the data available were inadequate . The orders reported in the literature of the destruction reac tion of ascorbic acid were conflicting . I t was reported as either zero , firs t or pseudo- first order reaction (Barron et al , 1 936 ; Peterson and Wal ton , 1943 ; Weissberger and Thomas , 1943) . Aerobic destruction of ascorbic acid was confirmed to follow firs t order kinetics (Freed e t al , 1949 ; Joslyn and Miller , 1949a) . Anaerobic des truction of ascorbic acid was also found to follow firs t order reaction kinetics (Huelin , 1953) . In heating processes , the des truction of ascorbic acid was found to be described by first order kinetics (Paulus et al , 1 9 78 ; Saguy et al , 19 78b ; Lathrop and Leung , 1980) . The first order kinetics was also found on the s torage of food products - Voj novich and Pfeifer ( 19 70) in wheat flour , corn soya milk , infant cereal ; Lee et al ( 1977 ) , Nagy and Smoot ( 19 7 7 ) 20 and Davidek et al ( 19 74) in fruit juices ; Lee and Labuza ( 19 7 5 ) , Kirk et al ( 1 977 ) , Reimer and Karel ( 1 97 7 ) and Dennison and Kirk ( 1 978) in intermediate moisture food . The data presented by Sistrunk and Cash ( 1 970) , Clydesdale et al ( 19 7 1 ) and Abrams ( 19 75) on the effect of heat on the ascorbic acid of food were analysed by this author and it was found that most of them could be treated as a first order reaction . On the other hand , Garrett ( 1956) s tudying the stability of ascorbic acid in a pharmaceutical preparation concluded that ascorbic acid has an initial pseudo-zero order reaction which subsequently become pseudo? first order reaction . The deviation from firs t order rate o f reaction of ascorbic acid was also found by Joslyn and Miller ( 1 949a) . Singh et al ( 1976 ) found that under limited supply of oxygen , the degradation of ascorbic acid in infant formulae could be described as a second order reaction whereas Laing et al ( 1978) concluded that the degradation rate of ascorbic acid in intermediate moisture food followed a zero order reaction . Lin and Agalloco ( 1979 ) reviewed the effect of temperature, pH and oxygen on the des truc tion kinetics of ascorbic acid and s tated that the order of reaction depended on both oxygen and initial concentration . The reaction rate and the activation energy of ascorbic acid des truction , either collected or calculated from the literature , are shown in Table 2 . 1 . Assuming that the destruction rate of ascorbic acid in various foods was a first order reaction , Chit taporn ( 19 77 ) had predicted the reaction rate and the activation energy using all data available -4 - 1 before 1 9 77 and found that the reaction rate was 2 . 33 x 10 s at 0 - 1 1 29 C and the activation energy was 88 . 2 kJ mole ? Subsequent t o 19 7 7 , more recent results have continued to show a wide variation , from 1 4 to 1 7 2 kJ mole - 1 ? 2 1 TABLE . 2 . 1 Reaction Rate Constants and Activation Energies for Ascorbic Acid Reference ilrenne r et a l , 1948 Product Canned food Lamb et a l , 1 9 5 1 Canned tomato j uice and tomato pas t l.' Huelin, 1953 Garret t , 1956 Jensen , 1967 Vojnovich and P f e i fer , 1 9 70 Blaug and Haj ratwala, 1972 Labuza , 1972 Davidek e t al , 1974 Ahrams 9 1 9 7 5 Ascorbic acid in ci trate? phosphate buffer solution Liquid - multivi tamin Seaweed Flour Ascorbic acid in buffer solution ( aerobic oxidat ion) General review Orange drink Frozen Brussc l sprouts Condi tions H i?h t"2lperature s torage 2 1-37 . 8 C , pH 4 . 35 S torage .. 2 1-37 . 8 ?C tempe rature 30- 100?C , p H 2 . 2 p H 6 . 0 from f i rs t order plot f rom pseudo-zero order plot Moisture 1 1 . 1 gH20/ 100 g sol id Mois ture 1 7 . 6 gH20/ 100 g solid Moisture 33 . 3 gH20/ 100 g solid temperature 26-45?C , water activity 0 . 65 water activity 0 . 55 water activity 0 . 25 temperature 60-85?C, pH 5 . 6 L-dchydroascorbic acid , . 4-30?C cook i ng temperature range Lee and Labuza , 1975 Intermediate moisture model temperature 23-45?C , food water activity 0 . 23-0 . 84 Flaumenbaum e t al Ci trus , s trawberry , tomato 1977 j uice and paprika puree Kirk et a l , 1977 Lee et a l , 1 977 Nagy and Smoot , 1977 Dennison and Kirk , 1978 Laing e t a l , 1978 Paulus et a l , 1978 Forti fied dehydrated model sys tem Mul tivi tamin model system Canned tomato j uice Canned single s t rength orange j uice Dehydrated model food system Intermediate moisture food system Spinach puree Reimer and Kare l , Dehydrated tomato j uice 1978 Saguy e t al , 1978 Lathrop and Leung. 1980 Grapefruit j uice Peas in b rine in TDT cans temperature 10-37?C , water activity 0 . 5-0 . 65 temperature 10-37 C , water activi ty 0 . 1-0 . 65 temperature 0-37 . 8?C , p H 4 . 06 ?pH 6 . 90 0 temperature 2 1 . 1-48 . 90C temperature 4 . 4-2 1 . 1 C temperature range 10-37?C water activity 0 . 10 water ac tivi ty 0 . 40 water activity 0 . 65 temperature 6 1- 105?C , water activity 0 . 69 water ac tivity 0 . 80 water activity 0 . 90 temperature 105- 130?C water activity 0 . 00 water activity 0 . 7 5 temperature 60-96?C temperature 1 10- 132?C * ** Calculated from the data presented in the reference Zero-order reac t ion was predicted . Act ivation Reac tion Rate Energ? 1 k X 1Q 4S- 1 kJ mole _ 1 (kcal mole ) 0 . 000 18 , 37 . 8?C 108 (25 . 7 ) * 0 . 00022 , 37 . 8?C 8 1 ( 19 . 3 )* 0 . 00383, 100?C 78( 1 8 . 6 ) * 0 .0 3 167 , 100?C 96 ( 2 2 . 9 ) * 0 .00289 , 70?C 9 7 ( 23 . 1 ) - 96(22 . 8) - 32( 7 . 7 ) - 55 ( 1 3 . 1 ) - 1 27 ( 30 . 3) 0 . 00228 , 45?C 94 ( 22 . 3) 0 . 00022 , 45?C 6 7 ( 16 . 0) 0 . 00005 , 45 ?C 46 ( 1 1 . 0 ) 0 . 0 1 500 , 85 ? C 76 ( 18 .0 ) - 37- 189 ( 8 . 8-45 . 0 ) 0 . 06 700 , 30?C 59 ( 14 . 1 ) 0 . 42778-0 . 47083 , 100?C - - 70-95 ( 16 . 7-22 . 6 ) 0 . 20000-0 . 88000 - 0 . 00 1 14-0 .0 1822, 37 ?C 34-8 1 ( 8 . 0- 19 . 2) 0 . 00 1 14-0 . 00981 , 3 7 ?C 48-84 ( 1 1 . 5-20 .0 ) 0 . 00028 , 37 . 8?C 1 4 ( 3 . 3) 0 . 00025 , 37 . 8?C 29 ( 6 . 9 ) - 1 1 2 ( 26 . 7 ) - 53( 1 2 . 7 ) 0 .00206 , 37?C 45( 10 . 7 ) 0 . 00839 , 37?C 67 ( 1 6 . 0) 0 . 0 1 397 , 37?C 77 ( 18 . 3) - 59 ( 14 .0 )* - 7 1 ( 1 7 . 0) * - 6 7 ( 16 . 0) ? 0 . 0768 1 , 1 30?C 30( 7 . 2) 0 . 00056 , 37 ?C . 103 ( 24 . 6) 0 .00006 , 37 ?C 68 ( 16 . 2)? 0 . 2 1267-0 . 5036 7 , 6 1 ?C 2 1-48(5 . 0- 1 1 . 3) 0 . 08333, 1 10 ?C 1 7 2 ( 4 1 ;0) 22 2 . 4 . 2 Riboflavin Riboflavin is comparatively s table to heat but uns table to light , especially in the visible spectrum (< 500 nm) . The sensitivity to light increases with temperature and pH (Harris and von Loesecke , 1960) . I t is s table to oxygen and acid but uns table to alkaline conditions (Bender . 1966) . Leaching is the main cause of riboflavin loss during food pro? cessing since it is a water soluble vitamin . Retention of 60% to 100% was found after blanching (Rein and Hutchings , 197 1 ; Barratt , 19 73) . The effect of cooking on riboflavin retention of various kinds of meats were s tudied , 56-98% re tention was found by Griswold et al ( 1947 , 1949) , 74% retention was found by Mcintire e t al ( 19 44) , 55-75% re tention was found by Noble ( 19 70) , whereas almos t 100% retention was found by Engler and Bowers ( 19 76) . Ang et al ( 19 75 ) reported that less than 10% loss of riboflavin was found af ter three hours holding at 82?C . Cain ( 1967 ) s tated that dehydrated beef and sweet potatoes r.etained all their riboflavin content . For milk , heat treatment was found to have little effect on riboflavin (Ford et al , 1969 ; Rolls and Porter , 1 9 73) . However , loss can be significant if milk is exposed to sunlight ( Singh et al , 1975 ; Sattar et al , 1 9 7 7 ) . The temperature was also found to have an effect on riboflavin des truction rate . In canning , different conclusions have been drawn . Hellendorn et al ( 19 7 1 ) showed that in canned meat and vegetable dishes , s ter? ilisation and s torage at 22?C for five days produced no significant losses in riboflavin . While Watt and Merrill ( 1963) reported that the losses of riboflavin in canned vegetables could be as high as 70% (including loss in preprocessing) ; except tomatoes and tomato juice that seemed to show better riboflavin retention which may be due to their higher acidity or higher ascorbic acid or less leaching during their processing . The loss of 0 -30% curing canning was also reported by Guerrant et al ( 1946 ); Lamb et al ( 1947); Wagner et al ( 1 947) ; Cain ( 1 96 7). Burger and Walters ( 19 7 3) reported 6% loss for canned chopped beef , 12% loss for canned corned beef and 29% loss for pork bacon . 23 So it would appear that riboflavin losses do occur on processing , including canning . These losses , in the case of wet treatment , are probably due to a combination of leaching , light and thermal degrad? ation . Very little kinetic work had been done on riboflavin . S ingh et al ( 1975) and Sattar et al ( 1 9 7 7 ) had studied the light induced losses of riboflavin and concluded that the destruction reaction was definitely first order in nature . Allen and Parks ( 1979 ) also found that the photodegradation of riboflavin in milk exposed to fluorescent light ( 2690 lux) could be described by first order reaction . The data presented by Ang e t al ( 19 75) could not be fitted to a first order reaction by the present author . Gillespy ( 1962) assumed first order reac tion and determined the activation energy for riboflavin destruction as 96 . 6 kJ mole- 1 ( 23 . 0 kcal mole- 1) . Chittaporn ( 19 77 ) also assumed firs t order reaction and calculated the kinetic reaction rate from the data collected from the li terature , (Table 2 . 2) and found that activation energy determined from the calculated "k" was 46 . 2 kJ mole- 1 ( 1 1 kcal mole - 1 ) . Singh et al ( 1975) found that the activation energy varied from 33 . 6- 1 7 2 . 2 kJ - 1 1 mole (8-4 1 kcal mole- ) in thei r study of milk depending on the type of container as i t affected the amount of light . From the latest data of Salunkhe et al ( 19 78) and Kramer et al ( 19 7 7 ) , the first order reaction was assumed and - 1 range from 43 . 3-63 . 4 kJ mole the food studied in Salunkhe et al the activation energy was found to ( 10 . 3- 15 . 1 kcal mole- 1 ) depending on - 1 and from 6 . 7-23 . 5 kJ mole ( 1 . 6-5 . 6 kcal ?ole- 1) for salisbury and beef patties with the TVP in Kramer e t al . The variation in the kinetic reaction rate and the activation energy reported may be due to the type of food , the ini tial concen? tration , the method of s tudy and the conditions being s tudied . However , i t is obvious that the data on the effect of heat are very limi ted . 24 TABLE 2 . 2 Reaction Rate Constants for Riboflavin Moisture Temp . k X 10 4 Reference Type of Product Content oc - 1 % s Singh e t al , 1975 Milk - 1 . 7 0 . 00 2 16 Singh et al , 1975 Milk - 4 . 4 0 . 00243 Guerrant e t al , 1945 Canned tomato juice - 5 . 6 0 . 00003 Guerrant e t al , 1945 Canned green lima beans - 5 . 6 0 . 00003 Guerrant e t al , 1945 Canned whole kernel? corn - 5 . 6 0 . 00004 Singh et al , 19 75 S torage of milk - 10 . 0 0 . 00306 Guerrant e t al , 1945 Canned tomato juice - 29 . 4 0 . 00006 Guerrant et al , 1945 Canned green lima beans - 29 . 4 0 . 00006 Guerrant e t al , 1945 Canned whole kernel corn - 29 . 4 0 . 00005 Guerrant e t al , 1945 Canned tomato juice - 43 . 3 0 . 000 18 Guerrant et al , 1945 Canned green lima beans - 43 . 3 0 . 00009 Guerrant et al , 1945 Canned whole kernel corn - 43 . 3 0 . 00009 Greenwood et al , 1944 Canned luncheon pork 55 . 0 99 . 0 0 . 0476 1 - - Cook and Dundaram, 1963 Boiled artichokes In water 100 . 0 0 . 02674 Greenwood et al , 1944 Canned luncheon pork 55 . 0 1 10 . 0 0 . 0 14 1 1 Greenwood et al , 1944 Canned luncheon pork 55 . 0 1 1 8 . 5 0 . 00 742 Greenwood et al , 1944 Canned luncheon pork 55 . 0 1 26 . 5 0 . 0 2 1 50 Cook and Sundaram, 1963 Boiled artichokes In water 1 2 1 . 0 2 . 38072 Kennedy and Ley , 197 1 Fish in pressure cooker - 1 2 1 . 0 39 . 30 36 1 2 . 4 . 3 Colour S ince the model system used in the present study is a mixed , complicated natural food system consisting of var ious raw mater ials 25 and ingredients , many reactions could be involved but only two main colour react ions , browning react ion and pigment/chlorophyll destruction , were studied and information was collected only on these colour changes . 2 . 4 . 3 . 1 Browning Reaction Browning reaction , which occurs in fooq during processing caused the colour change to brown or brownish-black , can be classif ied into two categories , enzymatic and non-enzymatic react ion . The enzymatic browning reaction can occur in food by the action of catalytic enz.ymes , phenolase or polyphenolase . As this react ion involves enzymes which would be destroyed by heat , so during thermal processing where the temperature is rather high , only non-enzymat ic browning reaction will play an important role in colour changes . There are three main types of non-enzymatic browning reaction , the carbonyl-amino acid reaction which is generally known as "Maillard" reaction , the caramel ization reaction which occurs at relatively high temperature with polyhydroxy-carbonyl compounds , and the oxidat ive reaction where ascorbic acid or polyphenols are converted to d i- or polycarbonyl compounds . The details o f mechanisms o f these react ions were reviewed by many workers (Hodge , 1 953 ; Reynold s , 1 963 ; Lea , 1 965 ; Reynolds , 1 965 ; Hurst , 1 9 7 2 ; Adrain , 1974 ; McWeeny et al , 1 974) . The intermediates , pigment s and melanoids formed by the reactions are altered by a number of factors . Their composition will depend , not only on the sugar and amino compounds involved but also on (a) the sugar : amino compound rat io ( Schnickels et al , 1 9 7 6 ; Warmbier , 1 97 6 ; Warmbier e t al , 1 97 6) , (b) the water content , the higher the water content , the quicker the rate of browning ( Stadtman et al , 1 946 ; Legault et al , 1 95 1 ; Pearson et al , 1 962 ; Labuza and Warren , 1 97 6) , (c ) the temperature o f the reaction , (d) the pH of the reaction mixture and its buffer capac ity (Pearson et al , 1 962) where the maximum brown colour was found to be produced between pH 5 . 6 and 5 . 9 and ( e) 26 the presence of other compound ? or ions such as ascorbic acid which was found to have an effect on the browning extent (Karel and Nickerson , 1 964 ; Clegg and Morton , 1 9 65 ; Clegg , 1 9 66) . In meat , Khayat ( 19 78) found that reducing sugar content was an important factor in brown colour development during thermal processing . Time and temperature were found to effect the rate o f browning reaction (Pokorny et al , 1 9 7 5 ; Warmb ier et al , 1 9 76) . Warmbier e t al ( 19 76) studied and found that the rate of p igment formation followed a zero-order kinetic reaction rate af ter an initial short induction period while the rate of glucose utilization and. loss of availab le lysine obeyed the first order reaction . Pokorny et al ( 19 75) studied the non-enzymic browning of cauliflower and found that it followed the kinetics of a f irs t order reaction at high temperatures and that of a zero order reaction at lower temperatures . Resnik and Chirife ( 19 79 ) s tudied the effect of moisture content and temperature on some aspects of non? enzymic browning of dehydrated apples , moisture content ranged from 0 nearly zero to 83% , and temperature ranged from 55-83 C and concluded that the rate of increase of on 282 which is associated with the presence of 5-hydroxy-methyl-furfural followed zero reaction kinetics . The kinetic parameters were collected and are shown in Table 2 . 3 . The activation energies for the browning react ion found b y various workers were in the same range , it was found to be more than 105 kJ mole- 1 ( 25 . 0 kcal mole- 1 ) . However , the variation in 1 1 k 1 1 was high as the methods of determination used by various workers were different . Therefore , the method of determinat ion mus t be followed in order to used those 1 1 k 1 1 values with the activation energy . TABLE 2 . 3 Reaction Rate Constants and Activation Energies for Non-Enzymatic Browning Reaction Moisture Ac tivation Reference Food Product pH Tempera5ure Content React ion 4 R!!fe Energy_ 1 rangs C gH20/ 100 g k X 10 S kJ mole _ 1 (dry basis) (kcsl mole ) S tadtman et a l , Dried apricot - - - - 109 ( 26 . 0) 1946 Legaul t e t a l , Unsul f ited - 20-49 5 . 4 0 . 00 139 , 49 ?C 166 ( 39 . 4) 1 947 carrot 6 . 2 0 . 00 1 7 4 , 49 ?C 163 ( 38 . 7) 8 . 0 0 . 00255, 49 ?C ? 159 ( 37 . 9 ) Unsulfi ted - 20-49 3 . 5 0 . 00266 , 49 ?C 1 7 7 ( 42 . 2) Onion Unsulfi ted - 20-49 5 . 3 0 . 00020 , 49 ?C 169 ( 40 . 3) whi te potato 7 . 6 0 .0005 1 , 49 ?C 1 6 1 ( 38 . 4) 8 . 9 0 . 00086 , 49 ?C 152 { 36 . 2) U::?sulfited - 20-49 7 . 4 0 .00006, 49 ?C 1 34 ( 3 1 . 9 ) sweet potato Legault et al , Sulf ited white - 20-49 5 . 3 0 . 000 1 1 , 49 ?C 1 7 2 { 4 1 . 0 ) 1951 potato 7 . 6 0 . 00020 , 49 ?C 1 5 1 (36 . 0) 9 . 2 0 . 00026, 49 ?C 143 { 34 . 0) Sul f ited - 20-49 5 . 4 0 . 000 1 1 , 49?C 168 (40 . 0) carrot 6 . 2 0 . 000 1 2 , 49 ?C 1 5 1 (36.0) 8 . 0 0 . 0001 3 , 49 ?C 147 { 3 5 . 0) Sulf ited - 20-49 2 . 1 - 1 7 6 (42 . 0) cabbage 3 . 5 - 160 ( 38 . 0) 7 . 1 - 147 { 35 .0) Hendel et al , Dried potato - 40-80 4 . 9 0 .05 1 39 , 80 ?C 1 55 { 37 . 0) 1955 - 9 . 4 0 . 07 7 78 , 80?C 1 34 { 32 . 0) 1 5 . 0 0 . 10000 , 80?C 1 18 ( 28 . 0) 33 .0 0 .0566 7 , 80?C 105 ( 25 . 0) 1 10 . 0 0 .027 78 , 80 ?C 105 ( 2 5 .0) 370 . 0 0 .0 1 4 1 6 , 80 ?C 109 ( 26 . 0) Bur ton , 1963 Homogenized 6 . 5- 93 . 3- 12 1 . 1 - 355 . 40000 , 1 1 3 (27 . 0) goa t ' s milk 6 . 6 1 2 1 . 1?C . Non-homogenized 6 . 5- 93 . 3- 1 2 1 . 1 - 42 1 . 80000 . 1 1 3 {27 . 0) goat ' s milk 6 . 6 1 2 1 . 1 ?C Hermann, 1970 Apple juice - 37 . 8- 1 30 - 1 . 42 16 7 , 1 1 3 (27 . 0) 1 2 1 . 1 ?C Hermann , 1970 Apple j uice - 37 . 8- 130 - 1 . 3486 7 . 87 {20. 7) 1 2 1 . 1 c Mizrahi et al Dehydrated - - 1 . 0 - 1 7 2 ( 4 1 .0 ) 1970 cabbage - - 1 8 . 0 - 109 { 26 . 0) Drilleau and Apple j uice - - 1 18- 166 Prioult , 197 1 (28-39 .6 )* Flink e t al , Milk - - - 2 . 7 7778 , 1974 100 ?C , O%RH 197 (47 .0) 4 1 . 66700 , 1 00?C , 1 1%RH 223 ( 5 3 .0) 1 1! . 1 1 100 , 1 00 C , 32%RH 1 39 ( 33 .0) Pokorny et al , Cauliflower - 40-50 - - 1 44 ( 34 . 2) 1975 50-80 - - 105 (25 . 1 ) Resnik Dehydrated - 55-83 0 . 0 - 1 7 2 {4 1 . 0) * and Chirife , apple 83 .0 - 1 22 ( 29 .0)* 1979 *5-HMF formation 2 7 2 . 4 . 3 . 2 Pigment/Chlorophyll Des truction In foods that contain chlorophylls , the change in colour from a bright green to an olive-green or olive-yellow colour on processing 28 has been the concern of food processors since the introduction of thermal processing . The change is due to the conversion of chlorophylls to their respective pheophytins and further breakdown products such as pheophorbides and chlorins (Mackinney and Weas t , 1 940 ; Westcott et al , 1 955 ; Gilpin et al , 1 959 ; Gold and Weckel 1 959 and Spencer , 1973) . The percentage of change of chlorophylls to pheophytins has been s tudied by many workers . Kaur and Manj rekar ( 1975 ) found that canned sarson? ka-sag (prepared mustard green) los t about 50% of the chlorophyll during processing . In green peas , Aczel ( 1 97 1 , 1 973 ) found that chlorophyll content was reduced by 10- 16% during blanching and then all chlorophyll was conver ted to pheophytin during s terilisation . The degradation of chlorophyll was found to be dependent on time of processing (Sweeny and Martin, 1 958 and Lee et al , 1 974) . Many workers found that the extent of degradation of chlorophyll depended on pH and heat source (Sweeney and Martin , 1 96 1 ; Buckle and Edward , 1970 ; Lee et al , 1 9 74) . Lee e t al ( 1974) also found that s t?am had more effect on chlorophyll than boiling water which had more effect than hot air and microwave . The effect of time and temperature on the degradation of chlorophyll has been s tudied by many workers . Gold and Weckel ( 1959) s tudied the conversion during s terilisation of canned green peas and found that i t was pseudo-first order reaction . Eps tein ( 1959) , also found that the loss of green colour of HTST processed peas was pseudo-first order . Mckinney and Weas t ( 1 940) stated in their work that the conversion of chlorophyll in aqueous acetone and acid solution was a first order reaction in respect to both acid and chlorophyll content . Sweeney and Martin ( 1958) found that i t could be described by either a zero order or first order reaction in heated broccoli . However , Schanderl et al , ( 1 962) , Gupta et al ? ( 1 964 ) and Haisman and Clarke ( 1975) found that the conversion of chlorophyll occured only above a threshold temperature of 50-60?C and the conversion was mos t probably a first order reaction . In 196 4 , Gupte et al investigated and determined not only the kinetics of chlorophyll degradation in spinach puree but also the thermodynamic energies for this degradation based on a f irst order reaction . Hayakawa and Timbers ( 1 97 7 ) studied the influence of various thermal treatments on the visual green colour of canned asparagus , green beans and peas and determined the kinetic reaction rate constant by assuming that the reaction was a f irst order . The kinetic reaction rate constant for chlorophyll was also s tudied by other workers such as Dietrich et al ( 1 970) for green beans , Lenz and Lund ( 1 974) for pea puree and spinach puree , Hermann ( 1 970) for spinach . Tan and Francis ( 1 9 62) who studied the effect of processing on the p igments and colour of spinach puree , provided a result ade? quate for calculating the kinetic reaction rate. The value of the kinet ic parameters determined by various workers are summarized in Table 2 . 4 . The kinetic reaction rate for chlorophyll a and b varied depending on the type of food , pH, temperature range . Lund ( 1 97 5b) concluded that the variability of results obtained in d ifferent laboratories may be due to the heating technique and the analytical method . He suggested that the activation energy for chlorophyll a should be 4 2-105 kJ mole- 1 ( 1 0-25 kcal mole-1 ) and for chlorophyll b , Ea should be lower because it appears to be more stable . 2 . 4 . 3 . 3 Total Colour Change There were some workers studying the total colour changes of f ood during processing . Unfor tunately , the data given were not enough for determining the kinetic parameters . However , the results presented by Salunkhe et al ( 1 978) on colour change during storage of various food were adequate . The scales were read from the Hunter? Colour and Colour-Difference Meter (Model D25D2 , Hunter Association Laboratory , Inc . Fairfax , V .A . ) . The kinetic parameters were deter? mined assuming f irst order kinetics and are shown in Table 2 . 5 . The average activation energy for L , a , b was 63 , 56 and 45 kJ mole-1 , - 1 respectively . Higher activation energy o f 1 35 kJ mole was found f or the decrease in greeness of Brussels sprouts during storage (Tij skens et al , 1 979 ) . Tlte rate of decrease which could probably be described by f irst order kinetics was 0 . 00 1 1 2 x 10-4 s -1 at -4?C . 29 TABLE 2 . 4 Reaction Rate Cons tants and Activation Energies for Chlorophyll Destruction Reference Food Product Mackinney and Buffer solution , Joslyn , 1941 chlorophyll a chlorophyll b Epstein , 1959 Green peas ; chlorophyll 11 chlorophyll b Gold and Peas ; Weckel , 1959 b lanched unblanched Schanderl In aci d solu?ion ; e t al , 1962 chlorophyll a ethyl chlorophyllidc a 01e thyl chlorophyllidc a free chlorophyllide a Gupte et a l , Spinach puree ; 1964 chlorophy ll a chlorophy J.l b Diel rich Green beans et al , 19 70 Hermann , 1970 ?plnacl & ; chl orophyll a chlorophyll b Timbers , 1 9 7 1 Peas Asparagus Green beanfl Spinach Lt:nz ond Lund , Pea puree 1974 Spinach puree pH Temperature oc - 0-50 - 0-50 - 12 1 . 1 - 1 48 . 9 - 12 1 . 1 - 1 48 . 9 - 1 1 5 . 6- 1 37 . 8 - 1 1 5 . 6- 1 37 . 8 - 25-55 - 25-55 -? - 25-55 - 25-55 6 . 5 1 26 . 7- 148 . 9 5 . 5 1 26 . 7 - 1 48 . 9 Natural 87 . 8- 100 . 0 N.:1tural 100- 1 30 Natural 100- 1 30 Natural 79 . 4- 148 . 9 Natur:1 l 79 . 4 - 1 '? 8 . 9 Natural 19 . 4- 1 1. 8 . 9 Natural 79 . 4- 1 48 . 9 6 . 5 79 . 4- 1 37 . 8 6 . 5 79 . 4- 1 37 . 8 Reaction Rate k l 2 1 . t?l X 10 8 - - - - 27 . 4 1 700 2 7 . 6 1700 - - - - - - 38. 00000 1 1 . 25000 7 . 9 5000 38 . 00000 ,, . 85000 25 . 58300 1 8 . 28300 3 . 40000 2 . 31700 Activation Energy_ 1 Remark kJ mole _ 1 (kcal mole ) 32 ( 7 . 5) 38 ( 9 .0) 52 ( 12 . 2) no lag 80 ( 19 .0) correction 68 ( 16 . 1 ) 53 ( 12 . 6) 44 ( 10 . 4) 44 ( 10 . 4) 44 ( 10 . 6) 45 ( 10 . 8} 65 ( 15 . 5) 32 ( 7 . 5) 50 ( 12 . 0) 53 ( 1 2 . 5) 42 ( 10 . 0) 50 ( 1 2 . 0) 63 ( 15 . 0) 59 ( 14 . 0) 6 3 ( 15 . 0) 92 (22 . 0) 80 ( 19 . 0) 30 3 1 TABLE 2 . 5 Reaction Rate Constants and Activation Energies for Colour Change L-scale a-Scale b-Scale Food Products k37 , 8?C Ea _ 1 k37 . 8?C Ea _ 1 k37 . 8?C Ea _ 1 kJ mole __ 1 kJ mole _ 1 kJ mole _ 1 x 1Q 1 (kcal mole ) X ?? ? (kcal mole ) X lQl (kcal mole ) 6 s 8 Ham and Chicken 0 . 00002 105 ( 25 . 1 ) 0 . 00007 - 0 . 00005 86 ( 20 . 4 ) Loaf Frankfurters 0 . 00004 48 ( fi. 5) 0 . 00006 70 ( 16 . 6 ) 0 . 0000 1 23 ( 5 . 4 ) Beef steak 0 . 00002 54 ( 1 2 . 9 ) 0 . 00003 104 (24 . 8) 0 . 0000 1 2 1 ( 5 . 0) Beef s tew 0 . 0000 1 51 ( 1 2 . 1 ) 0 . 00003 36 ( 8 . 6) 0 . 0001 2 3 ( 0 . 8) .. Cheese spread 0 . 00003 57 ( 13 . 6) 0 . 00005 5 1 ( 1 2 . 1) 0 . 00003 35 ( 8 . 3) Pineapple 0 . 00008 67 ( 16 , 0) 0 . 00024 47 ( 1 1 . 1) 0 . 00008 84 ( 19 . 9) Fruit cake 0 . 00006 6 1 ( 14 . 4) 0 . 00003 40 ( 9 . 5) 0 . 00009 64 ( 15 . 2) Chocolate Brownies 0 . 00003 57 ( 1 3 . 6) O . OOOOit 43 ( 10 . 2) 0 . 00003 40 ( 9 . 6) 2 . 4 . 4 Viscosity As the model sys tem used , baby food , consisted of about 4 . 5% of various starches , wheat , barley and corn flour and 30% of potatoes in composition , the viscosity of the baby food depended on s tarch gelatinization . 32 Starch granules from dif ferent sources have different sizes , they vary between 3 and 30 m? with respect to the average size of their largest diameter for wheat starch , corn and barley s tarch and between 10 and 100 m? for root and tuber starch , as . potato s tarch . They are insoluble in cold water but swell with water when heated . The temper? ature at which granule swelling occurs varies with different s tarches . The gelatinization temperature ranges form 59 . 5-7 7 . 0?C depending on type of s tarch with the lowes t temperature for barley s tarch and the highest for modified potato starch . In terms of viscosity , i t gradually increases with the increase in temperature . When the gelation temperature is reached , the viscosity will rise rapidly due to the resis tance of the swollen s tarch granules to displacement . A dynamic si tuation eventually prevails in which some of the granules are s till swelling while others are simultaneously disintegrating under the influence of continuous heating and s tirring (Katz , 1 938) . Maximum viscosity is ob tained when the increase in s tructural viscosity caused by swollen s tarch aggregates is counter? balanced by the decrease in viscosity resulting from disintegration and solubilization of the s tarch . As heating is continued , the viscosity decreases gradually due to the breakdown of s tarch structure . The change of viscosi ty during heating of the s tarch-water suspension can be followed on a recording viscometer (Anker and Geddes , 1944 ; Kesler and Bechtel , 1947 ; Crossland and Favor , 1 948 ; Corn S tarch , 1964 ; Knight , 1969 ) . The pattern of viscosity change varied from one s tarch to another depending on the chemical property of the s tarch (Corn S tarch , 1964) . S tarch concentration was also found to affect the pattern of viscosity change (Anker and Geddes , 1944) . 33 Besides , there are other factors affecting the viscosity change which are ( 1 ) temperature (Corn Starch , 1 964) , ( 2 ) degree of agitation (Katz , 1 938 ; Corn Starch , 1 964) , ( 3 ) pH of starch suspension (Corn Starch , 1 964 ; Whistler and Paschall , 1965) and , ( 4 ) presence of chemicals (Whistler and Paschall , 1 965) . Higher temperature , higher agitation rate , pH higher than 7 and lower than 4 , were found to accelerate gelatinization and subsequent breakdown during prolonged heating . Some ingredients had a retarding action such as sugar , dextrose and corn syrup . As discussed before , prolonged heatin? can cause the change in viscosity which means a change in texture of the product . Luh et al ( 1 964) studied the effect of conventional canning and UTST thermal processing on the viscosity change of food products . Unfor? tunately the data presented were inadequate for determination of kinetic parameters . In terms of consistency , a "z" of 23?C , 29?C and 20?C were found for fish pudding , liver paste and vanilla sauce during thermal processing (Ohlsson , 1 980) . These were equivalent to the approximate activation energies of 1 30 , 103 , 1 50 kJ mole - 1 ? 2 . 5 CONCLUSION The changes in food during heat processing and storage were found to be described by either zero , first or second order kinetics . Zero order kinetics was found only at high concentrations and then it tended to change to first order kinetics as the concentration decreased . Second order kinetics were also found in some reactions . However , most of the changes in food could be described by first order kinetics . There were a number of factors affecting the rate of change - temperature , pH , water activity , oxygen concentration and concentration f . c +2 d d f f o m1nor components e . g . u ? The temperature epen ence o rate o change and in particular the des truction rate of nutrients was exten? sively s tudied and for most reaction rates the Ar?henius equation was found to adequately describe the temperature dependence . 34 Two heating procedures , steady-s tate and unsteady-state , can be used for estimation of the changes in food during processing . Calcu? lation of kinetic parameters from the data obtained by the s teady-state method is simple but only small food samples can be used . Unsteady? state procedure , where food is heated in a can , gives adequate sample size for eating quality determinations but the calculation is complex . The rates of destruction of ascorbic acid and of changes in colour (browning reaction and chlorophyll des truction) , and in viscosity were found to be mos tly described by f irs t order kinetics . For riboflavin , only the photodegradation rate was describ?d b y firs t order kinetics . The react ion rates repor ted were found to be in a wide range . The activation energy of ascorbic acid ranged from 1 4 to 1 7 2 kJ mole - 1 . The range of 34- 1 7 2 kJ mole- 1 was repor ted for riboflavin . For browning reaction , chlorophyll destruction , to tal colour change and viscosity - 1 - 1 the range of activation energies were 87-223 kJ mole , 32-9 2 kJ mole , - 1 -1 45-63 kJ mole and 103-1 50 kJ mole , respectively . 3 . INVESTIGATION OF TESTING METHODS AND DEVELOPMENT OF PROCESS 3 . 1 INTRODUCTION The aim of the present research was to determine the kinetic parameters for the des truction of ascorbic acid and riboflavin and for the changes in colour and viscosity of foods during heating . As colour and viscosity required large sample size , the unsteady- 35 s tate procedure of heating in can had to be used . Ascorbic acid and riboflavin were chosen because the analytical methods were simpler than for other vi tamins and the kinetic parameters could be determined by ei ther steady-state or uns teady-s tate heating procedure . The feasi? bility and accuracy of the computer model developed for the unsteady? s tate procedure ( in cans ) , therefore , could be tes ted by comparison of the kinetic parameters determined for ascorbic acid and riboflavin from these two procedures-s teady and unsteady-s tate ? A baby food made from s trained beef and mixed vegetables was used in this experi? mental work . To determine the kinetic parameters , the concentration before and after heating for a specific time and temperature must be known , so the analytical methods were first s tudied to give assays of suffi? cient accuracy to follow the kinetics . The preparation method for homogenized , s trained baby food was also inves tigated to give standard raw material for all tests . The raw materials required were determined by setting the product charac? teris tics required . As only one product composition was used in the s tudy , frozen storage of the prepared raw baby food was necessary to provide exactly the same raw material for the heating tes ts . Using the unsteady-s tate procedure where foods were heated in cans , the canning process - the preprocessing conditions , the retort operation , the processing conditions - was studied to obtain accurate control of the process . 36 Then , the preparation method , the final formulation , the pre? processine conditions and the processing conditions were finalized to give a heating process which could be accurately controlled and measured . 3 . 2 INVESTIGATION OF TESTING METHODS The obj ect of this part of study was to find the simplest method , using the equipment available , which would give the accuracy required . The method chosen for each quality characteristic will be discussed separa?ely in the following section . 3 . 2 . 1 Ascorbic Acid Specialised instruments such as autoanalyser , microfluorometer were not available , so a simple method of chemical ti tration with 2-6 dichloroindophenol was investigated . However , the colour interference of the samples made it difficult to achieve an accurate result . A calorimetric method of Pearson ( 19 76) was tried . This method is based on the oxidation - reduction reaction of ascorbic acid and the indicator dye , 2-6 dichloroindophenol . The colour change was measured as absor? bance by the Spectronic 20 spectrophotometer at wavelength 520 nm with the green filter . A standard curve was prepared using various concen? trations of ascorbic acid solution showing the relationship between the concentration of ascorbic acid and the scale of the absorbance obtained . The concentration of ascorbic acid in the sample was directly calculated from the prepared s tandard curve . I t was found that this method could be used i f the sample size was small enough to prevent the colour interference . Reproducible results were ob tained where the total ascorbi c acid content in the sample was - 1 more than 0 . 25 mg g (Appendix 3 . 1a) , and the sample size was approx- imately 8- 10 g . The details of analytical method are in Appendix 3 . 2a . 37 3 . 2 . 2 Riboflavin The fluorometric method (AOAC , 1 9 7 7 ) was found to give duplicate results where the concentration was about 20-30 ?g g- 1 (Appendix 3 . 1b) . However , i t was found that when measuring the fluorescence the samples had to be randomized as the instrument readings were drifting . Through? out all s tages of the method , protection of solution from undue exposure to light was done by covering all glasswares with aluminium foil . The details of the method are in Appendix 3 . 2b . 3 . 2 . 3 Colour It is difficult to describe quantitatively what colour is , as what is actually seen is the overall appearance of the food which depends on more than the colour alone . Such qualities as surface texture , gloss , metallic characteris tics , translucency and many more can contribute significantly to the total visual effec t . In this s tudy , an obj ective method was used in order to obtain s imple quantitative data for des? cribing the ef fect of hea t on the colour change of the processed food . A DU-colour instrument (Neotec Ins truments , Inc . of Silver Spring , MD, 1 9 7 1 ) was used . The measurement was read in the CIE system of X , Y , and Z as this system has achieved world wide accep tance and hDs been used essentially unchanged for many years (Billmeyer , 1 968) . Furthermore , the CIE chromaticity diagram is also available showing the colour of the sample on a two dimensional scale of x and y where x = X/ (X + Y + Z) and y = Y/ (X + Y + Z) . That is , for any given colour in the colour space , it would be partially described by x and y and then a third number , the tris timulus value Y , must be cited to completely describe the colour as lightness or darkness . One important parameter in measuring the colour of the sample by a reflectance method was the thickness of the sample on the glass window which mus t be controlled . A metal ring of about 1 cm depth was used . I t was placed on the glass window, the sample was filled and the white cover was pressed agains t the ring to allow the excess sample to overflow . 38 3 . 2 . 4 Viscosity Viscosity is a physical property which is related to texture of food . It was the obj ect of this study to determine the change of the viscosi ty in processed foods which would relate to a change in the texture of the food . Since baby food is a non-Newtonian f luid , i t is common p ractice to define a so-called apparent viscosi ty by using a shear rate selected to , fal l within a range of practical interest . The Brookfield Synchrolectric (LV type) was used . The viscosi ty of non-Newtonian fluids depends on the rate of shear which is governed by the speed of rotation and size of spindle . There- fore , the speed of rotation of 0 . 5 s - 1 and the spindle diameter of 0 . 3 cm (size 4) , which had been found to give an adequate range of viscosity , were used . I t was also found that the time of shear did effect the viscosi ty reading . So i t was decided that the reading would be taken at 1 minute after s tarting . The temperature of the sample was 0 exactly controlled at 25 C as temperature affected the viscosity . - ? 3 . 3 DEVELOPMENT OF PROCESS The preparation of homogenized baby food and the canning process were s tudied . 3 . 3 . 1 Preparation of Baby Foods The composition of the baby food used was based on the canned beef and vegetable baby food on the market . The approximate composition was found to be beef 5% , mixed vegetables 45% , flour , corn f lour and barley flour 4 . 5 % , yeast extract 0 . 4% , salt 0 . 4% and water 44 . 7% . The concen? tration of ascorbic acid ?n the existing canned product on the market was too low to determine so 2 mg of ascorbic acid per lOO g of raw material mixed was added . The following composi tion was used for this preliminary experiment . 39 Beef 5 . 0% Carrots 14 . 0% Peas 9 . 0% Potatoes 22 . 0% Flour 1 . 2% Corn flour 2 . 5% Barley flour 0 . 8% Yeast extract 0 . 4% Salt 0 . 4% Water 44 . 7% Beef was cut and minced through 1 cm , 0 . 4 cm and 0 . 25 cm diameter p lates of a Kenwood mincer for 1 , 2 and 2 times , respectively , as fine division was needed . Vegetables , except peas which were frozen , were washed , peeled , d iced and then blanched in a steam blancher . A blanching time of 5 minutes was sufficient to destroy enzymes and therefore prevent enzymic browning reactions occurring . All raw mater? ials including the dry ingredients and water were disintegrated under vacuum of 68 . 9 kPa pressure in the JEFFCO wet disintegrator ( size 2 - ? Model 29 1 DIMOCK MACHINE , Jeffress Bros . Ltd) for 3 minutes and then left - under vacuum for another 2 minutes to draw out as much of the remaining air as possible . The vacuum disintegration was necessary so as to reduce the s i'ze of the food particles to a suitable size for the further s teps in processing . To prevent blocking of the homogen? iser , the slurry was screened through a 1 cm square screen before passing through the homogeniser . The homogeniser used was a "MINOR" homogeniser type K (APV Manton - Gaulin homogeniser) with two- s tages where the slurry was forced through a small annulus at a pressure of 34500 kPa to create a very high veloci ty which broke down the particles into minute form. The homogeniser was preferred to the colloid mill as the strained baby f ood obtained from the latter entrapped a lot of air bubbles which could possibly effect the quality of the s tored baby food . The strained s lurries were packed in SARAN bags under vacuum and frozen immediately in a plate freezer . The slurries were completely frozen within 2 hours . SARAN bags were used to prevent air/oxygen transmission into the bag . Rapid freezing was used to minimize the pre-heating des truction of the s tudied quality factors . The frozen 40 0 baby food was stored at -30 C where the rate of destruction of most vitamins was negligible (Fennema , 1 9 75 ) . As the initial product characteris tics required for each run were the same , the raw baby food had to come either from the same batch of raw material s lurry or the same proportion of various batches . However , because of the quantity of product required , i t became obvious that one s ingle batch could not be prepared for the whole study . Therefore a number of batches were made and equal amounts of each batch were mixed for each experiment . Sufficient batches were made to cover the whole study ,with an adequate safety margin . 3 . 3 . 2 Preprocessing 3 . 3 . 2 . 1 Thawing The raw strained baby food s tored in frozen s tate was thawed prior to further preprocessing . During thawing , foods are subj ected to damage by chemical , physical and microbial means although microbial problems are negligible in properly handled foods . High temperatures are detrimental to the quality of foods so mild temperature conditions should be used in thawing (Fennema , 1 975) . Two different thawing conditions were s tudied , a 30?C water bath and a water bath in a 25?C controlled room . The thawing time was 1 hou? in the 30?C water bath and about 2 hours in the water bath held in 25?C controlled room . As large amounts of frozen baby food were thawed , it was more difficult to control the condition of 30?C as more than one water bath was required . Therefore , for convenience and more accurate temperature control , thawing in the water bath in 25?C for 2? hours was used . 3 . 3 . 2 . 2 Preheating As the viscosity of baby food was related to gelatinization of s tarch , preh?ating to gelatinize the s tarch was necessary to give a consistent initial viscosity . Another purpose for preheating was to allow hot f illing to be used providing a vacuum in the cans . 4 1 The temperature for preheating was chosen as 70?C to lie within the general gelatinization temperature range for s tarch of 59 . 5-77 . 0?C . The heating was carried out in a steam j acketed pan . A s team pressure in the j acket of 190 kPa was maintained and the product stirred by hand . The time required for heating to 70 ?C was 7 minutes and this condition was used in all experiments . Af ter preheating , the heated baby food was filled into the prepared cans with the minimum possible headspace being left so as to minimize can to can variations in the temperature responses of the samples . The f illed cans were vacuum sealed and immersed in a water bath at 60?C . The time taken to reach a uniform temperature of 60 ?C was found to be 80 minutes . 3 . 3 . 3 Processing The cans taken from the 60?C water bath were processed in a retort under different processing conditions . Temperature measurement and retort operation were s tudied . Processing conditions were set according to the exis ting retor t . 3 . 3 . 3 . 1 Temperature Measurement S tandard 24 gauge (United States s tandard wire gauge) copper/ constantan thermocouples were used and connected to a 1 2-point Honeywell? Brown recording potentiometer operating on a 72 second print cycle . A tension method of thermocouple mounting were used . Holes were located at diametrically opposite sides of the can and were pierced through the can wall with a sharp point . The copper and constantan wires were separated and threaded through holes from opposite sides of the can . They were then carefully j oined and soldered . The j unction point was made as small as possible to give the temperature measurement at the exact point in the can . The wires and j unction point were held in position with adhesive tape on the outside of the can . Epoxy resin adhesive was applied on both sides of the hole and left overnight to complete hardening . For points near the can wall , following suggestions made by Packer ( 1 967 ) the constantan wire was always the shorter within . the can . Anti-sulphur , lacquered cans of 7 . 4 cm diameter and 10 . 8 cm height were used . For each processing run , a can with thermocouples 42 at five different points was f illed with preheated baby food and heated in the retor t . The temperature dis tribution through the food during processing was measured and recorded by the potentiometer . The thermo? couple arrangement is shown in Figure 3 . 1 and Table 3 . 1 . 3 . 3 . 3 . 2 Retort Operation The retort used was a laboratory-scale , horizontal autoclave (locally made by Berry Engineering Ltd . , Palmers ton North , New Zealand ) . I t was equipped with two venting valves , s team inlet , s team by-pass , cooling water inlet and drain water outlet , the s team pressure and temperature were controlled by an automatic pnuematic sys tem . At the end of the 2 minutes venting period , the drain valve and two vent valves were closed . The required retort steam pressure was reached within a few seconds af ter closing vents and the steam temperature could be controlled for the required period . At the end of the holding period , the retort pressure was reduced slowly over 4 minutes . This s tep was - necessary and had to be carefully controlled , as the high processing temperature involved may create very high pressures within the can of 200-300 kPa (Goldblith et al , 196 1 , p . 854) . If the retort pressure was released too quickly, distortion or buckling of the can could occur . Once the retort pressure was reduced to atmospheric , the cooling water was turned on and the retort was about 75% filled . This water level was maintained by continuous flow of cold water . The total cooling time was 40 minutes . The time taken to fill 75% of the retort was about 5 minutes . 3 . 3 . 3 . 3 Processing Conditions The system on the retort used was limited to temperatures below 1 30?C . In order to ensure satisfactory control a t all times , the maxi? a mum retort temperature used was 129 C . 1 e 2 + 3-- 4 e 5 - - -- - - - ........ ....... FIG . 3 . 1 Thermocouple Arrangement in a Can TABLE 3 . 1 Dis tance from the Centre to the Measured Points Point Number r* cm 1 0 . 0 2 1 . 2 3 0 . 0 4 0 . 0 5 2 . 5 * r is a dis tance from the centre of a can in diametral direction . h* cm 3 . 6 1 . 8 0 . 0 1 . 8 3 . 6 h is a d is tance from the centre of a can in axial d irection . 43 ? ? , ? 44 10 For a low acid food of pH of 5 . 5-6 . 0 , the F 1 2 1 ? 1 , which is the ? 1 t ? t ? ? ? t t 1 2 1 . 1 ?C for " z " of 10?C , equlva en processlng lme ln mlnu es a recommended is in the range of 10 to 1 5 . I t was decided t o carry out the exper iment at 1 29?C retort temperature for various processing 10 t imes to obtain the F 1 2 1 . 1 of 5 . 0 , 9 . 0 , 1 3 . 0 , 1 7 . 0 and 2 1 . 0 Heated samples were taken from the processed cans after cooling whereas control samples or zero time samples were taken randomly from the cans af ter removal from the 60?C water bath . Two samples of both the control and processed samples from each processing experiment were s tored overnight in a chiller at 10?C prio? to viscosity , colour , pH and dissolved oxygen measurements . All other control and processed 0 samples were s tored in -30 C frozen s torage for vitamin analysis . The control and heated cans were completely thawed in an ambient tem? perature water bath . Then the can content was totally mixed before the samples were taken for analysis . 3 . 4 ADJUSTMENT OF PROCESS The results from 3 . 3 suggested that adj ustment of the process was necessary . Experiments were carried out and the results obtained were used to determine the f inal process . 3 . 4 . 1 Formulation The ascorbic acid content in both control and heated samples was too low to obtain accurate results . The sample size required was large and caused colour interference in the ascorbic acid determination for the heated samples . The riboflavin concentration was also too low and a large sample size was needed causing an error from colour interference . Therefore , i t was decided to add both ascorbic acid and riboflavin into the raw prepared baby food so as to reduce sample size and colour inter? ference . Using the measured temperature distribution at the centre and at 0 the farthest point at the highes t processing temperature of 1 29 C and the longest processing time (F ?? 1 . 1 of about 2 1 . 0) with the kinetic reaction data from Chit taporn ( 1977 ) , the average ascorbic acid retention at each point es timated from: c exp (-k?t) 0 exp (-k x 0 . 02) is the final concentration af ter one time interval ?t 45 where c 1 k is the reaction rate calculated for various measured temper? atures (h- 1 ) 0 . 02 is the time interval , ?t (h ) , over which the temperature is assumed constant c is the initial concentration 0 and this can be continued for c2 , c3 , . . . cn for processing time of n?t . The average ascorbic acid retention of these two points was 69% . The necessary ascorbic acid to be added to give an accurate reading in the heated sample was calculated as 20 mg per 100 g of raw slurry . The riboflavin needed was calculated in a similar way as 2 . 5 mg per 100 g of raw slurry . From the colour measurement , all the heated samples were darker than the control . As x and y could be calculated from X , Y and Z data Billmeyer ( 1968) , it was found that there was a difference between x and y of the control and heated samples but the percentage change was the same for all heated samples subj ected to various degrees of heat treat? ment . Therefore , i t was concluded at this point that there was a change in colour during heat treatment but the change in x and y of the heated samples was the same , only the darkness (Y) of the samples changed . Only Y was therefore necessary to measure the change of colour during heating . The results of calculated x and y are shown in Appendix 3 . 3 . As the colour of the control samples was too dark , the composition of raw material was altered to produce a lighter colour in the control , thus providing more room for Y to change in the heated samples . The composition of mixed vegetables which governed the colour of the product as they were the main raw materials , were changed from 1 4% carrots , 9 % peas , and 22% potatoes to 10% carrots , 5% peas and 30% potatoes . The experiments were repeated using the modified composition fortified with ascorbic acid and riboflavin . The analysis of both vitamins were found to be satisfactory . The colour of both control and heated samples were improved as Y obtained from a new control samp le was 4 6 3 1-32 when the former control sample was 23-24 . Therefore , the final formulation was : Beef 5 . 0% Carrots 10 . 0% Peas 5 . 0% Potatoes 30 . 0% Flour 1 . 2% Corn flour 2 . 5% Barley flour 0 . 8% Yeast extract 0 . 4% Salt 0 . 4% Water 44 . 7% Ascorbic acid 0 . 2 - 1 mg g Riboflavin 25 . 0 ?g - 1 g 3 . 4 . 2 Preprocessing Conditions The viscosity of the control samples from various experimental runs were found to vary so that the change of viscosity with heat processing could not be predicted . As s tarch gelatinization depends on time and temperature of heating , rate of heating , degree of agitation , pH and other factors , it was difficult to obtain the same viscosity in the product unless all the factors involved were precisely controlled . Agitation by hand stirring may have been one of the important factors causing fluctuation in results in the preliminary experiment so a mechanical stirrer with controlled speed was used instead of hand s tirring for later work . Also , because of the complexity of the viscosity change of starch paste during heating and stirring , i t was decided to control the viscosity of the control sample in each experimental run at about maximum viscosity , then any subsequent reduction in viscosity could be attributed t o the effect of further heating . 47 The experiments were carried out at fixed s team pressure of 1 90-200 kPa in the j acket of the s team j acketed pan . The volume of material in the steam j acketed pan was fixed so that the rate of heating would be the same for all runs . Samples were taken at various times for viscosity measurement . The temperature and time of heating were recorded . From the results , the rates of heating were different and could not be controlled in the exis ting equipment . The viscosities of samples at various times were also different between experimental runs as a result of dif ferent rates of heating . This can be seen in Figure 3 . 2 . However , the maximum viscosity was reached af ter the tem? perature of the baby food rose higher than 87?C and af ter a time of heating varying from 10 to 14 minutes . At this point , it was believed that all the s tarches were fully gelatinized . Therefore the preheating was designed to achieve this in all samples . The s team pressure was 190-200 kPa and the final temperature of the baby food had to be higher than 87?C . The time of heating could be flexible depending on the amount of baby food to be heated . As the initial temperature could affect the rate of heating so the thawed s lurry had to be chilled for 45 minutes at 10?C before preheating . 3 . 5 FINAL PROCESS The final formulation decided , was : Beef 5 . 0% Carrots 10 . 0% Peas 5 . 0% Potatoes 30 . 0% Flour 1 . 2% Corn flour 2 . 5% Barley f lour 0 . 8% Yeast extract 0 . 4% Salt ? 0 . 4% Water 44 . 7% Ascorbic acid 0 . 2 - 1 mg g Riboflavin 25 . 0 )lg - 1 g 20 . 0 - 0. 16 . 0 tJ ....... ("") ' a ? X 1 2 . 0 :>.. -1-J ?? CJl 0 tJ CJl ..-i 8 . 0 ::> 4 . 0 o . o FIG . 3 . 2 0 10 I '-/' I ,.,. ..... ---./ 20 100 /-----:- - - 80 60 .. 40 30 40 50 Time (min) Time , Temperature and Viscosity Relationships During Preprocessing of Baby Food -- ----- . .. --- --tl temperature- time relationships for experiment temperature-time relationships for experiment temperature-time relationships for experiment viscosity-time relationships for experiment 1 viscosity-time relationships for experiment 2 viscosity-time relationships for experiment 3 48 ? (!) ? (!) t1 Ill ..... ? t1 (!) - 0 n - 1 2 3 49 Frozen coarsely minced beef was minced again through the 0 . 25 cm diameter plate of a Kenwood mincer twice and put (about 500 g ) in a plastic bag before s toring at - 10?C . Commercial frozen peas , carrot cubes and potato chips were used to ease the preparation s tep . Frozen minced beef was thawed , mixed with all frozen vegetables and other raw materials and 20 mg of ascorbic acid and 2 . 5 mg of riboflavin per 100 g of slurry , disintegrated under vacuum of 68 . 9 kPa pressure in a JEFFCO wet disintegrator for 3 minutes and then lef t under vacuum for another 2 minutes . This s lurry was screened and passed through a MINOR-homogen? iser which was operated at 34500 kPa pressure . The prepared slurry was vacuum packed in SARAN bags and frozen immediately in a plate freezer . The preparation of raw slurry was carried out in 1 6 kg batches providing enough slurry for all experimental runs . The frozen prepared slurry was kept at -30?C and thawed in a water bath held in a 25?C controlled room for 2? hours before further processing . Exactly 800 g of thawed 0 slurry from each batch was mixed and chilled at 10 C for 45 minutes giving exactly 12 kg for preheating . Preheating was carried out in a MERCER s team j acketed pan (30 cm diameter , maximum capacity - of 1 2 , 000 cm3) with a Pioneer mixer model - 1 2600 (Premier Colloid Mills Ltd . ) a t high speed o f 50 s and the s team pressure in the j acket of 1 90-200 kPa until the temperature of the baby food reached 87?C . Lacquered cans were then filled with hot baby food with minimum possible headspace and immediately vacuum sealed . The cans of baby food were then immersed in a 60?C water bath for 80 minutes before processing in the retor t . Eight control cans were randomly taken, 2 cans were kept at ambient temperature for viscosity and colour analysis , the remaining cans were kept at - 1 0?C for ascorbic acid and riboflavin analysis . 0 The remaining cans taken from the 60 C water bath were processed in a retort . One of the cans was equipped with 5 thermocouple junctions (Figure 3 . 1 ) . The retort was closed , and the thermocouple ends were connected to a 12-point Honeywell-Brown recording potentiometer . Retort operation was exactly the same as described in 3 . 3 . 3 . 2 . The temperature used and duration of processing were varied . 50 After cooling , two of the heated cans were kept at ambient temper? ature for viscosity and colour measurement , and the rest kept at - 10?C . Viscosity and colour measurement were carried out in the same day . Frozen control and heated cans for each experimental run were thawed in the ambient temperature water bath at the same time . The can content was mixed , then the sample was taken for analysis . 4 . TEMPERATURE DISTRIBUTION IN A CAN DURING PROCESSING 4 . 1 INTRODUCTION A maj or obj ective of this s tudy was to es tablish a calculation procedure which , given the processing conditions , could be used to predict the extent of processing of the various critical components of the food . Before describing the detai l , it may be helpful to set out the sequence of this part of the inves t1gation . Firs t , in order to have a basis for comparison a careful series 5 1 o f experimental tes ts were carried out . Because o f the temperature sensitivity of the reaction rates , temperatures should be known accur? ately within ? 0 . 25?C . And because temperatures varied with position , as well as with time , it was necessary to be able to predict temperatures at all positions within the can . For tes ting purposes , four points were considered sufficient?. If these could be fit ted then the others would presumably conform to the geometrical pattern . For prediction two broad approaches were used , one based on an analytical solution and the other using a numerical finite d if ference method , to the heat conduction equations . Because of the many calculations needed , both were carried out by computer . Thermal properties of the material were needed for these calculations ? and they were es timated from the experimental results . The predictions from the two calculation approaches were compared with the experimental results . In general both approaches , when the bes t thermal data were used , gave a very good fit and thus confidence to the predi ction procedure , except for a consistent irregularity in the early s tages of the cooling phase . This was not fully explained but some suggestions are advanced to account for i t and modifications to the cooling calculations allow for i ts effects . These procedures led finally to a calculation method which was sufficiently accurate for the kinetic predictions . 4 . 2 EXPERIMENTAL DETERMINATION OF TEMPERATURE DISTRIBUTION 52 The prepared , prehea ted baby food was f illed and sealed in the prepared cans as described in Chapter 3 . Two different retort temper? atures were used , 1 20? and 1 29?C , and the canned baby food was processed for various times to get an approximate microbiological lethality number 10 (F 1 2 1 . 1 ) of 5 , 9 , 1 3 , 1 7 and 21 min . The experimental runs were randomly performed . The detailed processing conditions together with the run number of each experiment performed in this study are shown in Table 4 . 1 . The retort operation was the same as described in section 3 . 3 . 3 . 2 . The temperature distribution in the can was measured at various points by thermocouples connected to the Honeywell-Brown recording potentiometer as described in Table 3 . 1 . The recorded temperatures at points 1 , 2 , 3 and 4 are shown in Figures 4 . 9 and 4 . 10 . TABLE 4 . 1 Experimental Run Number and Processing Conditions Initial Retort* Heating** Cooling* Cooling*** Approximate water 10 Run No . temper- temper- time time F 1 2 1 . 1 ature ature temper-oc oc s ature s intended oc min 7 60 . 0 1 20 . 2 38 16 19 . 4 2400 5 4 60 . 0 1 19 . 6 5 1 1 2 2 1 . 3 2400 1 3 9 6 1 . 0 1 20 . 0 5256 19 . 9 2400 1 7 2 60 . 3 1 19 . 8 6 1 20 20 . 8 2400 2 1 6 6 1 . 0 1 29 . 1 2952 20 . 8 2400 5 1 58 . 8 1 28 . 7 3384 20 . 6 2400 9 8 60 . 2 1 28 . 6 3456 22 . 0 2400 1 3 5 6 1 . 0 1 29 . 2 3744 20 . 2 2400 1 7 10 59 . 0 1 29 . 1 38 16 20 . 0 2400 2 1 * Average temperature calculated from the recorded temperatures obtained from each experimental run . 53 ** The interval be tween the time when the required retort temperature was reached to the time when the cooling water was turned on . *** The interval between the time when the cooling water was turned on to the end of cooling . 4 . 3 COMPUTER PROGRAMS FOR TEMPERATURE DISTRIBUTION CALCULATION Two computer programs based on the analytical solution and the numerical finite dif ference method were studied and compared with the experimental measurements ; the programs were written in FORTRAN IV language and run on a Burroughs B6700 computer . 4 . 3 . 1 Analytical Solution Me thod The content of the can are a finite cylinder at an initial temperature , TI , and with thermal diffusivity , a . When the can is put in a medium at temperature , TA , there is heat transfer in all three directions . From heat transfer theory , this complex three dimensional heat transfer can be broken down into the radial heat transfer and infinite slab heat transfer . I f YC is the solution for radial heat transfer YL is the solution for infinite slab heat transfer . For a short cylinder T -TA TI-TA (YC) (YL) where T is the temperature of any point at time , t . ( 4 . 1 ) From Carslaw and Jaeger ( 1959 , p . 199 and p . 100) , where heat dif fusivity is constant , YC where a is cylinder radius J ( S r/a) o n S J 1 ( S ) n n 2 2 (-S at/a ) n ? e r is dis tance from the centre in radial direction S is nth positive root of J ( S ) = 0 n o t is time (4 . 2) 54 --------------------------- ---- 4 oo (- 1 ) m YL = rr ?=0 ( 2m+1) cos where h is half-height of the cylinder (4 . 3) x is the distance from the centre in the axial direction . 55 2 Where at/a is less than 0 . 02 and r/a is not too small , the series is slow to converge but a short term approximation exists (CARSLAW and JAEGER , 1 959 , p . 330) . where z is YC = 1- (a 0 ? 5 erfc ( z) + (a-r) (ata) 0 " 5 i erfc ( z) + 0 . 5 4 1 . 5 (a-r) 2 (at) 0 ? 5 r ar (4 . 4) For the same reason , _where at/h2 is small , equation (4 . 5) has to be used instead of equation (4 . 2) (CARSLAW and JAEGER, 1 959 , p . 309) ? . YL = 1- (!n=O (- 1 ) n erfc ( ( 2n+l) h-x) + 2 (at) 0 ? 5 'f (- 1 )n erfc ( ( 2n+1) h+x) ) n=O Z (at) 0 . 5 ( 4 . 5) In the canning process , temperature distribution in both heating and cooling phases is required . In the heating phase , the temperature distribution can be calculated by T = (TA-TI ) ? ( r , x , t) + TI ( 4 . 6) where (r , x , t ) is 1- (YC) (?'1) at the point ( r , x) at time , t YC is the solution calculated by equation (4 . 2 ) or ( 4 . 4) YL is the solution calculated by equation ( 4 . 3) or ( 4 . 5 ) T is the temperature at (r , x) at time , t TA is the retort temperature TI is the initial temperature a is the can radius h is the half of can height r is a dis tance from the centre of the can in the radial direction x is a dis tance from the centre of the can in the axial direction 56 t is the total time from the beginning of the heating phase is the nth positive roots of J ( 8) = 0 . 0 In the cooling phase , i f the temperature o f the whole can content at the beginning of cooling is assumed to b? uniform and eq?al to the retort temperature (Hicks , 195 1 ) , then the temperature distribution can be calculated by T (TA-TI) ? (r , x , t) + (TC-TA) ? (r , x , t-t1) + TI where TC is the cooling water temperature t 1 is the heating time . (_4 . 7) The computer program was constructed based on the above theory ; equations ( 4 . 1 ) to ( 4 . 7 ) were used . For equation ( 4 . 1 ) and ( 4 . 2) , 6 terms in each series were calculated as Fleming ( 197 1 ) s tated that up to 3 terms of the series mus t be evaluated . EquatiQn (_4 . 4 ). and 2 ( 4 . 5) were used where at/a was less than 0 . 0 2 ; r/a was more than 0 . 1 2 and at/h was les_s th.:m 0 . 3 (Fleming, 1 9 7 1 ) . Where r/a was less than 0 . 1 , the value of YC was set equal to zero . The flow chart of the computer program and the details of the program are in Appendix 4 . 1 . The calculated temperatures from the computer program were compared with the ones calculated by hand calculator based on the processing conditions of run no. 6 for the heating phase to check the accuracy of the constructed program, and it was found that the calculated temperatures were identical (Table 4 . 2) . TABLE 4 . 2 Comparison of the Calculated Temperatures at the Centre of the Can Time CALCULATED TEMPERATURE ?C Fo * Fo * s c h Computer Hand Calculator 0 0 0 6 1 . 00 6 1 . 00 360 0 . 0404 0 . 0 1 89 6 1 . 26 6 1 . 26 720 0 . 0807 0 . 0379 66 . 79 66 . 78 1 080 0 . 1 2 1 1 0 . 0569 7 7 . 06 77 . os 1 440 0 . 1 6 1 5 0 . 0759 87 . 60 87 . 6 1 1 800 0 . 20 1 8 0 . 0948 96 . 75 9 6 . 74 2 1 60 0 . 2422 0 . 1 1 38 104 . 1 8 1 04 . 1 7 2520 0 . 2826 0 . 1 3 28 1 10 . 03 1 1 0 . 03 2880 0 . 3229 0 . 1 5 1 7 1 1 4 . 57 1 1 4 . 56 57 * Fo is the Fourier number of the radial direction which is equal to c at/a2 . Foh is the Fourier number in the axial direction which is equal to at/h2 . 4 . 3 . 2 Numerical Finite Difference Method The general heat transfer equation for unsteady-state in a f inite cylinder is (4 . 8) where C is heat capacity on a volumetric be.sis A is thermal conductivity which is assumed to be constant Using the numerical finite difference method , equation (4 . 8) becomes where r X Ti+l - Ti m?n m2n M is (n- l ) ?r is (m-1 ).6x >. c >. c >. c Ti - 2 T1 + Ti ( m+l ?n m2n m- l , n) (fuc) 2 Ti - 2 Ti + Ti ( m ,n+l m2n m2n- l ) (?r) 2 1 r Ti - ( m?n+l 2?r Ti m , n- 1 ) a (A) + a (B) + a (C ) T i represents temperature at time , t i+l T represents temperature at time t + ?t a is the thermal diffusivity which is f. /C . + + (4 . 9 ) At the centre , where n= l , equation ( 4 . 9 ) was modified by Albasiny ( 1960) as lim 1 3T a2T r-+0 - = --r ar ar 2 >. 3T a2T >. -r ar 2 ar then caT a 2T 2 >. - + 2>.? ar a:x:2 ar2 Ti+l - Ti Ti - 2 T i + Ti m2 1 m2 1 = a ( m+l z 1 m2 1 m- 1 z 1 ) + ?t (fuc) 2 so Ti - 2 Ti i + T 2 a ( m2 2 m1 1 m20 ) ( 4 . 10) (?r) 2 58 Assuming that the temperature at the point below the centre line is equal to the temperature at the corresponding point above the line , the temperature at the centre (m=1 , n= 1 ) and the temper? ature along the height and the radius can be calculated by (4 . 1 1 ) , (4 . 1 2 ) and (4 . 1 3 ) , respectively . 6t Ti+1 _ Ti m, 1 m, 1 6t Ti+1 _ Ti 1 , n l,n 6t Ti - Ti 2a ( 2?n 1 ?n) + a(B) + a (C) (6x) 2 (4 . 1 1 ) ( 4 . 1 2) (4 . 1 3 ) 59 The computer program was constructed based on the above equations by assuming the initial temperature at all points was equal throughout the can , while the temperature at the surface was equal to the retort temper? ature during heating and equal to the cooling water temperature during cooling . The details of the program are in Appendix 4 . 2 . Using this program , the degree of accuracy of temperature dis tri? bution prediction was dependent on the number of time increments , 6t , and dimensional increments , 6r and 6x . The dimensional increments , 6r and 6x , of less than 0 . 008 and 0 . 0 1 0 m and the time increments of 7 . 5 seconds should be used (Teixeira , 1 9 7 1 ) . The dimensional increments , 6r and 6x of 0 . 0037 and 0 . 0054 m and the time increment of 6 seconds were used in this study . 4 . 4 THERMAL PROPERTY DETERMINATION To use the two programs to find the temperature distribution , only one thermal property , the thermal diffusivity , a i s needed . This property can be calculated from the experimental temperature data using the analytical solution of the heat transfer equation . The analytical solution for heat transfer can be re-expressed as : where T - TI TA - TI A B is is 2 -Fo f3 1-Ae c n Be 2 -Fo TI /4 X 00 J ( 8 r/a) o n 2?=1 4 00 - l: TI m=O f3 J 1 ( f3 ) n n (- 1 )m ( 2m+l) ( 2m+1 ) Trx cos 2h ( 4 . 14) If Y is (T - TI) / (TA - TI) , where T is the centre temperature , and only one term in each series is considered , equation (4 . 14 ) simplifies to : ln Y cons tant - 2 af3 1 t (-2 a 2 CtTI + -) 4h2 ( 4 . 1 5) From a plot of ln Y agains t time , t , the slope of the regression . 2 2 2 2 line on the stra1ght part will be equal to - (af3 1 /a + arr /4h ) . Knowing S 1 = 2 . 4048 and the dimensions of the can used , a = 0 . 037 m , h = 0 . 054 m , the thermal diffusivity can be calculated as illus trated in equation (4 . 16) . 60 2 _ a ( ( 2 . 4048) (0 . 037 ) 2 2 + TT ) 4 (0 . 054) 2 slope -slope 5070 . 4568 2 - 1 m s ( 4 . 16 ) This method has been used by other workers (Olson and Jackson , 194 2 ; Teixeira , 1969) . The graph plotted of ln Y versus t ime is a straight line , af ter the initial heating lag period , and only one 6 1 term in the summation i s adequate (Hicks , 1 9 5 1 ) . Therefore , the above method should result in an accurate thermal. dif fusivity calculation as long as the temperature measurement is accurate . In the preliminary experiments , the canned baby food was processed under various temperatures and the centre temperature was measured with time . The thermal diffusivity was calculated from the slope obtained . The results are shown in Table 4 . 3 . The average thermal diffusivity was found to be 1 . 5737 x 10-7 m 2 s- 1 with the standard deviation of 0 . 0678 x 10 -7 m 2 s - 1 ? This value of "a" was similar to data given by Teixeira ( 19 75) , Crumpton and Treadgill ( 1 9 7 7 ) and Lenz and Lund ( 1 97 7a) for other food systems . Crumpton and Treadgill ( 1 9 7 7 ) s tated in their study that the retort temperature had less effect on thermal diffusivity than the physical state of the material . The above results agreed with Crumpton and Treadgill ' s study as the deviation of calculated thermal diffusivities at different retort temperatures was less than the deviation of calculated thermal dif fusivities of various experimental runs at the same retort temperature . This may have resulted from the variation in the contents from can to can , which was significant in o ther studies . The variation of thermal diffusivity between cans was 6 . 46% (Hurwitcz and Tischer , 1956) and 10- 1 5% in work carried out by Jackson and Olson ( 1 940) . Heterogeneous packs were found to result in even greater varia? tions (Esselen , 1 9 5 1 ) . Therefore , it was concluded that it was valid to use the average thermal diffusivity for all processing temperature conditions studied, as the baby food was homogeneous and the experimental variation small . 62 TABLE 4 . 3 Diffusivities of Baby Food at Various Temperatures Retort Temperature Diffusivity X 10 7 Correlation Coefficient oc 2 - 1 R2 m s 1 28 . 3 1 . 57 1 7 0 . 999 1 . 5359 1 . 000 1 . 6229 0 . 999 1 . 4677 0 . 999 1 . 5465 0 . 999 1 20 . 6 1 . 5456 0 . 999 1 20 . 0 1 . 6 10 1 0 . 999 1 11 . 1 1 . 5564 0 . 998 1 . 7064 0 . 999 - ? Some of the raw materials were changed in s tate so as to save time in preparation (section 3 . 5) , frozen potato chips and carrot cubes and also frozen minced beef were used ins tead of the fresh ones . The thermal diffusivity of the baby food was redetermined and found to be 1 . 5429 -7 2 - 1 - 7 2 - 1 0 x 10 m s with the s tandard deviation of 0 . 0 196 x 10 m s at 1 20 C -7 2 - 1 - 7 2 - 1 and 1 . 52 7 7 x 10 m s with the s tandard deviation of 0 . 03 1 8 x 1 0 m s at 1 29?C . The difference between these two means was tes ted and found to be insignificant . De tails of the measurements and analysis are shown in Appendix 4 . 3 . Therefore , the mean thermal diffusivity of 1 . 5353 x 10-7 m 2s- 1 with s tandard deviation of 0 . 026 1 x 10-7 m 2s- 1 was used for all the processing conditions s tudied . 4 . 5 COMPARISON BETWEEN PREDICTED TEMPERATURES FROM THE TWO COMPUTER PROGRAMS - ANALYTICAL SOLUTION AND NUMERICAL FINITE DIFFERENCE The. predicted temperatures from both programs based on 3 points in the can of run no . 6 were almos t identical (Table 4 . 4 ) . The differences in temperatures were mos tly about 0 . 1 to 0 . 2?C in both heating and cooling phases . In the heating phase , the predicted temperature by the numerical finite difference program was higher than the predicted temperature by the analytical solution program while in the cooling phase , the numerical finite difference program gave a lower predicted temperature . The difference was greater at the outside point than the centre of the can in the beginning of both 0 heating and cooling phases . The greatest difference was 0 . 4 C for the centre and 0 . 9?C for the outside point in the heating phase . 63 This difference could be due to the slower convergence in the heating phase of the analytical solution . Also , as the temperature gradients were high at the beginning , the temperatures of the can contents changed rapidly , thus smaller time s teps should have been used to obtain more accurate approximation in the numerical finite difference program . I n the cooling phase , the differences were larger , these could b e due to the assumption made in the analytical solution program that the initial temperatures of the can contents were uniform and equal to the retort temperature ; this resulted in higher predicted temperatures . The differences in predicted temperatures by these two programs based on run no . 6 are also shown in Figures 4 , l and 4 . 2 for the centre point and the outside point , ( r/a , x/h) of ( 2/ 3 , 2/3) . The residuals (predicted temperatures by analytical solution - predicted temperatures by numerical finite difference method) were calculated for both the centre point and the outside point . The calculation was done at 1 . 2 minute intervals , the distribution of residuals is shown in Figure 4 . 3 . The mean residual was 0 . 07?C with a s tandard deviation of 0 . 34?C for the centre point and 0 . 07?C with a s tandard deviation of 0 . 54?C for the outside point . These differences were small and could be considered insignificant . Therefore , to tes t the accuracy of predictions , only predicted temperatures from the analytical solution program were compared with the experimental temperatures . TABLE 4 . 4 Comparison of Tempera tu res Predicted by the Analytical Solution and the Numerical Finite Difference Programs TEMPERATURE ?C at the centre at r /a = 1 /3 , at r /a = 2/3 , Time Fo Fo x /h = 1 /3 x/h = 2/3 c X s Analy- Analy- Analy- tical Finite tical Finite tical Finite Heating 0 0 0 6 1 . 00 6 1 . 00 6 1 . 00 6 1 . 00 6 1 . 00 6 1 . 00 72 0 . 0081 0 . 0038 6 1 . 00 6 1 . 00 6 1 . 00 6 1 . 00 6 1 . 74 62 . 64 144 0 . 0 162 0 . 0076 6 1 . 00 6 1 . 00 6 1 . 02 6 1 . 09 66 . 76 68 . 1 6 2 1 6 0 . 0242 0 . 0 1 1 4 60 . 99 6 1 . 02 6 1 . 29 6 1 . 50 73 . 46 74 . 68 288 0 . 0323 0 . 0 152 6 1 . 05 6 1 . 1 3 62 . 05 62 . 36 79 . 86 80 . 7 9 360 0 . 0404 0 . 0 1 89 6 1 . 26 6 1 . 43 63 . 34 63 . 7 7 85 . 44 86 . 1 4 720 0 . 0807 0 . 0379 66 . 7 9 67 . 24 74 . 1 1 74 . 60 103 . 1 7 103 . 35 1080 0 . 1 2 1 1 0 . 0569 77 . 06 7 7 . 44 86 . 04 86 . 38 1 1 1 . 97 1 1 2 . 04 1440 0 . 1 6 1 5 0 . 0759 87 .60 87 . 88 96 . 1 5 96 . 36 1 1 7 . 1 3 1 1 7 . 1 7 1 800 0 . 2018 0 . 0948 96 . 7 5 96 . 93 104 . 09 104 . 2 1 1 20 . 48 1 20 . 50 2 1 60 0 . 2422 0 . 1 1 38 104 . 18 104 . 29 1 10 . 1 6 1 10 . 23 1 22 . 79 1 22 . 80 2520 0 . 2826 0 . 1328 1 1 0 . 03 1 10 . 09 1 1 4 . 78 1 1 4 . 81 124 . 43 1 24 . 43 2880 0 . 3229 0 . 1 5 1 7 1 1 4 . 57 1 1 4 . 60 1 1 8 . 27 1 1 8 . 28 1 25 . 6 1 1 25 . 6 1 2952 0 . 33 1 1 0 . 1 554 1 1 5 . 34 1 1 5 . 36 1 1 8 . 86 1 1 8 . 87 1 25 . 8 1 1 25 . 8 1 Cooling 72 0 . 0081 0 . 0038 1 1 6 . 0 7 1 1 6 . 09 1 1 9 . 4 1 1 19 . 42 1 24 . 82 1 23 . 38 1 44 0 . 0 1 62 0 . 0076 1 1 6 . 7 7 1 1 6 . 7 8 1 1 9 . 90 1 1 9 . 8 1 1 1 7 . 0 1 1 1 4 . 7 8 2 1 6 0 . 0242 0 . 0 1 1 4 1 1 7 . 44 1 1 7 . 4 1 1 19 . 98 1 19 . 65 106 . 5 1 104 . 57 288 0 . 0323 0 . 0 152 1 1 7 . 98 1 1 7 . 85 1 1 9 . 23 1 18 . 69 96 . 49 95 . 00 360 0 . 0404 0 . 0 189 1 1 8 . 23 1 1 7 . 96 1 1 7 . 63 1 16 . 94 87 . 7 5 86 . 64 7 20 0 . 0807 0 . 0379 1 1 1 . 96 1 1 1 . 24 102 . 39 101 . 60 60 . 1 6 59 . 87 1 440 0 . 1 6 1 5 0 . 07 59 82 . 22 69 . 83 2 1 60 0 . 2422 0 . 1 1 38 57 . 80 48 . 97 64 1 30 125 ,....._ u '0 Q) 1 15 lo-t ;:I +J CO lo-t Q) 105 p, s Q) ? 95 85 75 65 55 45 35 0 65 10 20 30 40 50 60 70 80 90 Time (min) FIG . 4 . 1 Comparison of Predicted Temperatures from the Computer Programs at ( r/a , x/h) of (0 . 0 , 0 . 0 ) (--------) predicted temperatures from the analytical solution computer program (--- ---) predic ted temperatures from the numerical f inite difference method program 1 30 1 2 5 ,-.... u 0 '-" 1 1 5 QJ H ;:::l .j.J CO H 105 QJ p_, r:; QJ ? 95 85 7 5 65 55 45 35 66 0 10 20 30 40 so 60 70 . 80 90 Time (min) FIG . 4 . 2 Comparison of Predicted Temperatures from the Corn uter Programs at (r /a , x/h) of (2 /3 , 2 /3) (--------) predicted temperatures from the analytical solution program (--- ---) predicted temperatures from the numerical finite difference program r-. o...e '-" :>-. () ? <1) ;::! 0"' <1) I-I ? r-. o...e '-" :>-. () ? <1) ;::! 0"' <1) I-I ? 30 a) median .. 0 . 0 1 o c mean = 0 . 07 oc standard deviation = 0 . 34 oc 20 10 0 -0 . 7 5 -0 . 55 -0 . 35 -0 . 1 5 0 0 . 1 5 0 . 35 0 . 45 60 ,..... 40 1- 20 1- 0 -2 . 25 Residual ( ?C) b ) median = -0 . 01 oc mean = 0 . 07 o c standard deviation "" 0 . 54 oc .... .rT ll _l _l j_ -1 . 50 -1 . 00 -0 . 50 0 0 . 50 1 . 00 1 . 50 Res idual (?C) 67 FIG . 4 . 3 Distribution of Residuals for Comparison of the Analytical Solution and the Numerical Finite Difference Method for Run no . 6 a) at the centre point , (r /a , x/h) of ( 0 . 0 , 0 . 0) b) at the point (r/a , x/h) of ( 2/3 , 2 /3) 68 Theoretically , in the heating phase , the analytical solution could give more accurate prediction than the numerical f inite difference method as it was based on the exact heat transfer for the uniform initial tem? peratures while the numerical finite difference was an approximate pre? diction . In the cooling phase , the temperature predicted by the numerical f inite difference method should be more accurate as the actual predicted temperatures at the end of the heating phase were used . In the analytical solution , the initial temperature of the can contents in the cooling phase was assumed to be uniformly equal to the retort temperature and this may result in inaccurate prediction , especially for a short heating time process . The time consumed by these two programs was found to be dependent on the number of points and the time increment required . Where only a few points are required in temperature prediction , the analytical solution method will take less time than the f inite difference method program . Where a large number of points are required , the f inite difference method will consume less time and should be used as it will be cheaper . 4 . 6 COMPARISON OF THE PREDICTED TEMPERATURES FROM THE ANALYTICAL SOLUTION PROGRAM AND THE EXPERIMENTAL TEMPERATURES The comparison of experimental temperatures and the analytical solution predicted temperatures was done on 4 points in the can for the processing conditions of runs no . 6 and no . 7 . The mean value of -2 2 - 1 the thermal dif fusivity o f 1 . 5353 x 10 m s was used for all the processing conditions . 4 . 6 . 1 Comparison of Temperatures in the Heating Phase As can be seen from Figures 4 . 4 and 4 . 5 , the calculated temper? atures were close to the measured temperatures in the heating phase . The temperature difference was in the range of 0 . 5- 1 . 0?C at the beginning where the temperature was lower than 100?C , then , it decreased to 0 . 2-0 . 5?C where the heating times were longer and temperatures were higher . - 1)0 u 0 '-' 120 Q) "" ;:l 1 10 -1-J 111 too "" Q) 0.. 90 s QJ e-. 80 70 bO ?0 40 0 10 20 ( a ) a t - 130 u 0 '-' 120 ? QJ "" 110 ;:l -1-J 111 100 "" QJ 0.. 90 s QJ e-. 80 60 50 ? 40 0 10 20 ( c ) a t FIG . 4 . 4 69 ,....._ 130 u ?...- 120 Q) "" 1 10 ;:l -1-J 111 100 "" Q) 0.. 90 s Q) e-. 80 ? 70 \ '\ \ 60 \ \ 50 \ 40 30 40 50 bO 70 80 90 100 0 10 20 30 40 50 60 70 80 90 100 Time (min) Time (min) r / a - 0 . 0 x /h .. 0 . 0 ( b ) a t r / a - 0 . 0 x/h - 1 / 3 , - 130 u 0 '-" 120 QJ "" 1 10 ;:l -1-J 111 100 "" ? QJ \ ?- 90 \ QJ \ e-. dO \ \ \ \ 70 \ \ 60 \ \ 50 \ \ 40 30 40 50 60 70 . 80 90 lOO o ? 10 20 30 40 so 60 70 80 90 lOO Time (min) Time (min) r / a = 1 / 3 , x / h = 1 / 3 (d ) a t r / a ;:; 0 . 0 x / h = 2 / 3 , Comparison of Experimental Temperatures and Predicted Temperatures from the Analytical Solution Computer Program for Run no . 6 (retort temperature was 1 29?C) ( ) experimental temperatures (---- ---) predicted temperatures 120 ,....._ u 1 10 0 ........ 100 QJ ,... ::1 90 +J CO ,... 80 QJ 0. E: 70 QJ H 60 120 ,....._ u 1 10 0 ........ 100 90 80 70 60 "" '7 :;." "' V f f f f 0 lO 20 30 40 ? 60 70 80 90 100 JIO Time (min) ( a ) a t r / a = 0 . 0 , x / h = 0 . 0 ? ? ? ? ? '\ '\ '\ ? '\ \ 0 10 20 30 40 ? 60 70 80 90 100 110 Time (uiin) ( c ) a t r / a = 1 / 3 , x / h = 1 / 3 120 ,....._ u 110 ? 100 QJ ,... ::1 90 +J CO ,... 80 QJ 0. E: 70 QJ H 60 50 40 120 ,....._ u 1 10 0 ........ lOO QJ ,... 90 ::1 +J CO ,... 80 QJ 0. 70 E: QJ H '0 50 40 70 '7 '7 V - 1 r '1 r; 'I r; '/ "/ 10 20 30 40 ? 60 70 80 90 100 110 Time (min) ( b ) a t r / a = 0 . 0 , x / h = 1 / 3 0 10 20 30 40 ? 60 70 80 90 lOO 110 Time (min) ( d ) a t r / a = 0 . 0 , x / h = 2 / 3 FIG . 4 . 5 Comparison of Experimental Temperatures and Predicted Temperatures from the Analytical Solution Computer Program for Run no . 7 (retort temperature was 1 20?C) (------- ) experimental temperatures (--- --- ) predicted temperatures 7 1 The larger difference at the beginning of heating could have resulted from the equations used . When time was small , the value of ? ( r , x , t) in equation ( 4 . 6 ) was zero . Therefore , the predicted temper? atures were equal to or nearly equal to the initial temperature . The deviation of the predicted temperatures from the experimental temper? atures could also have been caused by the errors in the thermocouples . These errors were firstly the inaccuracy of p lacing the thermocouple j unctions as only one millimetre could effect the temperature , and secondly the conduction through the thermocouple wires which could be high at the beginning of heating phase as the temperature difference between outside and the j unction is high . . This conduction also depended on the thermal diffusivity of the food . There?ore , the cal? culated temperatures could possib ly be more accurate than the experi? mental temperatures . The residual ( i . e . the experimental temperature - the predicted temperature) was calculated for the centre point and shown in Appendix 4 . 4 (a) for runs no . 6 , 7 , 8 and 9 . The distribution o f the residuals was the normal distribution . The residual mean varied from run to ? 0 - ? run , from - 1 . 1 to 0 . 4 C , with the residual s tandard deviation from + 0 . 4 to + 0 . 8?C . This s tandard deviation was less than the 1 . 7?C found by Lenz ( 19 7 7 ) which was described as resulting from the biolog? ical variability of the physical constants . 4 . 6 . 2 Comparison of Temperatures in the Cooling Phase An irregular phenomenon was found in the cooling phase (Figures 4 . 4 and 4 . 5 ) . 0 The temperature rapidly decreased to 100 + 5 C and sometimes held there for 1-2 minutes , then , gradually decreased again. This irregular cooling curve was also found by other workers (Powers et al , 1952 ; Board et al , 1960) Powers et al ( 1952) explained in their s tudy that the rapid cooling occurred because the home-type canning j ars used could vent during processing and a high vacuum could ensue , which , in turn , led to vigorous boiling during cooling when the headspace s team condensed causing rapid cooling of the contents . In 1949 Townsend et al in their comparative heat penetration s tudy in j ars and cans , found that the contents of j ars occasionally cooled faster than those of cans although the later heated faster . They attributed the rapid cooling to the contents being stirred by "boiling" . Board et al ( 1960) also found this rapid cooling phenomenon in cans . The cooling curves obtained when the retort pressure was reduced to 608 kPa or less during cooling showed fas ter cooling than that calculated for the conduction mechanism and also some of them showed irregular f luctua- tions in rate of cooling . They concluded that the mechanism of cooling appeared to depend on whether cooling was predominately by conduction or if it was accelerated by movement of the contents of the can . Cooling by conduction was found in mos t of the cans where they were cooled under 1620 kPa superimposed pressure . I t was also stated that in the more viscous produc ts , swch as baked beans , cream s tyle corn and solid meat , boiling with consequent movement of mater- ials in the can was probably the main cause of non-conductive cooling . 72 The phenomenon of boiling of the can content when the pressure was released was also found by Hemler et al ( 1 952) . The residuals were calculated as in 4 . 5 . 1 , the residual dis tribution is shown in Appendix 4 . 4 (b ) for experimental runs no . 6 , 7 , 8 , and 9 . The residual mean and the residual s tandard deviation were calculated by assuming that the residual d is tribution was a normal distribution . The residual mean varied from -0 . 9 to -3 . 3?C - with the standard deviation varying from ? 2 . 2 to ? 4 . 5?C . The residual medians were -0 . 6 t o -2 . 7?C . This 0 indicated that the predicted temperatures were 0 . 9 to 3 . 3 C higher than the experimental temperatures . The residual s tandard deviation found was higher than those s tated by Lenz ( 19 7 7 ) and could not be treated as the reault of the biological variability of the physical constants . Thes? higher values were due to the irregular cooling curve found in the present experiments . Experiments were performed with different materials in the can , namely , water , s tarch solution at the same concentration as in the baby food (4 . 2%) , vegetable puree and the homogenised baby food . The other materials were filled into the cans withcut any headspace as before . The baby food was filled into the cans with different head? spaces - 0 , 0 . 6 , 1 . 3 .and 1 . 9 cm . The heat penetration curves and the cooling curves are shown in Figure 4 . 6 . In the can of water , con? vective heat transfer occurred in both heating and cooling . S tarch solution also showed a similar heating and cooling pattern except that it was s lower in heating and had a break point in the cooling curve at the temperature of 60?C which could be explained by the change in \ - ou '-' QJ 1-< ;:l +-1 ? 1-< QJ 0... s QJ H 7 3 - Ill - IH u 120 u 0 120 '-' ? QJ 110 1 10 1-< QJ 1-< ;:l 100 ;:l lOO +-1 ? +-1 ? 1-< 1-< QJ 90 90 0... QJ s 0... QJ 10 s ao H QJ H 70 70 60 60 la la 40 40 30 30 10 20 lO 40 lO 60 70 80 90 100 0 10 20 30 40 lO 60 70 10 90 lOO 1 10 Time (min) Time (min) ( a ) ( b ) 125 120 uo - 110 u ? 0 110 ........ lOO QJ 100 1-< \? ;:l "? 90 +-1 90 ??:; ? 1-< ??'\ 10 QJ 10 ?;? 0... \?t\ s t? 70 QJ 70 H \'\? ,, 60 60 \? \? la - la 40 40 30 30 ? io 2? 30 40 50 60 70 80 90 100 1 10 120 0 10 20 30 40 50 60 70 80 90 100 1 10 Time (min) Time (min) ( c ) (d ) FIG . 4 . 6 Heat Penetration Curves for Different Can Contents and Different Head spaces (a) for water in a can without any headspace , (b) for s tarch solution in a can without any headspace , ( c) for vegetable puree in a can without any headspace , (d) for baby food in a can with , (_ ) no head space (-_ -) 0 . 6 cm head space (-_ - -) 1 . 3 cm headspace (- - - - -) 1 . 9 cm headspace . ------------------------------------ the state of the starch paste . For puree and baby food with no head? space , similar heating and cooling patterns were found as before ( in section 4 . 5 ) , with the irregular cooling curve phenomenon . With different headspaces , the irregular cooling curve s till occurred . 74 From the results obtained , the irregular cooling curve might be caused by boiling and s team condensation in the can . When the pressure was released , boiling could have occurred and the temperature in the can would have decreased rapidly because of loss of latent heat due to evaporation of water . When the pressure in the can was reduced to the atmospheric pressure and the temperature was lower than 105?C , boiling s topped , s team in the can condensed giving the latent heat to the system and the temperature was held there for 1-2 min , and then the can contents were further cooling by the conduction heat transfer . This phenomenon created two parts in the cooling phase involving two different thermal dif fusivities . Therefore , in the cooling phase , the assumption of constant thermal diffusivity was invalid . It might be possible to follow this irregular cooling curve by using the numerical f inite difference method . However , it would be very complicated as the thermal diffusivity cannot be assumed cons tant . Further experimental investigation was needed in estimating the extent of boiling and the change in thermal diffusivity where A and C had to be determined separately . But there was no equipment available for measuring the A and C , therefore , it was not possible to use this method to follow the irregular cooling curve in this s tudy . However , the predicted temperatures from the analytical solution program and the numerical f inite difference method program were identical ( in section 4 . 5 ) so it was considered valid to modify the analytical sol? ution program so that the cooling curve of the predicted temperatures fitted the cooling curve of the experimental temperatures . 4 . 6 . 3 Comparison of Temperatures in the Overall Process The residual dis tribution , the residual mean and the residual standard deviation were also calculated for the overall process . The same method as described in section 4 . 5 was used . The residual distribution is shown in Appendix 4 . 4 ( c) for run no . 6 , S , 7 and 9 . The residual means for the overall process varied from -0 . 4 to - 1 . 2 ?C with s tandard deviation varying from + 2 . 5 to + 3 . 4 ?C . As the s tandard deviation found in the heating phase described in section 4 . 6 . 1 was fairly small , this high standard deviation was mainly due 7 5 to the high deviation between the predicted temperatures and the experi? mental temperatures in the cooling phase described in section 4 . 6 . 2 as a result of the irregular cooling phenomenon . Therefore the analytical solution program could be used for the heating phase but had to be modified for the cooling phase . 4 . 7 MODIFICATION OF THE ANALYTICAL SOLUTION PROGRAM The two parts of the cooling phase were referred to as the "beginning of the cooling stage" and the " later cooling s tage" , where the beginning of the cooling stage was defined as a s tage s tarting from the time when cooling water was turned on to the time when the 0 temperature reached 105 C and then the later cooling stage s tarted at 105?C and continued to the end of cooling phase . This is shown in Figure 4 . 7 . 4 . 7 . 1 The Beginning of the Cooling Stage As higher thermal diffusivity used in the cooling phase would result in lower predicted temperatures , the thermal d i f fusivities of -7 -7 -7 -7 2 - 1 1 . 5353 x 10 , 2 . 0 x 1 0 , 2 . 2 x 1 0 , 2 . 5 x 1 0 m s were used in the analytical solution . The predicted temperatures were compared with the experimental temperatures for five different experimental runs . 7 6 1 20 ,-.... u 1 10 0 ..._, Q) H ;:I 100 .jJ ell H Q) s-Q) 90 E:-l 80 Begin- k? ning of . 1 I the I cooling 1 stage 1 70 60 ? Later cooling s tage 50 0 10 20 30 4 0 50 60 70 80 90 Time (min) FIG . 4 . 7 Diagram Showing Different Parts in Heat Processing 7 7 -7 2 - 1 The thermal diffusivity o f 2 . 2 x 10 m s was found t o give the best approximation at the centre and at (r/a, x/h) of ( 0 , 1 / 3 ) and ( 1 / 3 , 1 /3) . The variances of the predicted temperatures at the centre , using various thermal -7 2 . 2 x 10 , and 2 . 5 x -7 -7 diffusivities of 1 . 5353 x 10 , 2 . 0 x 10 , -7 2 - 1 10 m s , from the experimental temperatures were determined using 1 . 2 minute intervals . The plot of variance versus thermal diffusivity is shown in Figure 4 . 8 . The thermal diffusivi ty Of 2 . 2 X 10 -7 m2s- 1 f d ? ? i i Th thi was oun to g1ve m1n mum var ance . us , s thermal diffusivity would give the best approximation of temperature at the centre of the can . that lower area . ??ere r/a was more than 1 / 3 and x/h was more than 1 / 3 , it was found thermal diffusivity of 2 . 2 x 10-7 m2s- 1 could not be applied . The -7 2 - 1 value o f 1 . 5353 x 1 0 m s gave a better approximation in this The temperatures at (r/a , x/h) of (0 , 0 ) , ( 1 /9 , 0) and ( 2/9 , 0 ) were measured experimentally to determine the extent of r where x was equal to 0 at which the thermal diffusivity of 2 . 2 x 1 0-7m2s- 1 could be used . The experimental temperatures were compared with the predicted temperatures calculated with thermal diffusivities of 2 . 2 x 10-7 and 1 . 5353 x 10-7 m2s- 1 It was found that neither of these thermal dif fusivities gave well fitted predic ted temperatures at ( 1 /9 , 0 . 0 ) , and ( 2 /9 , 0 . 0) points . The higher thermal diffusivity of 2 . 2 x 10-7 m2s- 1 was found to result in the lower predicted temperatures while the lower th 1 diff ? ? of 1 . 5353 x 10-7 m2s- 1 hi h d . t d t erma us1v?ty gave g er pre 1c e emper- atures than the experimental temperatures . Therefore , the thermal -7 2 - 1 diffusivity o f 2 . 2 x 1 0 m s should be used to prevent an overestimation of microbiological lethality factor . -7 2 - 1 In conclusion , the thermal diffusivity o f 2 . 2 x 1 0 m s was used for temperature calculation of all points in the centre area where r/a and x/h were less than or equal to 1 / 3 . Where r/a and x/h were more -7 2 - 1 than t / 3 , the thermal difffusivity o f 1 . 5 353 x 1 0 m s was used . 35 30 ;--.. N u 0 '-" Q) () 25 s:: cu ?r-1 1-l cu ::> 20 15 10 5 0 - 7 l . OxlO \ \ \ - 7 1 . 5xl0 \ \ - 7 2 . 0x10 -- ??1 -7 2 . 5xl0 Thermal diffus ivity (m2 s-1) FIG . 4 . 8 Variance versus Thermal Diffusivity , (0 0) run no . 6 (G-----?1 ) run no . 7 (o c ) run no . 8 (G- --c) run no . 9 78 79 4 . 7 . 2 The Later Cooling Stage 0 When the temperature of the food reached 100 ? 5 C , the temperature was found to decrease much more slowly . Thus , the computer model had to be further modified by setting the temperature at which the smaller thermal diffusivity would be used . Again the thermal diffusivity in thi.s stage and the significant temperature for the beginning of this s tage were determined by trial and error . It was found that the temper- a -7 ature should be set at 105 C with a thermal dif fusivity of 1 . 32 x 10 2 -1 m s Therefore , the computer program was constructed for the early 1 . i h h 1 diff ? of 2 . 2 x 10-7 m2s- 1 for coo 1ng s tage us ng t e t erma usiv1ty the centre area of r ? a/3 and x ? h/3 , the thermal diffusivity of -7 2 - 1 1 . 5353 x 1 0 m s for the outside area where r/a > 1 / 3 and x/h > 1 /3 and in the later cooling s tage the. thermal diffusivity was set at -7 2 - 1 1 . 32 x 1 0 m s , for every point in the can where the temperature was lower than 105?C . In the centre area , where the thermal diffusivity used in the calculation was changed from 2 . 2 x 10-7 m2s- 1 in the beginning of the cooling to 1 . 32 x 10-7 m2s- l in the later s tages , it was found that the calculated temperatures using 1 . 32 x 10-7 m2s- 1 for the first few minutes were higher than the earlier predicted temperatures causing f luctuation in the cooling curve and deviation from the experimental temperatures . Therefore , further modification of the computer model was required . However , in the outside region where the thermal . -7 2 - 1 - 7 2 - 1 diffusivity changed from 1 . 5353 x 10 m s to 1 . 32 x 1 0 m s , the results obtained were reasonable and modification was not necessary . The computer model was further modified for the centre area by assuming that the temperature at every point in this area at the beginning of the later cooling s tage were uniform and equal to the set 0 temperature of 105 C . The heat transfer equations applied in this later cooling stage were simulated from the heating phase , TA and TI in equa tion ( 4 . 6 ) were substituted by TC and TLIMIT giving : T = YCOOL (TLIMIT - TC) + TC (4 . 1 7 ) where YCOOL is (YC) (YL) 0 TLIMIT is a set temperature which was 105 C in this s tudy TC is a cooling water temperature . This equation was used to predict the temperatures in the later cooling s tage for all points in the centre area where r/a was less than or equal to 1 / 3 and x/h was less than or equal to 1 / 3 with the -7 2 - 1 thermal diffusivity of 1 . 32 x 1 0 m s 4 . 7 . 3 Conclusion 80 A modified computer program was cons tructed providing the oppor? tunity to use any three thermal dif fusivities in each part of processing and to vary the can size , the time and distance increment , the processing temperature and processing time , the set temperature . The temperature distribution in the can in the heating phase was 7 2 - 1 calculated by the following equations , using "a" o f 1 . 5353 x 10- m s For the heating phase , where at/a2 was less than 0 . 02 and r/a was not less than 0 . 1 : YC 1- (ao o .. 5 5 erfc ( z) + (a-r) (ata) 0 . 5 ierfc ( z) + 4 1 . 5 r ar (9a2 - 7r2 - 2ar)at 2 ) i erfc ( z) 32a l . 5 r2 ? 5 where r/a was less than 0 . 1 : YC = 0 . 0 (a) (b) / where 2 at/h was less than 0 . 3 : YL 1- (E_ (- 1 ) nerf c ( ( 2n+1 ) h-x) + E_ n-0 2 (at) 0 . 5 n-0 (- 1 ) nerf c ( ( 2n+1 ) h+x) ) 2 (at) 0 ' 5 YC = 2 where at/a was more than 0 . 02 : J ( 8 r/a) w o n 2nz..= 1 8 J ( 8 ) n 1 n e 2 (-8 at/a ) n 2 where at/h was more than 0 . 3 : 4 , T H C 5 0 , 5 0 ) , 0 C 1 0 ) , X J I B C 1 0 ) , 8 R A C 1 0 ) ; X J O B C 1 0 ) 0 0 0 0 0 1 0 0 - -2 0 0 C 0 1- H-1 0 iJ X J U ( 2 0 0 ) ' A R G ( 2 0 0 ) _ _ _ _ __ 0 0 0 0 0 2 0 0 3 U o D A T A A R G / o , o , o . t , o . 2 , 0 ? J ? 0 . 4 , 0 , S , Q , 6 , Q ? 7 ' 0 ' 8 ' 0 ? 9 ' 1 ? 0 ' 0 0 0 0 0 3 0 0 4 0 0 * 1 e l 1 l e 2 , 1 . 3 1 1 t 4 1 1 e S , l e 6 , l , ? , l . M , 1 . 9 , 2 e O , 0 0 0 0 0 4 0 0 5 0 0 * 2 e l 1 2 a 2 1 2 e 3 1 2 a 4 1 2 a 5 1 2 1 6 1 2 e 7 1 2 a R I 2 a 9 # 3 e 0 1 3 a l # 3 a 2 1 3 t 3 1 3 e 4 1 3 t 5 ' 0 0 0 0 0 5 00 ___{;) o_o _ __ _ ---* _ J ? 6 , 3 ? 7 , 3 ? a , 3 ? 9 , 4 ? o , 4 ? 1 , 54 _. 2 , 4 ? 3 , 4 ? 4 , L s , 4 ? ..6.L L .J L 4 _._fiL LL. ? ..? ? ? o _, ___ ___ _ ?-- __ _ _ _ _ _ o o o o o 6 o o 7 0 0 * 5 a l # S a 2 ' 5 ? 3 ' 5 ? 4 ' 5 ? 5 , 5 e o , . 7 , s . 6 , 5 t 9 ; 6 , 0 , 6 . 1 , 6 ? 2 , 6 ? 3 ; 6 , 4 , 6 a 5 ' 0 0 0 0 0 70 0 8 0 0 * 6 a 6 1 6 a 7 ' 6 ? 8 ' 6 ? 9 , 7 a 0 , 7 a 1 , 7 ? 2 , 7 e 3 , 7 t 4 , 7 e 5 , 7 e 6 ; 7 a 7 , 7 ? 8 , 7 e 9 , e . o , O O O O O b O O 9 0 0 * 8 a l , B a 2 ' 8 ' 3 ' 8 ? 4 ' 8 ? 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DJ.ll...a_ 0 L()_.Jl.LQ , a I ___ _ ___ _ __ Q 1H> 0 1 4 Q u_ 1 5 0 0 D A T A X J O / l a 0 1 0 t 9 9 7 5 , 0 a 9 Y 0 0 , 0 ? 9 7 7 6 , 0 a 9 6 0 4 , 0 e 9 3 8 5 , 0 ? 9 1 2 0 , 0 0 0 0 1 5 0 0 1 6 0 0 * O t 8 8 1 2 1 0 t 8 4 6 J , O . R 0 7 ? , 0 ? 7 6 5 2 , 0 ? 7 1 9 6 , 0 e 6 7 1 1 , 0 t 6 2 0 1 1 0 e 5 6 6 9 , 0 0 0 0 1 6 0 0 1 7 0 0 * O t 5 1 1 U , O e 4 5 5 4 , Q , 3 9 d O , O o 3 4 0 0 , 0 a 2 8 1 8 , 0 t 2 2 3 ? , Q , l 6 6 6 , 0 e 1 1 0 4 ' 0 0 0 0 1 7 0 0 1 -8 0 0 * O t 0 5 5 3 -, 0 t 0 0 2?:>? - 0 e 0 4 8 4 , .. 0 , 0 9 6 8 , ?0 e l 4 2 4 , ?0 -. -1 8-?0 , ? 0 e 2 2 4 3 , - - ? 0 0 0 0 1 8 0 0 9 0 0 * - o , 2 6 0 1 , ? U , 2 9 2 l , ? 0 . 3 2 0 2 , ? u , 3 4 4 3 , ? 0 , J 6 4 3 , ? Q , 3 8 0 1 , O O O O l Y O O 2 0 0 0 * ? o . J 9 1 8 , - u , 3 9 Y 2 , ? 0 . 4 0 2 6 , - u . 4 0 1 R , - o . 3 9 7 t , ? o . 3 B B 7 , o o o o 2 o o o 2 1 0 0 * ? O a 3 _ 7 6 6 , ? 0 , 3 6 1 0 , ? 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' 0 ? / 0 0 0 0 3 7 0 0 ---:Y&06 ---- -RE-A O ( ? ? I ) U C , 0 X ' 0 I f F h U HT -2 , 0 T ' S C 1 -5 )( # -l -l-, TA, T C, TIME & , C T H1E - - -- --- - --{)00-0 3 8 .00 - . 3 9 0 0 W R I T E ( 6 , 3 0 ) 0 I F F 1 , 0 I F F 2 , T I , T A , T C 0 0 0 0 3 9 0 0 4 0 0 0 W R I T E C 6 , 3 9 l Q C , 2 t O * n X , 1 1 S C , 1 / S X 0 00 0 4 0 0 0 4 1 0 0 3 0 F O R M A T C 1 H O , ' T H E N M A L D l f F U S I V I T Y I N H E A T I N G P H A S ? ( M M / S l = " ' 0 0 0 0 4 1 00 --4-2-0o - - -- -- -* - - F 1 2 ? l 0 ' l l , " T H E f< M AL --O l f F U S I V I H '-l N ?.fH3-t?-s?t4-/-s -} ::.J.t, ___ -- - -- -- - -G-0004200 4 3 0 0 * F 1 2 . 1 0 , / / , " I III I T I A L T U? P f. R A T l i R E < C > = " , F 1 2 e 2 , / / 0 0 0 0 4 3 0 0 4 4 0 0 * " R E T O R T T E M P E R A T U R E < c > = ' , f l ? ? 2 , / / 0 0 0 0 4 4 0 0 ; 4 5 0 o * " C O O L I N G T E M P E R A T U R l ( C ) : " , F 1 2 ? 2 , / / ) 0 0 0 0 4 5 0 0 g '-' (") 0 1.? c: rt ro ., 1-d ., 0 )Q ., ? ..... 00 N -46 0 0 4 7 0 0 4 8 0 0 4 9 0 0 -S-OO o 5 0 ? 0 5 1 0 0 5 2 0 0 ---5.3..0 0 5 4 0 0 5 5 0 0 5 6 0 0 --5-1 D o - -- 3 9 * * * .. * * FO-R ?I AH " C A N R A [J I U S C M ) = ?? , f t 2 . 5 , ./ - ------- -- - - ---? -- -- --" C A N H E I G H T C ? ) : " , F l 2 ! 5 , / " S I Z E O F O I M E h S I O N L [ ? S S P A C E I N C R E ? E N T I N R D I R E C T I O N = " ' F 1 2 t 5 1 / -'-'- .S I Z [ l+f" .() I ME N S I UN L l ? S S P A C f I -N C H E M E N :r -I U-.X -O I Rt C T -I ON = " 4 F 1 2 t ! H / / / " T E ? P E R A T U R E D J S T R I ? U T I O N I N A C A N " / / / ) THI E = u N-N ?:: ( T I M ? S + .C T I M[ ) I D T D O 4 2 N = l , N N . T I ME = T I M E + D T f" O C ? O I F F 1 * T I M E I O C / D C FO X = D i f F 1 ? T I M E I O X / D X 5 8 0 0 D O 5 8 I = l , S X + l s-9 o o?- - -- - - -o-r x = r L o A T ' r ? t > t s x 6 0 0 0 I F C F O X ? l T a O e O J ) G O T O l l u 6 1 0 0 C A LL 5 L A B ( F O X , V L , b J X ) _ __ 6 2 0 0 G O TO 80 6 3 0 0 1 1 0 X l ? O I X * O X 6 4 0 0 C A L L L S L A B ( F Q X , Y L , D X , X L ) 6 5 0 o s o n o s ? J = l , s c + t 6 6 0 0 ?JC = F L O A T ( J ? l > I S C 0700 - - - - l f ( F OC a L T ? 0 ? 0 2 ) G (J T i.J 1 2 0 6 8 0 0 O D 4 9 J J = l 1 6 o u o o 4 6 o o 0 0 0 0 4 7 0 0 0 0 0 0 4 b O O I 0 0 0 0 4 9 0 0 0 0 0 0 5 0 0 0 0 0 0 0 5 0 5 0 0 0 0 0 5 1 0 0 0 0 0 0 5 ? 0 0 _o u .o o 5 J o o 0 0 0 0 5 4 0 0 0 0 0 0 5 ? 0 0 0 0 0 0 5 6 0 0 _Q .(J 0 0 5 7 0 0 0 0 0 U 5 B O O 0 0 0 0 5 9 0 0 0 0 0 0 6 0 0 0 I O u 0 0 6 l O O 0 0 0 0 6 2 0 0 o u o o 6 J o o O O O U 6 4 0 0 0 0 0 0 6 5 0 0 o o o o 6 o o o 6 9 0 0 4 9 B R A C J J ) : B ( J J ) ? D J C -ijQ O ____ _ __ ..CALL C Y U J D _( F O C , Y C 1 B , B R A , X J O B , X J I 13 2 u o G O T o 9 0 0 0 1 2 0 I f ( O I C ? L T ? O ? l > G O T u 1 0 0 {) 1) 0 0 6 7 0 0 0 0 0 0 6 b O O 0 0 0 0 6 9 0 0 -- ----- ? 8 8 8 t ? 8 8 0 0 0 0 7 2 0 0 0 0 0 0 7 J O O 0 0 0 0l 4 0 0 7 38 0 R =DC *U I C ? 4 0 H ? l' L 6 y L N 0 ( f 0 C_D c _ ! __Q c_ ?_ B __ L suo 0 0 76 0 0 1 0 0 Y C = l ? O 7 1 0 0 9 0 YHE A T = Y C * Y L J.aO.o _ _ J.u.i? l ) = C 1 ? Y H E A T > * C T A ? T 1 ) + T I 7 9 0 0 T F C T I ?E a L E e T I M E S l G O T o 2 0 0 8 0 0 0 T D E L = T I ? E - T I H E S 8 1 0 0 C F O C = u i F F 2 ? T D E L / O C / u C --$2 g .o ----- - --C-F -O-)( ::..o I F f 2 * T rH .. L I D X I U X 8 3 0 - C I X = O I X 8 4 0 0 I F C C FO X e L T e 0 . 0 3 ) G O T O 1 4 5 8 5 0 0 C A L L S L A B C C F O X , C Y L , C I X ) -8..6.0 0 -- -- - - GCl -1' 0 -1 5 5 8 7 0 0 1 4 5 C X L =C I X * O X 8 8 0 0 C A L L L S L A ? C C f U X , C Y L , D X , ? X L ) 8 9 0 0 1 5 5 C I C = O I C 9 0 0 0-- - -l-F?C C.. F.u.C _. L T .. 0 ? .0 2 > G 0 !..!l ...J. .6 5 01l"UUT5UU 0 0 0 0 7.6 0 0 o o o o 7 7 o o - - -- ----? - --- - ---- ---?- -------- _.?l 0 0 0 7 6 0 0 0 0 0 0 7 9 0 0 o o o o a o o o 0 0 0 0 8 1 0 0 !) {) .0 .0 8 2 0 0 I 0 0 0 0 8 J O O 0 0 0 0 8 4 0 0 ' 0 0 0 0 8 ::> 0 0 I -- ...0 0 0 0 8 6 0 0 0 0 0 0 8 7 0 0 0 0 0 0 8 tl O O 0 0 0 0 8 9 0 0 0 .0 0 0 9 0 0 0 ? (X) w 9 1 0 0 D O 5 5 J J = 1 , 6 9 2 0 0 5 5 B R A C J J ) = tl ( J J ) * C I C 9 3 0 0 C A L L C Y l t?J 0 C C f u C , C Y C , B , !:J f< A , X J 0 8 , X J I 8 ) - 9 4 0 0 G O T O 1 7 5 9 5 0 0 1 6 5 l f ( C I C ? L T e O e l l G n T O l U ? 9 6 0 0 C R = D C * C I C 9 7 0 0 C A L L L C Y L N O ( C F O c , c y c , u c , C H ) -9?0o - - ?n r o 1 7 5 9 9 0 0 1 8 5 C Y C ? 1 . 0 1 0 0 0 0 1 7 5 Y C OO L =C Y C * ? Y L 1 0 1 0 0 T C J , I > =T H C J , I ) + ( T C -T A > ? < l - Y C O O L l ? ? 2 0 0 G O T O S6 1 1 0 3 0 0 2 0 0 T C J , I > = T H C J , I ) 0 4 0 0 S A C O N T I NUE 1 0 5 0 0 11 R I T E C o , 5 9 > T I M f _ l .O 6 0 0 5 9 f. U n 1>1 A T C / I " T I "1 E C S ) = " , F 1 2 ? 2 , I I __ _ _ . _____ __ . ____ ??- _ _ 1 0 70 0 * " X O I R E C T ! Il N A C R U S S , .!i O I R E C T I U N , D O ri N " / / ) 1 0 8 0 0 D O 6 0 J c 1 , S C + 1 . 1 0 9 0 0 6 0 ? n i T E C ? , 7 9 l C T C J , J > , J = l , ? X + 1 ) . 1 1 0 0 0 7 9 f O R M A T C 1 2 F 1 0 e 2 ) 1 1 1 0 0 4 2 C O N T I N ? E 1 1 2 0 o S T 1 1 P 1 1 3 0 0 ? N O _1 1 4 0 0 _ _ .S U BR O U T I NE C Y L IJ O C F u , y c , H , B H A , X J 013 , X J I 8 ) ___ _ 1 1 5 0 o O I ME N S I O II: t H 1 0 l , X J I B C 1 0 ) , 8 ,? A C 1 0 ) , X J 0 8 ( 1 0 ) 1 1 6 0 0 C O M M O N X J 0 ( ? 0 0 l , A R G C 2 0 0 ) 1 1 7 0 0 D O 1 I =l ' 6 . ltBOo .............I F.: CBtiU b.b.T ..e Uu l H l.GlJ T li 3 ?2 1900 -- 0 - 2.-J.a..1L152 - --- --1 2 0 0 0 l f C BR A C I ) ? A R G C J ) ) 5 , 4 1 2 , 2 1 0 0 2 C O N T I NU E l 2 2 0 0 4 X J O B C I ) ? X JO ( J ) ?*O ?- - - - ---- G O - --1'0 - -t 1 2 4 0 0 5 I r c J . G T a l > J = J ? l 1 2 5 0 0 X J O B C i l = X J O ( J ) + ( X J O C J + l > - X J O ( J ) ) / C A R G C J + l ) ? A R G ( J ) ) * 1 2 6 0 0 * C U R A ( I l ? A R G C J ) ) .1.2 1 0 0 - ...1.1 0 l O .l -- --- ---- - --------?--- ? - - ? - - , 1 2 8 0 0 3 X J O B C I > = < 0 ? 7 9 7 Y / H R A C 1 ) ) * * 0 ? 5 * ( C O S C U R A ( l ) ? 0 ? 7 8 5 4 ) + 0 ? 1 2 5 / 1 2 9 0 0 * BR A C I ) ? S I N ( H R A C I ) ? O e 7 8 5 4 ) l 1 3 0 0 0 1 C O N T I N U E -1 ? 1 0 0 - - ? C -= O 1 3 2 0 0 u o 6 1 = 1 , 6 1 3 3 0 0 6 Y C = Y C + 2 e O * X J O B C I ) / H C l ) / X J I 8 C I ) * E X P C ? B C 1 ) * * 2 * F O ) 1 3 4 0 0 R E T U R N ? ? 5 0 0 ? N O --- --- ----- ?- U U O O 'J l O O 0 0 0 0 9 2 0 0 0 0 0 0 9 3 0 0 0 0 0 0 9 4 0 0 0 0 0 0 9 5 0 0 ! 0 0 0 0 9 6 0 0 0 0 0 0 9 7 0 0 -0 0 0 0 9 ti O 0 0 0 0 0 9 9 0 0 0 0 0 1 00 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 2 0 0 0 0 0 1 0 3 0 () 1 0 0 0 1 0 4 0 0 0 0 0 1 0 5 0 0 0 0 0 1 8 6 0 0 0 0 0 1 7 0 0 0 0 0 1 0 ti O O 0 0 0 1 0 9 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 1 2 0 0 I O U 0 1 1 J O O 0 0 0 1 1 4 0 0 I 0 0 0 1 1 5 0 0 0 0 0 1 1 6 0 0 0 0 0 1 1 7 0 0 . . D..O .QJ J 8J) () ' QUO 1 1.iOJL 0 0 0 1 20 0 0 0 00 1 2 1 0 0 0 0 0 1 2 2 0 0 --0?-0 -1 2 3 0 0 0 0 0 1 2 4 0 0 0 0 0 1 2 5 0 0 0 0 0 1 2 6 0 0 0 0 0 1 2 7 0 .0 .. 0 0 0 1 2 d 0 0 0 0 0 1 2 9 0 0 0 0 0 1 3 0 0 0 _Q .Q.O l 3 1 0 0 0 0 0 1 3 2 0 0 0 0 0 1 3 3 0 0 0 0 0 1 3 4 0 0 .. 0 o.o 1 3 5 0 .0 ..... 00 .p. 1 3 6 0 0 S U B R O U T I N E S L A R < r o , y L , D J O O O l J b O O 1 3 7 0 0 Y L = 1 ? 2 7 3 2 3 9 5 * C C O S C 1 e 5 7 1 4 J * U > * E X P C ? F 0 * 2 ? 4 6 7 4 0 1 ) + 0 0 0 1 3 7 0 0 1 3 a o o ? c ? t > I J . ? ? c o s c 3 . o ? 1 . 5 7 1 4 3 ? u > ? E X P < ? Y . O ? F o ? r . 4 6 7 4 0 1 > + o o o 1 3 a o o -l-3-9 0 0 * C + 1 ) / 5 ? u * C 0 S C 5 ? u ? 1 ? 5 7 1 4 3 * 0 hE X P < ? 2 5 ? 0 * F 0 ? 2 ? 4 6 7 4 0 U + --- --- - - - -- -? - 0 0 0 1 3 9 0 0 1 4 o o o * c ? t > l t . o ? c o s c 7 . o ? t ? 5 7 1 4 3 * U > ? E X P < ? 4 9 ? 0 ? F o ? 2 ? 4 6 7 4 0 l > + o o o 1 4 o o o 1 4 1 0 0 * ( + 1 ) / 9 , 0 * C O S ( 9 , 0 * 1 e 5 7 1 4 3 * D ) * [ X P C ? 8 1 ? 0 * F 0 ? 2 ? 4 6 7 4 0 1 ) + 0 0 0 1 4 1 0 0 1 4 2 0 0 * C ? t ) / l l . O * C U S ( 1 1 ? 0 * 1 ? 5 7 1 4 3 * D > ? E X P < ? 1 2 1 ? 0 ? F D * 2 ? 4 6 7 4 0 1 ) ) 0 0 0 1 4 2 0 0 -4-4?0 --- ----- -R?TUR-N - -- - - - - - -- ----O Q0 1 4 l? 1 4 4 0 0 E N D 0 0 0 1 4 4 0 0 1 4 5 0 0 S U B R O U T I N E L C Y L NO C F O? Y C , U C , R > 0 0 0 1 4 5 0 0 1 4 6 0 0 X = C D C ?R ) I 2 ? 0 / C F O * D C * * 2 ? 0 > * * 0 e 5 0 0 0 1 4 0 0 0 -l-470 0 A -= E R FN < X > - - -----?---- - - - - -- -- - -? --- .0-00 1 4 7 0-0 1 4 8 0 0 E l = O , S 6 4 2 8 9 5 8 * E X P C ? X ? X > ? X * A 0 0 0 1 4 8 0 0 1 4 9 0 0 X 2 = X -+ x 0 0 0 1 4 Y O O I 1 5 o o o E 2 = 0 ? 2 ? * < A ? x 2 ? t.: q . ... o o o l 5 o o o j -t-5 1 0 0 - - - -? C = 1 ? ( ( D C lk ) * * 0 ? 5 ?* A + ( DC ?? h ( F G -a OC * -*h-0 )-*-*-?-?+..4/. ----- -- - -- ----- - 0 0 0 5 .1 .00 -- l 1 5 2 0 0 * O C I R * * l e 5 * E 1 + ( 9 * D C * * 2 ? 0 ? 7 , 0 * R * * 2 t 0 ? 2 ? 0 ? U C * R ) / 0 0 0 1 5 2 0 0 1 1 5 3 0 0 * C 3 2 e 0 * D C * * 1 ? 5* R * * 2 ? 5 > ? F D * U C * * 2 ? 0 ? E 2 ) 0 0 0 1 5 3 0 0 1 5 4 0 0 R E T U FHJ 0 0 0 1 5 4 0 0 ' -t 5 5 0 0 E N 0 -- - ? - ?- - 0 0 0 1 5 5 0 0 1 5 6 0 0 S U O R O L J T I N E L S L A A C F o , y L , U X , X L ) 0 0 0 1 5 6 0 0 1 5 7 0 0 Y L = l ; O 0 0 0 1 5 7 0 0 1 5 8 0 o x r o = C r u ? o x ? ? 2 ? o > ? ? o . 5 o o o l S b O O ' -1- 5 9 0 o --- - - -ao -1 o 2 += 1 , 3 --- -- - ----- -- ---- ----- - !l ? oJ 5 9?o , 1 6 0 0 0 N = I ? 1 0 0 0 1 6 0 0 0 Ulli O Y t a ( ( 2 * N + 1 ) * D X ? 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OOL I N G P HA S E < M M I S > = " , f 1 2 t 1 0 , / / 0 0 0 0 0 9 0 0 1 0 8 0 * " I N I T I A L T E M P E R A T U R E C C z ? , f 1 2 ? 2 , / / 0 0 0 0 1 00 0 1 0 * " R E T O R T T E M P E R A T ? R E C c > : " , f 1 2 ? 2 , / / 0 0 0 0 1 1 0 0 1200 -- --*- " COuli NG T? t4P?.R-A T UR E ! C ) = " , E 1 2 ? 2 .# // ) --? -- - __ - __ _ __ _ --? - ? .0 00 0 1 ? 0 0 1 3 0 0 D E L X = u X I F L 0 A T ( 14 M . 1 ) 0 0 0 0 1 3 0 0 I 1 4 0 0 O E L R = o R / F L O A T t N N ? l ) O U 0 0 1 4 0 0 1 5 0 0 W R I T E C 6 , 2 l O R , D X * 2 ' D E L R , U E L X 0 0 0 0 1 ? 0 0 _l.6.QIJ.. __ .2 _ __[ DR tU l .t !.' ___ _ J:.A I? R.AlJ I U S .C M >_ ; " .L f 1 2 ? S ..e_/ /_: - -- - __ ____ ___ ___ ____ ?- -- _ __ _ D .U O 0 1 6 0 0 1 70 0 * " C A N H E I G H T C M ) ? " , f 1 2 t J , / / 0 0 0 0 1 7 0 0 1 8 0 0 * " S I Z l O F D I ? E N S I O N L E S S S P A C E I N C R E M E N T I N R D I R E C T I O N = " ' 0 0 0 0 1 8 0 0 1 9 0 0 * F 1 2 ? 5 , / / ? D 0 0 0 1 Y O O -1-9 ?0------- - ? ? __n __ __ _ S I Z- E ur O H 1E N S I ON L l b S S P A C f I NCREME-NT I -N X - o-I-R-E-c T H lN = " ' Q u 0 0 1 Y 5 u 2 u o o ? r t 2 ? 5 , / / / / o u o o 2 o o u 2 1 0 0 * " T E ? P E R A T U R E U I S T R I B U T I O N I N A C A N " / / / ) 0 0 0 0 2 1 0 0 2 2 0 0 P R ? f R E Q / D l L T A 0 0 0 0 2 2 0 0 it 88 6?11Y o=? ? ?-MM? 1 -- - ---- -- - - ---- _ .. __ _ _ -%? 8 ? l ? ' 2 5 0 0 D O 1 0 N = l ' N N ? l 0 0 0 0 2 5 0 0 ? ?90 0 1 0 ? I ( M , N ) tt T I N g o o 0 2 6 0 0 N QO 0 2Q tt& 1, M?-- - OOOU4-0 2 8 0 0 T I C M I N N > = T A ii 0 0 0 0 2 6 0 0 2 9 0 0 20 T C M I N N ) c T A H 0 0 00 2 9 0 0 3 0 0 0 D O 3 0 N & 1 , N N 0 0 0 0 3 0 0 0 I 3HIO TICMMIN)?TAH - - --0-0003?0 1 3 2 0 0 3 0 T C MM I N ) & T A H 0 0 0 0 3 2 0 0 ? 3 3 0 0 L L tt O a O 0 0 0 0 3 3 0 0 3 4 0 0 C H A N G? = T I M E H / U E L T A 0 0 0 0 3 4 0 0 -3--5--eO ---BD _.. -G - --I-& 1 , ?-H A NG? - - - - ?-?-- --- ----- ?-- --- ------------ --- -- - - -- -O OO O l?OO 3 6 0 0 DO 50 N = 2 , N N ? l 0 0 0 0 3 6 0 0 3 7 0 0 D O 5 0 H == 2 , M f 1 ? 1 0 0 0 0 3 7 0 0 3 6 0 0 5 0 T Oi l N > = ( 0 1 r r 1 * C < T l 01 + 1 , N ) ? 2 * T I C M , N ) + T I 01? 1 , N ) > I C D E L X * * 2 ? 0 ) ) + 0 u 0 0 3 C) 0 0 ?? * UI Ff -1 -t 4 -( -l --I -4 ? N-+ 1 ? l t .( ? t- D * l-H ? .., #-!!! -W ? LR** 2?0-> . - ----- O?O-U .3 9.CW 4 0 0 0 * D J E f 1 / f L O A T C N ? 1 > ? < < T I M , N + 1 ) ? T l ( M , N ? 1 ) ) / ( 2 * D E L R ? ? 2 ? 0 ) ) ) * 0 E L T A + 0 0 00 4 0 00 I 4 1 0 0 * T C M I N ) 0 0 0 0 4 1 0 0 4 2 0 0 D O 6 0 N = 2 , N N ? 1 0 0 0 0 4 2 00 4--W-G -6-0 -T? -< -l- # -N- J.a..<-G-1-F-f 1 * ( (-2- ? l-l < 2 ? ?? _) ?-? :r 1-{ ?l? ,N-}-+/-U?-8( ...... -2-t-0-)-+ - - --- --- -- --- ---- --00004 30<> 4 4 0 0 * D l f f 1 ? C < T I C 1 , N + l ) ? 2 ? T I ( l ' l? ) + T I C 1 , N ? 1 ) > / 0 EL R * * 2 e 0 ) + 0 0 0 0 4 4 0 0 4 5 0 0 * O i r f t /r L O A T C N ? 1 ) * ( C T I C 1 , N + 1 ) ? T I ( 1 , N? 1 ) ) / ( 2 ? D E L R * * 2 ? 0 > > > ? D E L T A + 0 0 0 0 4 5 0 0 4 6 00 * T I ( l , N ) 0 0 0 0 4 6 0 0 ? "d ? H ::< ? N z ? t1 1-'? (") Ill ...... "%j 1-'? ::l 1-'? rt ('!) ? 1-'? Hl Hl ('!) t1 ('!) ::l (") ('!) ? ('!) rt ::r' 0 0.. . ? "d t1 0 )Q t1 ? ...... CXl (j\ ?- - - --{}0-7-0 -- -#-=-;? , t-? M ? l ---- ?- - ---- - -------- - - ? - - -- - ?- -?-- 4 8 0 0 7 0 T C M , 1 > = < D I F F 1 ? C C T l C M + 1 , 1 > ? 2 ?T I C M , 1 ) + T l C M ? 1 , 1 ) ) / 0 E L X * * 2 ? 0 ) + 2 ? 0 ? 4 9 8 0 * O l f F 1 ? ( ( 2 * T I C M , 2 > ? 2 ? T I < ? '> 1 ) ) / 0 E L R * * 2 ? 0 > > * D E L T A + T I C M , 1 ) 5 0 0 T C 1 , 1 l = C D i f F 1 * ( ( 2 * T I ( 2 , 1 ? 2 ? T I ( 1 , 1 ) ) / 0 E L X * * 2 ? 0 > + 2 ? 0 * 5100 * 0 I-ff-1-? .C ..?-2 -* T I C 1- -# 2 ) ?-2 i ...:r I--'1 , -1 -l l /-U .?--t.--Ri -* 2--t ?U-l ..) -*-D-?--t. TA+T I ( 1 , t -l--- 5 2 0 0 D O 8 0 N = 1 , N N ? l 5 3 0 0 O D 8 0 M = 1 , M t1 ? 1 5 4 0 0 8 0 T I C M , N ) = T C M , N l --55-0? _ _ U-M?-;U -t4??0.? L U- ?-- - - - --- -- -- -?--- 5 6 0 0 L l sL L + 1 5 7 0 0 I F C L L . L T ? P R ) G O T O 4 0 5 8 0 0 L L = O - -U0 00 4 1 o u O u 0 0 4 d O O 0 00 0 4 Y O O 0 0 0 0 5 0 0 0 -00-0 0 5 1 0 0 I 0 0 0 0 5 2 0 0 ' 0 0 0 0 5 3 0 0 o u o 0 5 4 0 0 , - _Q?_Q.05 5 .0 0 0 U 0 0 5 6 0 0 0 0 0 0 5 7 0 0 0 0 0 0 5 8 0 0 5 9 0 G W R I T E C 6 , 3 l T I M E 0 0 0 0 5 9 0 0 -trf.H11r 3 FORMA-H-I?/ " HEAT 1 Nu - t +ME.-\-5-7 ? 1'- ,-f-+2 ? 2 ' 11 - - - - --- - ---?00-{)?00 6 1 0 0 * " X O I H E C T I O N A C R O S S , R D I R E C T I ON D O W N " / / ) 0 0 0 0 6 1 0 0 6 2 0 0 0 0 9 0 N = l , N N 0 0 0 0 6 2 0 0 , 6 3 0 0 9 0 W R I T E < 6 , 4 ) C T I C M , N ) , l-1 = 1 , 1-i H > 0 U 0 0 6 3 0 0 o -4 0 0 -- -- - 4 f O R t?1 A T C 1 2f 1 0 , 2 ) - - - 0 0 0 0 6 4 0 0 6 5 0 0 4 0 C O N T I N U E O u 0 0 6 5 0 0 6 6 0 0 T I M E = O ? O 0 0 0 0 6 ? 0 0 6 7 0 0 L L = O ? O 0 0 0 0 6 7 0 0 ?0 C 11 A Nu-?-=4 -I M-?--C-1 it?-L?l--A - --- - - ?--? -- - -?{}.06?00- 6 9 0 0 00 5 M= l , M M 0 0 0 06 Y O O 7 0 0 0 T I C M , NN > = l A C 0 0 0 0 7 0 0 0 7 1 0 5 T C H, N N > = T A C 0 0 00 7 1 0 0 ???--------???????? . 00007200 3 0 0 I C M M , N > ? T A C 0 0 0 0 7 3 0 0 4 0 0 1 5 T C MM I N ) D T A C 0 0 0 0 7 4 0 0 ?5 0 0 D O l4 U I = 1 , C H A NG E O O O Ol7 5 0 0 -600 00 -SO?-ff-N*--1- 00-oQO 70 0 00 1 50 M ? 2 , M M ? t 0 0 0 0 7 7 0 0 7 8 0 0 1 5 0 T C M , N ) c ( O i f f 2 * C C T I C M + 1 , N ) ?2 ? T I C M , N ) + T I C M ? 1 , N ) ) / C O ?L X * * 2 ? 0 ) ) + 0 0 0 0 7 6 0 0 7 9 0 0 * D I F f 2 ? C C T I C M , N + 1 > ? 2 ? T I C M , N ) + T I C M , N? 1 ) ) / 0E L R * * 2 ? 0 ) + 0 U 0 0 7 9 0 0 . ? w 0 I r r-1-t F t. 0 A T 0 ? -- - H ? (-( T-ti m N +-t -) - T 1\M ' N- 1 --tt-t-t?*O Etit11rrz-nt1 ) ) * 0 F. l T Jt+--- -- - - - -- %<> 0 8 0 0 0 8 1 0 0 * T I C M , N > 0 0 0 0 8 1 0 0 8 2 0 0 D O 1 6 0 N = 2 , N N ? t 0 0 0 0 8 2 0 0 \ 8 3 0 o 1 6 0 T C 1 , N ) = C 0 I F F 2 * ( ( 2 * T I C 2 , 10 ? 2 *?( 1 , N ) ) I 0 E l X * * 2 ? 0 ) + 0 0 0 0 8 3 0 0 6 4 0 o * ------e-t f-f 2-*-< -t+i-HTtt+-1 -t--2-* l T< -1 _, tH + T ) > If> EL R * * z ? 0 ) + 0 0 0 0 8 4 0 0 850 0 * D l fF 2 / f L O A T C N? 1 ) * { ( i i C 1 , N + t ) - T I 1 , N? 1 ) ) / ( 2 ? D E L R ? * 2 ? 0 > > > ? D E L T A + 0 0 0 0 8 ? 0 0 I 86 0 0 * T I ( 1 , N ) 0 0 0 0 8 6 0 0 RI2? 1 ?A 0? r- ? r ?-) ? < t-i ? i-!-< t; 1t-H+i-r1 -}-?*+ f-t-M? t >. r 1 c ?1? t ,-t-H -toEt)(*. 2, o >. 2 ?"0-'* -- ---- - = 2 ? 8 ? _ _ F 2 ? C < 2 * T l ( M , 2 ) ? 2 ? T I C M , 1 ) ) / U E L R * * 2 ? 0 > > ? D E L T A + T I C M , 1 ) 0 0 0 0 8 9 0 U . 9 o o o t r t , t l = < o i r r 2 ? < < 2 * T I < 2 , t > ? 2 ?T I < t , t > > t o r L x ? ? 2 ? o > ? 2 ? 0 * _ o o o o 9 u o u I t? CXl "' 9 1 0 0 * D I F f 2 ? C C 2 ? T I C 1 , 2 > ? 2 * T i l l ' 1 ) ) / 0 E l R * * 2 ? 0 > > * D E L T A + T l l 1 , 1 ) 9200 DO 18??-1-----9 30 0 D O 1 8 0 M = i , M M ? 1 9 4 0 0 1 8 0 T l t M , N > = T C M , N ) ? 9 5 0 0 T I ME = T I M E + D E L T A 0 0 0 0 9 1 0 0 - - -?!12GO 0 00 0 9 3 0 0 0 0 0 0 9 4 0 0 --9-6-t)o- ?t:t--+ t - ---- - -- ------- ---- -- --------- O O O O Y 5 0 0 -ooo 0 9 6 0 0 o u o 0 9 7 0 0 9 7 0 o I F C L L . L l ? P R ) G U T O 1 4 0 9 8 0 0 L L = O 9 9 0 0 W R I T E { 6 , 1 3 > T I M E 1 0 0 u 0 13 F 0 R#A T -< -l --l -" - - -- -- -?ttOL --t? -I Ut-< S -)-::-n -,-F--1---r-..-2-H I - 1 0 1 0 0 * " X D I R E C T I ON A C R O S S ' R D l H E C 1 l ON D O W N " / / ) 1 0 2 0 0 D O 1 9 0 N = l , ? N ? l 8 8 - -- ----1 ? ? () e- M ? f l ? f , 4 ) ( T l 01 1 N ) , t? = 1 , M M l - - ----- - ---- - . - 1 0 5 0 0 S T O P 1 0 6 0 u E N D 0 0 0 0 9 (;) 0 0 0 0 0 0 9 9 0 0 -- - -- -- -----0 0 0 --l o o o u 0 0 0 1 0 1 0 0 0 0 0 1 0 2 0 0 0 0 0 1 0 3 0 0 - ? - o o .o 1 0 4 0 'J 1 0 1) 0 1 0 ? 0 0 O U 0 1 0 o O O ? CXl CXl APPENDIX 4 . 3 Thermal Diffusivi ty Determination Results Thermal Mean Thermal S tandard Retort (oC) Diffusivity Diffus ivity Run No . Temperature X 1 0 7 x2 1Q 1 7 Deviation x ? - 1 m-s m s 7 1 20 . 2 1 . 549 1 3 1 19 . 5 1 . 55 1 1 4 1 19 . 6 1 . 5090 1 . 5429 9 1 20 . 0 1 . 5459 2 1 19 . 8 1 . 5593 6 1 29 . 1 1 . 5305 1 1 28 . 7 1 . 49 16 8 1 28 . 6 1 . 5694 1 . 5277 5 1 29 . 2 1 . 5452 10 1 29 . 1 1 . 50 16 TOTAL MEAN .m2s- 1 1 . 5353 X 10 STANDARD DEVIATI?N 0 . 026 1 X 10 m2s- Tes t of Significant Difference Between Means x1 xz = 1 . 5429 s 1 0 . 0 196 1 . 5277 . s2 0 . 03 18 s ?4 (0 . 0 196) 2 + 4 (0 . 0 3 18) 2 8 = S . E t 0 . 02639 3 1 7 0 . 026393 1 7 ;fl + l 5 5 0 . 0 1 169 1 . 5429 - 1 . 5277 0 . 0 1 169 0. 9 102 m2s- 1 0 . 0 196 0 . 03 1 8 - 7 - 7 n 1 n2 10 5 5 189 7 Therefore , there is no significant difference betweeen these two means . 1 90 APPENDIX 4 . 4 Dis tribution of Residuals for Determining Accuracy of the Analytical Solution for Calculating Temperatures (a) In the Heating Phase 30 ,__ ,...... ? 20 1- :>. (.) s:: Q) ;::1 0" Q) ? ? 10 0 -2 30 ,...... ? '-" 20 :>. (.) s:: Q) ;::1 0" Q) ? ? 10 r- 1- 1- ? Run no . 6 median -0 . 50 ?C mean -0 . 45 ?C standard deviation = 0 . 80 ?C 1--- I - 1 0 1 2 Run no . 7 median mean standard deviation = 0 . 46 ?C .---- 1-- i-- ? r-- 1-- 0 Run no . 8 median 30 mean = .... standard deviation = 1- .....- f-- ,___ ,-- ? 1-- 1-- 0 0 . 6 1 ?C o ? 0 42 c . 0 . 50 oc i-- i-- h -0 . 7 -0 . 3 0 . 1 0 . 5 0 . 9 1 . 5 60 ,...... ? '-" 40 :>. (.) s:: Q) ;::1 0" Q) ? ? 20 0 median mean standard Run no . 9 = 0 . 85 oc 0 . 90 oc deviation 0 . 46 oc 0 -0 . 1 0 . 3 0 . 9 1 . 3 1 . 7 2 . 1 -0 . 15 0 . 75 1 . 35 1 . 95 2 . 55 0 Residual ( C ) ,...., ? -...; :>.. (.) ? Q) ::l 0" Q) ? ? ,...., ? - :>.. (.) ? Q) ::l 0" Q) ? ? (b) In the Cooling Phase 60 40 20 0 - 13 median mean standard -9 Run no . 6 deviation - 5 - 1 1 -0 . 5 7 oc -3 . 00 oc ' 4 . 38 oc ,...., ? '-' :>.. (.) ? Q) ::l 0" Q) ? ? s Res i d u aL (? C ) Run no . 7 median -0 . 82 ?C mean -2 . 68 ?C 30 3 87 ?C standard deviation -r- . ? 20 - r- 10 r- - - r-- 0 rr _j - 13 -9 -5 - 1 0 1 3 60 40 20 0 - 15 30 r- 20 r- 10 - 0 - 13 median mean standard - 11 median mean standard - c -9 1 91 Run no . 8 -0 . 94 oc -3 . 2 7 oc deviation = 4 . 47 oc - 7 - 3 1 Run no . 9 -2 . 64 ?C -3 . 30 ?C deviation = 2 22 ?C . r- r- 1- r-- r- f-- - 5 - 1 1 1 ( OC ) Re s i d u a - iN! .._, ?-. () c::
  • , B R A C 1 0 > , X JO A C 1 0 ) 0 0 0 0 0 1 0 0 ? &05 COMMON XJUC200)?A?G 200> ? Q P J O ? 1 1 0 D A T A A R G I O , O t 0 e 1 t O e 2 t 0 ? 3 ' 0 ? 4 t U e 5 t O e 6 t O e 7 t O e 8 t O t 9 t 1 t O t 0 0 0 0 0 1 1 0 1 1 5 * 1 1 1 t 1 e 2 t 1 ? 3 t 1 e 4 t l e 5 t 1 , 6 t 1 e 7 t l e 8 t 1 t 9 t 2 e O t g u o U 0 1 1 5 I 1 ? 0 * 2 , 1 t 2 e? t 2 e 3 t 2 e 4 t 2 e 5 t 2 e 6 t 2 e 7 t 2 e 8 t 2 e 9 t 3 t O t 3 t 1 t 3 e 2 t 3 e 3 t 3 e 4 t 3 e 5 t 0 0 0 0 1 2 0 , 1 ? ? * 3 ? 6 , i ? , 3 ? 8 , 3 ? 9 , 4 ? 0 , 4 .1 ' 4 I t , 4 .3 , 4 .4 , 4 ? 5 , 4 I 6 , 4 ? 7 , 4 ' 8 t 4 ? <;, 5 ? g , JLQ_Q_QO 1 ??- 'I 1 ? * 5 ? 1 ' 5 ? t 5 ? , 5 , 4 , , 5 , , 6 ,5 , , ? , e , , 9 , 6 e O t 6 ? 1 ' 6 ' , 6 . , 6 . 4 t 6 ? ? , 1l ,. " ? ' y ? u , .. 1 B J 6, o , 1 1 1 1 ' o ? 1 "' c o ' u , 1 tu " , u , 1 z 11 ::u u ' 1 u o:, , u ? u o c ::u V.U..!L u u ? .9 L 2 1 0 * O t 0 6 7 Y t 0 e 0 4 7 6 t O e 0 2 7 1 t 0 ? 0 0 6 4 t l e O t 1 e O t l e O t 1 e O t l t O I 0 0 000270 2 7 5 D A T A u i 2 ? 4 0 4 R t 5 ? 5 2 0 1 t 8 ? 6 5 3 7 t 1 1 t 7 9 1 5 t 1 4 t 9 3 0 9 t 1 8 ? 0 7 1 1 t O a t O ? t O ? / 0 0 0 0 0 2 7 5 2 6 0 D A T A X J I B I 0 ? 5 1 9 1 , ? o a 3 4 0 3 t Q , 2 7 l S , ?Q , 2 3 2 5 t 0 ? 2 0 6 6 t ? 0 ? 1 8 9 0 t O ? , O ? t O ? / 0 0 0 0 0 2 ? 0 1 r4b. !il ? E:A!J ( 5. I) u c I 0 X, u If F 1 , Ll I f E (, D 1 f E 3, () T, s {;, s X, T I , I A I I c' T I M r s, .Q_Q_QQQ_2_??.?--- ! ?' o ? e r 1 1-1 ? , T L H1 I T , A x , A c ? TIOOUUZ9 o 1 t s , tii R I T E ( 6 , 30 ? 0 i f F 1 , 0 1 Ff2 , D l f f 3 t T I , T A ? T C 0 0 0 0 0295 : . Q o ? ? ? ., _,.? ? ..WR1 lt., 6 ? .3 .? l.?) C ? 2 ? .P ?O.X.t. J/...S CJ 11.S X ? - ? -? ? - . ..0 .0-0 0 0 3 0 0 9 - (") 0 a 1'1 Ql a ...... 1.0 ? J\l.!) 30 roaMAlC 11-Hh" TH?RMAI Qlfftt S. l ? ITY ItJ JU::...A T IN? PHASEO!MISV!.!!...L--. ____ .Q .U OQO J Q !;) J l O * F 1 2 o l 0 , / / , " l H E R M A L u l F f U S I V l T Y I N C U U L I N G S T A R T ) C M M / S ) c " , 0 U 0 00 3 1 U 3 1 ? * F 1 2 o l 0 , / / , '' l H l R M A L U l F F u S I V l T Y I N L A T E R C U O L I N G ( M M I S ) c " , O u O O O J 1 5 3 ? 0 * ? 1 2 . 1 0 , / / , ' ' I N I T I A L T E M> P ? R A f U n E C C > = " , F l 2 ? 2 , / / O U O Q 0 3 2 U ?? ? * h RL6u?J ?E?tE?e???L l C = , F lr ? ?' / 1 0 U 0 0 0 3 2 5 ?? 3 0 * " C W J. N M t:. U R t. C C ) =" ' 1 ? 2 ' I/ \TUO 01TJ11> J J s 3 9 F o R M A T < ? C A N R A o r u s c M > = '' , F 1 2 . 5 , 1 o o o o O J 3 5 J 4 0 * " C A N H E 1 GH T C M > = " , f 1 2 ? 5 , 1 0 0 0 0 0 3 4 0 ? ? S * " S I Z E Q E a I ME N S I 0 N L E. SS SPA C E I N C R ?MEN T I N R D 1 R f C I I 0 N = " ' . __ -8 1.1 0 0 0_ 3 4 ? ?0 * F12 . ? ' ' 0 0 0 0 3 5 0 3 ? 5 * " Sl Z l u f D l M E N ? I U N L t. S S S P A C E I N C R E M E N T I N X O I H E C T I O N = " ' 0 0 0 0 0 3 5 ? 3 0 0 * F 1 2 . ) , / l / 0 0 0 0 0 .3 6 0 J ? 5 * '' T E 1'1 P t. R A T U R t: u 1 5 T H I iJ U T l 0 N HI 1\ C A ?? '' I I I > 0 0 0 0 0 3 6 5 ]r 0 TIME=O --? -- - - ---? -uuoutn 7 u - 3 7 5 NN = C T l ME S + C T I ME > I U T 0 0 0 0 0 3 7 5 l ij O D O 4 2 N ? l , N N 0 0 0 0 0 3 8 0 )b5 T I M E ?T I ? E + O T 0 0 0 0 0 3 8 ? 3 ? () F o C = D ! F i l * T H1 E / lJ C / D C O u 0 0 0 3 9 U 375 FOX=uiFF l *I 1 ME IOXiiJX --?-.. --. -- - - 0 UU00 j 9 ? 4 u o B o s s r = l , s X + l g u o o o 4 o u 4 U ? I X ? FL O A T ( I ? t ) / S X 0 0 0 0 4 0 5 4 1 o I F C F OX ? L T ? O ? O J ) GO T O 1 1 0 0 0 0 0 0 4 1 0 4 t 5 C A ? L ? L fi 8 CF 0 X , Y L ' D I X ) ?-- 0 0 0 G 0 4 1 ? 4 ' 0 G O J u a o o u o 0 4 2 0 4 ? ? 1 1 0 X L = O I X ? D X 0 0 0 0 0 4 2 5 4 ? 0 C A L L L S L A B C F O X , Y L , D X , X L ) 0 0 0 0 0 4 3 0 1 ? .. . . 3s-- . 4!4o o =-FLO? r J ? t > s e ? - ?-. o o o o 0 4 4 o ? f 4 ? 5 I F f OC ? L T ? 0 ? 0 2 > G O T U 1 2 0 0 0 0 00 4 4 5 r 4 ? c DO 49 J;= 1 , 6 ? 0 0 0 0 0 4 5 o 4 55 4 " BA A ( J J -B C J J > ,. 0 1 C . ?ite 004 55 406 0 C A L L C Y L Nu C F O c , y c , a , ? R A , X J U B , X J I B > 0 0 0 0 0 4 6 0 4 5 G O T O 9 0 0 0 0 0 0 4 6 ? 4?0 1 2 0 I f ( O I? ? L l . O . l ) GO TU 1 0 0 0 0 0 0 0 4 7 0 r? 5 R?DCAu C ??47? i 4 ij 0 C ALL L C Y L N O < Fu c , y c , o c , R > 0 0 0 0 0 4 6 0 4 9? 5 G O T o 9 0 0 0 0 0 0 4 8 5 4 ? ?go Y C ?t ? L 0 0 0 0 0 4 9 0 411 5 v H t 1\ = y c w v c ?? ---{) o1} e e 4 9 5 5 V Q T H C J , ? > = C l ? Y H ? A T > ? < T A " T l > + l i 0 0 0 0 0 ? 0 0 1 su1? s I F C T I H E ? L l e T I M E S > GO T O 2 0 0 0 0 0 0 0 ? 0 5 : ? 0 T O E L = T i t-? E ? T i t? t: ::i 0 0 0 0 0 ? 1 0 I i 5?5 A*F'LUATli?U*1JX/- 11\lOO!J l !;) 5 . 0 ?L I H? I c o X / A X o ogo o 5 2 0 ? ? 5 afL T { J ? l > ? D C / SC . . 0 0 0 0 525 ? J o - ? - -4? L l M T c O C I A C ? ? - -? ..,. _,.. ' 0000 0 5 3 0 1 ...... \0 V1 ? t F' ( T C J I l ) ? LT ? T L t M ll'-ctr -r tt -tttttJ-: - -u-t1 (W1.:t5 J'S 5 " 0 I F C A . G T ? A L I H I T > G u T O j Q O 0 0 0 0 0 !) 4 0 ? 4 ? I f C X . G T ? X L I M J T l G u T O 3 0 0 0 0 0 0 0 5 4 ? 5 !) 0 C F U C = O l f f 2 * T U C L I D C I O C 0 0 0 0 0 ? 5 0 S?a 8b0f?Dlf>t2* fDEL7DX7DX -- ---- --, 8 3 8 5 ? 8 5 ? 5 8 0 0 ?F U C = D J F F 3 * f DEL / D C I O C 0 0 0 0 0 5 6 ? 5 1 0 F O X = U F F 3 ? 1 D E L / O X I D X 0 0 0 0 0 5 7 0 5 r 5 I C A ? G I ?At I ?? I I ) G L? --Tt11f0i) --- --- ---- - ? --- - -o o 0 6 0 5 7 5 5 8 0 I F ( X ? G l ? X L 1 t" l T > G'i.J 1 0 4 0 0 0 0 0 0 0 ? 8 0 S d ? G O T O 5 0 0 0 0 0 0 0 5 8 5 5 ? 0 3 0 0 C F O C = J l f f l ? f D [ L / D C / u C 0 0 0 0 0 !) 9 0 5?5 CFOX==u iFF 1*TDEL/OX71JX - - - - -?? ----- - - - \ to t> 0 0 !> 9 5 6 u o 40 o c r x= o r x . o o o o o 6 o o 6 U 5 I t C C f u X . L T ? 0 ? 0 3 ) G U T O 1 4 ? 0 0 0 0 0 6 0 5 6 1 0 C AL L S L A B ( C f O X , C Y L , C l X > , 0 0 0 0 0 6 1 0 615 r_;o TU 1" ?5 -? - - ---- -- - ----------- ---- -- -- ??- -- - ?- ------ -- - 0 0 0 0 0 6 1 5 6 ? 0 1 q 5 C X L = c i X * u X 0 0 0 0 0 6 2 0 ? ? ? C A L L L S L A ? C C ? u X , C Y L , U ? , C X L ) O u 0 0 0 6 2 ? 6 J O 1 5 ? c r c =u t c o o o o o o 3 o 6 J5 bF ( ??QC ? LT ? 0 ? 02) GIT 4'-trt-? - - ------- --- ??? - ---- - -- ?? - - - o-o 0 00 6 3 !) 6 4 0 0 ? ? JJ= l , b 0 0 0 0 0 6 4 0 6 4 ? 55 B R A ( J J > =B C J J ) * C I C 0 0 0 00 6 4 5 6 ? 0 CALL C V W U ( C F U C , C Y C , B , B R A , X JOB , X J l B > 0 0 0 0 0 6 5 0 J l 60-6?5 5 6 6 0 1 6 5 I F C l C ? L l ? U ? 1 ) ? 0 T L 1 b ? 0 0 0 0 0 6 6 0 6 ? ? C R = DC * C I C 0 0 0 0 0 6 6 5 6 ( 0 C A L L L C Y L N O < C F O C , C Y C , U C , C R ) 0 0 0 0 0 6 7 0 w??r .c? . tv. ? 0000067!) ? 0 e?>y . 18 5 i ?C '( C D l ? ! ' ? . ? 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C A L L L C Y L N O ( C f O C , <. Y C ,o Q C. ,o C t. U 0 0 0 0 0 7 7 0 G (I l 0 275 0 0 0 0 0 7 7 !:> 7 (; 8 5 c y c = 1 ? () - -? -- -- --- ---- --- -o 0 "() 0 0 7 8 0 7 ti ? 2 ? 5 Y C?? l ? ? J C ? ? Y l ? 0 0 0 0 0 7 6 ? _ml ? G Yo 5 ? '( c 0 0 L * ( 'T ? 1 M I T -- ?? )-? ? c ____ - ---- ----?- ---- -------------?-- - - ] 8 8 8 8 ? ? g 6 ? o 2 0 0 T C J , I > = T h C J , I > o u o oo ts o o 6 CJ 5 5 ? C O N T l N U E . 0 0 0 0 0 d O !:> g 1 ? ? R I T ? C ? , 5 9 l T l M E 0 0 0 0 0 8 1 0 ? S'] OnM I 11 " _ ?i?..(..!) )??? 1 2 _. _2 2 _/ / __ ___ -- --- -? _ __ Q Q O O O ts l ? ? 6 0 * " X D I R EC T I O N A C R O S S , R D I R EC T I O N D O W N " / / ) 0 0 0 0 0 8 2 0 6 2 5 DO 6 0 J ? l , S C + l 0 0 0 0 0 8 2 5 e 6e ?g ___ _jj_ ? ? ? ! ? lli1lia! ? ? , I > , ?-? 2_'_ s x + 1 > ---- -- - - J&8 ooo_ oo tssa lg I ? o 4 2 N U E . ? 0 0 0 4 0 8 ? ? ? T O P 0 0 0 0 0 ? 4 ? 8 ? 0 UJ o 0 0 0 0 0 tj 5 CJ e?r::. ???sRut? I It-1E c Y I tw < r .L ,j .C _, .f. , B k J .. .x.J..D. B.L x.J .lfil_ o o o o o () s ? 8 ? 0 u Ht E N S I O t-. IH 1 0 l , X J 1 8 { 1 0 1 , 1l R i? C l O-) , X J O B C 1 0} - --- -- - -- - ---- - -- - -- - 0 0 0 0 0 8 6 0 6 t 5 C O M M O N X J O C 2 0 Q ) , A R b ( 2 0 0 ) 0 0 0 0 0 d 6 5 a t o u o 1 I = 1 , 6 o o o o o a 7 o --8.1.'? 1? C BR A Cll..a.!.La..1L.89 l G(l Jf: _ _J _ ?---? _D .O O Q 0 8 7 5 1 aLu o o 2 J= t .. t ? 2 o o o o o b e o a u s l t C B R A l i ) ? AR ? ( J ) ) 5 , 4 ,o 2 O u 0 0 0 ti 6 !:> 8 '? 0 2 C 0 ?J T f N ? E 0 0 0 0 0 b 9 0 , a?f. 4 ): Joa 1 =x Ju c J > . ooooo11.2.5.. _ 1 9 0 Q 0 T CJ 1 0 o 0 0 {) 90 o ! 905 s I r e , T a t > J? J ? t ? - o o g o o 9 o 5 ? 9 1 0 X 0 l ) a J C + C X J Ci C J+ l ) ? X J O C J ) ) / C AR G C J+ 1 > ?A R G C J ) ) * - - 0 0 0 0 9 1 0 ? ? .0..0...2 1.5 ' 9 i O ? 0 T O 1 0 0 0 0 0 ? 2 0 9 ? 5 3 X J O B < l > = < 0 ? 7 9 7 ? / B R A C I ) ) ? * 0 ? 5 ? C C ? S C B R A ( l ) ? O e 7 6 5 4 ) + 0 ? 1 2 5 / O U 0 0 0 Y 2 5 9 ? 0 * BH A C f > * ?fN < ? R A C l ) ? O t 7 6 5 4 ) ) O O O O O Y 3 0 9j5 1, LON I Nli OO.Q ?O 't.35 940 Y C c O 0 0 0 0 9 4 0 9 ? 5 00 6 1 = 1 1 6 0 0 0 0 9 4 5 g;g 6 vp ? v c +2 ? 0 * X JO B < I > I B < l > I X J I B < l > ? E x P < ? B < l ) * * 2 * F O > o o o o o 9 s o 1 ' ' R TURN O O Q0..0_ 9.5 5_ I 9 o o l N O 0 0 0 0 0 9 6 0 9 ? 5 S U B R O U l i N E S L A B C F Q , y L , D > 0 0 0 0 0 9 6 5 9 f( O Y L c 1 ? 2 7 3 2 3 Y S * C C O S C l e 5 7 1 ? 3 * U > ? E X P C ? F 0 * 2 ? 4 6 7 4 0 1 ) + 0 0 0 0 0 Y 7 0 9 ? * ? - t )?J,O*LU?C3,u?1 ,571? 3*U > ?EX?? ?9aO*f? *2a467401 Li O U 0 0 0 Y 7 !:> ' 9eo ? * ? + 1 ) ? . o ? C O S C 5 ? 0 * 1 ? ? 7 1 4 3 ? D> ? E. X ?- 2 5 ? 0 * 0 *2 ? 4 6 7 4 0 1 ) + --?oo O O ll V 8 b 9 ? 5 * ( ? 1 ) / 7 ? 0 * C OS C 7 e 0 * 1 ? 5 7 1 4 3 * 0 > ? X P C ? 4 9 ? 8 * f 0 ? 2 ? 4 6 7 4 0 ? ) ? 0 8 0 0 0 9 8 5 :?g : ? ! i ? ' 9 ? o ? ? o? c 9 . o ? t : ? 7 4 3 * 0 ? ? ? P < - 8 ! ? ? r o : 2 ? !g!:2zl?t >> 8a88??g ...... 1.0 ....... 1 0 ? 0 R E T U R N o o o o 1 o o o 1005 ENo - - - --- -o--cr o-o1--o os 1 0 1 0 S U B R O U T I N E l C Y L N D ( f Q , Y t , O C , ? ) 0 0 0 0 1 0 1 0 -tm X ? C D C ?R ) I 2 . o / C f O * O L * * 2 ? 0 ) * * t e 5 0 0 0 0 1 0 1 5 A =ER f N( X ) 0 0 0 0 1 0 2 0 ---------;E"'--,1,--'=--;o.r.-;.5-=--;u'---"'4? 8 9 5 b *?X p C .. X * X T-x * A - --- - - -- - --- - - - -- u -o 0 0 t 0 2 5 1 0 J O X 2 = X + X O u 0 0 1 U 3 0 1 0 ? ? l 2 ? 0 ? 2 ? * l A - X 2 ? l 1 ) O u 0 0 1 0 3 ? 1 0 4 0 Y C = l ? ( ( O L / h ) * * O e 5 * A + < D L ? R ) * ( F 0 * D C * * 3 ? 0 J ? ? 0 . 5 / 4 / O u 0 0 1 0 4 u 10?5 * OCIR**1 e5*[1+('J*DC**2 ?6?7,0?t'.**2a0?2?0*uC?R>I ------- -- - - - ?uO-G -1 0 4 !> l o ? o * C J 2 , 0 * D C * ? 1 . 5 * R * * 2 ? 5 > ? r o ? o c ? ? 2 ? 0 ? E 2 > o o o o t o 5 o 0 !) 5 R E T U R N 0 0 0 0 1 0 5 !) 1 0 ? 0 EN D 0 0 0 0 1 0 6 0 1-o-t S - SOBR1JtJT1n --r-St:ltff(ru--,-- " t. "? Ll X -,xt:1 ------- ----- - ----- - ----- --- -- - - ? -D U 0 0 1 0 6 ? 1 0 ' u Y L = 1 e 0 0 0 0 0 1 0 7 U 1 0 7 5 ? f O = < F u * U X ? ? 2 ? G l * * O ? ? ! 0 0 0 0 1 0 7 5 1 0 b o D O 1 0 2 1 = 1 , 3 O u 0 0 1 U 8 U toos ???1?1 --------- -- --- ---- o o o{) 1 v 8 5 1 0 ? 0 Y t = C < ? * N + l ) * O X ? X L ) / ? ? 0 / X F O 0 0 0 0 1 0 9 0 1 0 ? 5 Y 2 = C < z ? N + l ) * D X + X L ) / 2 ? U I ? F ? 0 0 0 0 1 0 9 5 1 VQ 1 0 2 YL? Y L? ( ( ? l ) * * h * < E H f N ( Y l ) + l k F N < Y 2 ) ) ) 0 0 0 0 1 1 0 0 1us RETuRt? - -- ? ? -? -- -o o oo t 1 o 5 1 1 0 E N D 0 0 0 0 1 1 1 U 1 P 5 t U N C T l 0 I,, l R r N ( X ) 0 0 0 0 1 1 1 ? 1 ? 0 D A T A P le 1 , A 2 , A 3 , A 4 , A 5 / U ? 3 2 75 9 1 1 , 0 ? 2 5 4 d 2 95 9 , ? 0 ? 2 8 4 4 9 6 7 4 , 0 0 0 0 1 1 2 0 i ?5 * 1 ? 4fl413 7 4' ?t ?T570TIT ? Oo 14 054 - - ---ou-o-o--tt 2 5 ? J o l f X ? G T e O e O l GO T O 1 3 ? 0 0 0 0 1 1 3 0 l l ? s ? = M l > * X o o o o 1 1 3 !) f1:? 13 t?:tt2?? 1 + P * X ) g? ? ? : ? 1 1 ? 0 T 3 ? T 2 * T 1 0 0 0 0 1 1 5 0 1 1 ? 5 T 4 = T 3 ? T l 0 0 0 0 1 1 5 5 0 T S = T 4 ? T 1 O u 0 0 1 1 6 0 lt65 ?R[N=?XPC ?x*Xl*CA1*11+A2*12+A3*T3+A4*14+A5*15) ??01 1 6? 7' 0 E TURN 0 0 0 0 1 1 7 0 I 1 5 NO 0 0 0 0 1 1 7 5 ...... \,() 00 1 99 APPENDIX 4 . 6 Comparison of Experimental Temperatures and Predicted Temperatures from the Modified Analytical Solution Program ( ) experimental temperatures (--- ---) predicted temperatures (a) Run no . 8 (retort temperature was 1 29?C) 12S ......... 125 ......... u 120 0 u 120 0 ........ ........ 1 10 QJ H ;::l lOO 1 10 QJ .... ;::l 100 4-.1 4-.1 Ill .... 10 QJ p., s 10 QJ E-< Cll .... 90 QJ p., s 80 Q) E-< 70 r.o 60 so 50 r.o 40 JO lO 0 10 20 lO 40 so 60 70 80 90 lOO 1 10 0 10 20 lO 40 so 60 70 80 90 100 1 10 Time (mi_n) Time (min) ( a ) a t r / a = 0 . 0 , x / h = 0 . 0 ( b ) a t r / a 0 . 0 x / h = 1 / 3 ......... 12S ? 120 ........ '\ ......... 12S u 120 0 ........ QJ 1 10 \ H \ ;::l lOO \ 4-.1 Cll \ .... QJ 90 \ p., s 10 \ QJ \ E-< \ 70 \ 1 10 Q) H ;::l 100 4-.1 Cll .... 90 QJ p., s 80 Q) E-< 10 \ r.o \ 60 \ so so 40 40 lO 30 0 10 20 lO 40 so 60 70 80 90 lOO 1 10 0 10 20 lO 40 so 60 70 80 90 lOO 1 1 0 Time (min) Time (min) ( c ) a t r / a = 1 / 3 x / h = 1 / 3 , ( d ) a t r / a 0 . 0 , x / h = 2 / 3 (b) 1:0 ,....... u ?..... 1 10 QJ lOO 1-< ;:J +J 90 cu 1-< QJ .iO 0. t::; Cl) ]0 E-< 60 50 40 30 120 ,....... u 0 1 10 '-" QJ 100 1-< ;:J .,.J 90 cu 1-< ? 80 0. s Cl) 10 E-< 60 so 40 30 0 0 Run no . 9 ( retort temperature was 1 20 C) ,....... u ? QJ 1-< ;:J +J cu ? 1-< ? QJ ? ' ? ? Cl) '/ E-< -'/ ?----l 10 20 30 40 so 60 70 1:0 90 100 1 10 120 Time (min) ( a ) a t r / a = 0 . 0 x /h = 0 . 0 - ,....... \ u 0 \ '-" ? \ ? Cl) \ 1-< h \ ;:J /, +J /, \ cu \ 1-< I. \ Cl) I 0. /, \ s \ QJ I. E-< \ \ .....___, 0 10 20 JO 40 so 60 70 80 90 lOO 1 10 120 Time (min) ( c ) a t r / a = 1 / 3 x / h = 1 / 3 , 200 120 1 10 -?--?- ./"- lOO 90 80 ]0 60 so 40 30 0 10 20 30 40 ?0 60 ]0 ?il ?0 100 1 10 120 Time (min) ( b ) a t r / a = 0 . 0 , x / h = 1 / 3 120 1 10 100 A A 90 ;, A 80 A /, 70 I. /, 60 so 40 30 0 10 20 JO 40 ?0 6? 70 80 ?0 IIlO 1 10 120 Time (min) ( d ) a t r / a = 0 . 0 x / h = 2 / 3 APPENDIX 4 . 7 Method of Quality Retention Calculation for Micro? Organisms and Ascorbic Acid For Micro-Organisms 0 For generally basis , z = 10 C , . d . d 50?C - 130?C ?. assum1ng temperature range stu 1e was Ea 2 . 303 X 0 . 0083 X ( 50+273) X ( 1 30+273) 10 - 1 250 kJ mole 20 1 From Lund ( 19 7 7 ) ; o 1 2 1 . 1oC was found in the range of 0 . 48- 1 . 40 min , and 0 . 15 min o 1 2 1 . 1oC average = 0 . 68 min From from k -2 . 303 D 2 . 303 0 . 68 3 . 3868 . - 1 m1n lnS lnk 1 + Ea/RT1 lnS ln 3 . 3868 + 250/ (0 . 0083 x ( 1 2 1 . 1 + 273) ) 7 7 . 8L?07 s 6 . 3943 x 1033 min- 1 ln No/N = s f t e-Ea /RT d t 0 for the time interval ? t ; ln No/N S e-Ea /RT ?t where T was the average temperature over t , ?t . 202 So No/N could be calculated from the temperature data , N calculated at the end of ?t became No for the next ?t . The calculation was repeated to ob tain the final concentration at the end of processing time . 10 Then , F 1 2 1 . 1 could be determined from : ln No/N 250 1033 X e - (0 . 0083 X 394 . 1 ) 6 . 3943 X Subs ti tute , final No/N from the calcu?ation , the equivalent time , 0 t , at 1 2 1 . 1 C can be determined . For Ascorbic Acid From Chi t taporn ( 19 7 7 ) , Ea k lnS 84 . 2 kJ mole - 1 840 x 10-3 h- 1 a t 1 29?C 1 4 ; 10-3 min- 1 at 1 29?C -3 84 . 2 = ln ( 14 X 10 ) + 0 . 0083 X 402 3 . 66 32 x 1 09 min- 1 Calculation could be done same as for micro-organisms . 203 APPENDIX 4 . 8 An Example of Lethality Calculation (a) Predicted Temperatures and Lethality Calculation at the Centre Point for Run no . 6 PREDICTED AVERAGE TEMPERATURE?C TEMPERATURE?C 6 1 . 0 6 1 . 0 6 1 . 00 b l . O 60 . 99 60 . 99 6 1 . 02 6 1 .05 6 1 . 1 5 6 1 . 26 6 1 . so 6 1 . 74 62 . 14 62 . 55 62 . 12 6 3 . 69 64 . 40 65 . 12 6 5 . 9 5 66 . 79 67 . 7 2 68 . 65 69 . 65 70 .65 7 1 . 69 72 . 74 7 3 . 8 1 74 . 88 7 5 . 9 7 7 7 . 06 78 . 14 79 . 2 3 80 . 30 8 7 . 38 82 . 44 8 3 . 50 84 . 54 85 . 58 86 . 59 87 . 60 88 . 58 89 . 57 90 . 5 1 9 1 . 46 92 . 38 9 3 . 30 94 . 1 8 9 5 . 06 95 . 90 96 . 75 99 . 56 98 . 37 99 . 14 99 . 92 100 . 66 101 . 4 1 102 . 12 102 . 83 103 . 50 104 . 18 104 . 82 105 . 4 7 106 . 08 106 . 69 107 . 2 7 107 . 86 108 . 4 1 108 . 9 7 109 . 50 1 10 . 03 1 10 . 5 3 1 1 1 . 0 3 I l l . 5 I 1 1 1 . 99 1 1 2 . 44 1 1 2 . 89 1 1 3 . 32 1 1 3 . 75 1 14 . 16 1 14 . 57 1 14 . 95 1 1 5 . 34 1 1 5 . 70 1 16 . 07 1 16 . 42 1 16 . 78 1 1 7 . 0 3 1 1 7 . 29 1 1 7 . 2 1 1 1 7 . 1 3 1 1 6 . 52 1 1 5 - 92 1 14 . 7 7 1 1 3 . 62 1 1 2 . 0 3 1 1 0 . 44 108. 53 106 . 62 104 . 50 102 . 39 10 1 . 52 100 . 66 99 . 82 98 .99 98 . 06 9 7 . 1 3 96 . 1 2 95 . 1 1 9 4 . 04 9 2 . 9 7 9 1 . 86 90 . 75 89 . 6 1 88 . 48 87 . 32 86 . 1 7 8 5 . 0 1 8 3 . 86 82 . 70 8 1 . 55 80 . 4 1 79 . 2 7 78 . 14 7 7 . 02 7 5 . 9 1 74 . 8 1 7 3 . 7 3 7 2 . 65 7 1 . 59 70 . 54 Final concentration Calculate F ?g 1 . 1 (min) MICROBIOLOGY e -Ea/RT No/N ' 5 . 3 394- 39 1 . 0000 9 . 0064 1 . 000 1 1 . 5 366- 38 1 . 000 1 2 . 6340 1 . 0002 4 . 50 1 8 1 . 0003 7 . 6 1 58 1 . 0006 I . 2725-37 1 . 0010 2 . 0959 1 . 00 1 6 3 . 3922 1 . 0026 5. 39 1 3 1 . 004 1 8 . 399 5 1 . 0065 1 . 2835-36 1 . 0099 1 . 9246 1 . 0 149 2. 827 1 1 . 02 19 4 . 0749 1 . 03 18 5 . 7656 1 . 0452 8 . 0203 1 . 0635 - - 1 . 09 7 3-35 1 . 0878 I . 4 754 I . 1 1 99 1 . 9526 1 . 1 6 16 2 . 5440 1 . 2 1 56 I . 2576 1 . 2840 4. 1429 1 . 3742 5 . 1960 1 . 4899 6 . 4 108 1. 6354 7 . 8353 I . 8243 9 . 4700 2 . 069 1 I . I 32-34 2 . 3836 I . 34 1 2 2 . 7986 1 . 5737 3. 3452 1 . 8287 4 . 0682 2. ! I l l 5 . 0525 2 . 3833 6 . 226 1 - 2 . 4675 6 . 64 16 2 . 1 536 5 . 2200 1 . 5 163 3 . 20 1 1 8 . 7 1 2-35 1 . 9 5 1 3 4 . 2429 1 . 3848 1 . 824 7 1 . 1 503 9 . 6556-36 1 . 0769 6 . 6852 1 . 0526 4 . 5478 1 . 0355 2 . 9652 1 . 0230 1 . 8652 1 . 0 144 1 . 1409 1 . 0088 6 . 8346-37 1 .0053 4 . 0259 1 . 003 1 2 . 3444 1 . 00 18 1 . 355 7 1 . 00 10 7 . 8 1 16-38 1 . 0006 4 . 50 1 8 1 . 0003 2 . 5983 1 . 0002 1. 506 1 1 . 0001 8 . 7803-39 1 . 0001 2 . 3946 -8 x 10 No 5. 1 8 1 3 ASCORBIC ACID e -Ea/RT No/n 1 . 8 10 1- 14 1 . 000 1 1 . 8 101 1 . 000 I 1 . 8 1 35 1 . 000 1 1 . 8369 1 . 000 I 1 . 8978 1. 000 1 2 . 0 168 1 . 000 1 2 . 2099 1 . 000 1 2 . 49 1 1 1 . 000 1 2 . 8747 1 . 000 1 3 . 3787 1 . 000 1 4 . 0237 1 . 0002 ?4 . 83 16 1 . 0002 5 . 8250 1 . 0003 7 . 0342 1 . 0003 8 . 4857 1 . 0004 1 . 0200- 1 3 1 . 0004 1 . 2 208 1 . 0005 1 . 4537 1 . 0006 1 . 7 205 1 . 0008 2 . 0234 1 . 0009 2 . 36 3 1 1 . 00 10 2 . 74 1 2 1 . 00 1 2 3 . 1 588 1 . 00 14 3 . 6 1 39 1 . 00 16 . 4 . 107 1 I . 00 18 4 . 6376 1 . 0020 5. 2055 I . 002 3 5 . 809 1 1 . 0026 6 . 4435 1 . 0028 7. 1074 1 . 003 1 7 . 797 1 1 . 0034 8 . 5 1 10 1 . 0037 9 . 2482 1 . 004 1 1 . 0004- 1 2 1 . 0044 1 . 0775 1 . 004 7 I . 5590 I . 005 1 1 . 2 352 I . 0054 1 . 3 148 1 . 0058 1 . 3952 I . 0062 1 . 4 7 54 1 . 0065 1. 555 1 1 . 0069 1 . 6352 1 . 0072 1 . 706 1 1 . 0075 1 . 7270 1 . 0076 1 . 6467 1 . 007 3 1 . 4564 1 . 0064 1 . 1996 1 . 0053 9 . 3257- 1 3 1 . 004 1 6 . 9409 1 . 003 1 5 . 5549 1 .0024 4 . 8842 1 . 002 1 4 . 268 1 1 . 00 1 9 3 . 6747 1 . 00 16 3 . 1243 1 . 00 14 2 . 6305 1 . 00 1 2 2. 1986 1 . 00 10 1 . 8269 1 . 0008 1 . 5 1 19 1 . 0007 1 . 2481 1 . 0005 1 .029 1 1 . 0005 8 . 4857-14 1 . 0004 7 . 0007 1 . 0003 5 . 7842 1 . 0003 4 . 7888 1 . 0002 0 . 8664 No 1 7 . 35 10 (b) 10 Calculated Final Concentration and F l Z l . l Details run no . 6 ; at centre point final microbiological concentration x 10 9 f inal ascorbic acid concentration 10 F 1 2 1 . 1 (microbiology) , min 10 F1 2 1 . 1 (ascorbic acid) , min run no . 6 ; r=O . O , x=1 . 8 cm f inal microbiological concentration x 10 1 1 f inal ascorbic acid concentration 10 F 1 2 1 . 1 (microbiology) , min 10 F1 2 1 . 1 (ascorbic acid) , min run no . 7 ; at centre point f inal microbiologicAl concentration x 10 final ascorbic acid concentration 10 F1 2 1 . 1 (microbiology) , min 10 F 12 1 . 1 (ascorbic acid) , min run no . 7 ; at r?O . O , x? l . 8 cm f i nal microbiological concentration x 10 10 f inal ascorbic acid concentration 10 F1 2 1 . 1 (microbiology) , min 10 F 1 2 1 . 1 (ascorbic acid) , min Based on Experimental temperature data 8 . 7 2 1 4 No 0 . 8609 No 5 . 4795 1 8 . 1 2 10 3 . 7258 No 0 . 8478 No 7 .0904 19 . 9 7 1 0 3 . 1 369 No 0 . 8391 No 5 . 10 16 2 1 . 2242 7 . 4204 No 0 . 8279 No 6 . 207 1 2 2 . 8505 Based on Predicted temperature data 2 . 3946 No 0 . 8664 No 5 . 1 8 1 3 1 7 . 3510 5 . 6827 No 0 . 8522 No 6 . 9653 1 9 . 3440 1 . 5574 No 0 . 8444 No 4 . 6284 20 . 4651 7 . 8255 No 0 . 8349 No 5 . 5 1 1 5 2 1 . 8386 204 % Difference 0 . 6 5 . 4 4 . 3 0 . 5 1 . 8 3 . 1 0 . 6 9 . 3 3 . 6 0 . 8 1 1 . 2 4 . 4 205 APPENDIX 4 . 9 Distribution of Residuals for Determining the Accur acy of the Modified Analyt ical Solut ion Program for Calculating Tempertures ( a) In the Overall Process Run no . 6 median mean 30 standard deviation = ' r--- _....... ? r---'-' :>-. 20 f- (.) Cl 1-- Cl) ;::3 0' Cl) 1-1 ? 10 f- 1-- 0 0 . 24 oc o . 7 1 oc L 90 oc 30 _....... ? '-' :>-. 20 (.) Cl Cl) ;::3 0' Q) 1-1 ,---- ? 10 ? -2 . 5 -0 . 5 1 . 5 3 . 5 5 . 5 0 -0 . 75 60 _....... ? '-' :>-. 40 (.) Cl Cl) ;::3 0' Cl) 1-1 ? 20 0 median mean Re s i dtJ.a l ( ?C ) Run no . 7 standard deviation 0 . 85 ?C 0 . 15 ?C 1 . 4 7 ?C 60 :>-. 40 (.) Cl Q) ;::3 0' Cl) 1-1 ? 20 0 - 3 . 25 - 2 . 25 - 1 . 25 - 0 . 2 5 1 . 2 5 2 . 25 -5 Re s i d u a l ( ?C ) Run no . 8 median 0 . 6 7 oc mean 0 . 76 oc standard deviation = 1 . 00 oc 0 . 7 5 1 . 75 2 . 7 5 3 . 75 Re s i d u a l ( o c ) Run no . 9 median 0 . 43 oc mean 0 . 13 oc standard deviation 1 . 4 1 oc - 3 - 1 1 3 (b) In the Cooling Phase Run no . 6 median 2 . 1 3 oc mean = 2 . 2 7 oc 30 r- 1 . 70 ?C - ? '-" :>. (.) c (1) ;j 0" (1) 1-4 ""' - ? '-" :>. (.) c (1) ;j 0" (1) 1-4 ? standard deviation = 20 f- 10 1-- 0 - 1 . 5 30 r- 20 f- 1-10 I-- 0 - 3 . 2 5 ......-- r--- -? '-" :>. r---- (.) c (1) ;j 0" (1) 1-4 t---- ? I 0 . 5 2 . 5 4 . 5 6 . 5 Re s i d u a l ( ? C ) Run n9_ ? 7 median - 1 . 46 oc mean - 1 . 50 oc 0 standard deviation = 0 . 9 1 c - ? '-" :>. (.) c (1) r- ;j 0" r-- Cl) 1-4 ? r- f-- - 2 . 25 - 1 , 2 5 -0 . 25 0 . 75 Re s i d u a l (? C ) 30 r- 20 f-- 10 1- 0 - 1 . 75 30 20 10 0 -5 median mean standard r- 0 median mean standard -3 206 Run no . 8 = = deviation = 1 . 29 ?C ,.--- r--- f--- ,.---- 1-- - 1-- 1 . 75 3 . 7 5 Res i d u a l ( ? C ) Run no . 9 = - 1 . 75 oc = -1 . 34 oc deviation = 1 . 65 oc - 1 1 3 Res i d u a l (? C ) 207 APPENDIX 5 . 1 Analytical Resul ts ( a ) Ascorbic Acid CONCENTRATION x 10 Z mg g - l Mean Concen- 2 Standard Dev-Run No . Sample tration ?1 10 iation x 10 2 1 2 3 mg g mg g- 1 120?C 7 control 25 . 00 ( 6 ) 24 . 46 ( 7 ) 24 . 04 ( 2 ) 24 . 50 (8 ) 0 . 48 ( 8 ) heated 23 . 23 ( 9 ) 2 1 . 80 (4 ) 22 . 34 (8 ) 22 . 46 ( 7 ) 0 . 7 2 ( 0 ) 4 control 26 . 48 ( 2 ) 25 . 66 ( 2 ) 26 . 2 8 ( 0 ) 26 . 14 ( 1 ) 0 . 43 (8 ) heated 23 . 72 (4) 23 . 97 ( 5 ) 23 . 7 9 (4) 23 . 83 (8 ) 0 . 1 3 ( 6 ) 9 control 25 . 84 ( 2 ) 25 . 95 (4) 26 . 05 ( 2 ) 25 . 95 (9) 0 . 1 1 ( 5 ) heated 2 3 . 54 ( 7 ) 2 3 . 64 ( 6 ) 23 . 65 (9 ) 23 . 60 (9 ) 0 . 06 (2 ) 2 control 23 . 89 ( 7 ) 24 . 48 ( 9 ) 24 . 1 1 ( 3 ) 24 . 16 (9 ) 0 . 30 (9 ) heated 2 1 . 00 ( 1) 22 . 16 (9 ) 2 1 . 95 (4) 2 1 . 7 1 ( 5 ) 0 . 62 ( 8 ) 129?C 6 control 25 . 3 2 ( 0 ) 25 . 7 5 ( 2 ) 25 . 47 ( 6 ) 25 . 68 (9 ) 0 . 30 (0) heated 2 3 . 89 (9 ) 24 . 5 3 ( 7 ) 23 . 88 (0) 24 . 10 (0 ) 0 . 37 ( 1) 1 control 23 . 6 1 ( 7 ) 23 . 9 7 ( 1 ) 24 . 09 ( 8 ) 23 . 89 (8 ) 0 . 25 ( 1 ) heated 22 . 46 ( 1 ) 2 1 . 5 3 ( 7 ) 2 1 . 54 ( 3 ) 21 . 84 (4) 0 . 5 3 (4) 8 control 2 5 . 45 ( 2 ) 2 5 . 26 ( 2 ) 25 . 16 ( 7 ) 25 . 29 ( 1 ) 0 . 15 (0) heated 2 3 . 2 0 ( 8 ) 2 3 . 4 1 ( 9 ) 22 . 7 9 ( 7 ) 23 . 04(4) 0 . 3 3 (4) 5 control 24 . 7 1 ( 5 ) 25 . 47 ( 6 ) 24 . 28 (8) 24 . 82 ( 7 ) 0 . 60 ( 3 ) heated 2 3 . 04 (0 ) 22 . 06 ( 5 ) 22 . 59 (2 ) 22 . 5 6 ( 2 ) 0 . 49 ( 3 ) 10 control 2 3 . 58 (0 ) 23 . 3 9 ( 9 ) 22 . 9 1 (0 ) 23 . 29 ( 3 ) 0 . 35 ( 5 ) heated 2 1 . 12 ( 1 ) _?0 . 70 ( 0 ) 21 . 03 ( 7 ) 2 0 . 9 5 ( 9 ) 0 . 22 ( 1 ) ( b ) Riboflavin CONCENTRATION Mean Standard Run No . Sample IJg g- 1 Concentration Deviation 1 2 3 4 - 1 - 1 IJg g IJg g 120?C 7 control 2 5 . 16 ( 1 ) 25 . 92 ( 5 ) 25 . 14 (8 ) 25 . 42 (0 ) 25 . 4 1 (9) 0 . 36 ( 1 ) heated 25 . 09 (0) 25 . 47 ( 3) 2 3 . 9 8 ( 0 ) 24 . 05 (9 ) 24 . 65 (8 ) 0 . 7 5 ( 9 ) 4 control 25 . 9 5 ( 5 ) 25 . 35 ( 6 ) 25 . 37 ( 8 ) 2 5 . 34 (6 ) 2 5 . 59 (0) 0 . 34 (0 ) heated 24 . 63 ( 6 ) 24 . 89 (0 ) 23 . 27 ( 2 ) 24 . 6 1 ( 1) .24 . 3 5 ( 0 ) 0 . 7 3 (0 ) 9 control 26 . 07 ( 2 ) 26 . 0 3 ( 6 ) 26 . 26 ( 7 ) 25 . 8 7 ( 8 ) 26 . 06 ( 6 ) 0 . 16 (0) heated 24 . 7 8 ( 9 ) 24 . 8 1 (0) 24 . 2 7 ( 2 ) 24 . 1 7 ( 2 ) 24 . 64 (2 ) 0 . 25 ( 1) 2 control 25 . 66 ( 9 ) 25 . 1 2 ( 2 ) 26 . 1 3 (4) 25 . 8 5 ( 1) 25 . 94 ( 2 ) 0 . 23 ( 9 ) heated 24 . 02 (6 ) 24 . 00 ( 7 ) 24 . 86 ( 1) 24 . 0 7 ( 3 ) 24 . 24 ( 7 ) 0 . 42 ( 7 ) 129?C 6 control 25 . 5 9 ( 3 ) 25 . 78 ( 2 ) 24 . 99 ( 3 ) 24 . 7 6 (9 ) 25 . 2 8 ( 2 ) 0 . 48 (4) heated 25 . 14 (9 ) 25 . 04 ( 1) 24 . 2 5 ( 9 ) 24 . 52 ( 7 ) 24 . 74 ( 7 ) 0 . 42 (4) 1 control 2 5 . 54(4) 25 . 87 ( 5 ) - - 25 . 70 (4) 0 . 19 ( 5 ) heated 25 . 40 (5 ) 24 . 17 (8) 24 . 32 (2 ) - 24 . 63 (8 ) 0 . 63 (0 ) 8 control 25 . 88 ( 3 ) 25 . 5 2 ( 5 ) 26 . 49 ( 0 ) 23 . 70 (9 ) 25 . 40 ( 7 ) 1 . 20 ( 1) heated 24 . 13 ( 2 ) 24 . 25 (4) 23 . 65 ( 1 ) 24 . 2 1 (3 ) 24 . 06 ( 3 ) 0 . 28 (9 ) 5 control 26 . 2 2 (0 ) 26 . 36 (4) 26 . 10 ?7 ? 26 . 16 ?4? 26 . 2 l f l? 0 . 38 p ? heated 24 . 36 ( 5) 24 . 14 (0) 25 . 28 0 24 . 81 5 24 . 65 5 0 . 5 1 6 10 control 26 . 44 ( 2 ) 25 . 7 7 (6 ) 25 . 90 ( 3 ) 26 . 49 ( 1 ) 26 . 15 ( 1) 0 . 3 7 (0) heated 24 . 32 (4) 24 . 10 (8 ) 25 . 00 ( 8) 24 . 42 ( 1 ) 24 . 46 (0 ) 0 . 38 ( 3 ) (c ) Colour The colour of both control and heated samples were duplicate measured . The instrumental readings of X, Y and Z were transferred to x, y and Y by : x = X/ (X + Y + Z ) y Y/ (X + Y + Z ) 208 The x and y of both control and heated samples of each processing run are shown below : X y c/c Run No . 0 Control Heated Control Heated X y c c c c 0 0 1 29?C 6 0 . 44 0 . 45 0 . 44 0 . 44 1 . 02 1 . 00 1 0 . 44 0- 45 0 . 44 0 . 44 1 . 02 1 . 00 8 0 . 44 0 . 44 0 . 44 0 . 44 1 . 02 1 . 00 5 0 . 44 0 . 45 0 . 44 0 . 44 1 . 02 1 . 00 10 0 . 43 0 . 44 0 . 44 0 . 44 1 . 02 1 . 00 1 20?C 7 0 . 44 0 . 45 0 . 44 0 . 44 1 . 0 2 1 . 00 4 0 . 44 0 . 45 0 . 44 0 . 43 1 . 02 1 . 00 9 0 . 44 0 . 45 0 . 44 0 . 44 1 . 02 1 . 00 2 0 . 44 0 . 45 0 . 44 0 . 44 1 . 02 1 . 00 As can be seen from above figures , c/c of both x and y were 0 constant . The c/c of x was about 1 . 02 and of y was 1 . 00 . Therefore i t 0 could be concluded that only Y can be used to describe the change of colour of baby food caused by heat in this s tudy and the readings , Y , are shown in the following table . ?209 Reading , y Run No . Sample Mean , Y 1 2 1 20?C 7 control 30 . 4 30 . 2 30 . 3 heated 26 . 9 26 . 9 26 . 9 4 control 3 1 . 2 30 . 7 30 . 9 heated 27 . 2 26 . 6 26 . 9 9 control 30 . 1 30 . 1 30 . 1 heated 25 . 1 25 . 1 25 . 1 2 control 30 . 6 - 30 . 7 30 . 6 heated 24 . 2 24 . 0 24 . 1 -? 1 29?C 6 control 30 . 8 30 . 2 30 . 5 heated 26 . 2 26 . 0 26 . 1 1 control 30 . 3 30 . 3 30 . 3 heated 25 . 3 25 . 6 25 . 4 8 control 30 . 4 30 . 4 30 . 4 heated 24 . 9 24 . 9 24 . 9 5 control 30 . 1 30 . 3 30 . 2 heated 23 . 2 23 . 8 23 . 5 10 control 30 . 9 30 . 9 30 . 9 heated 23 . 7 24 . 0 23 . 8 2 1 0 (d ) Viscosity Reading of Viscosity S tandard Run no . Sample Mean Reading Deviation 1 2 3 4 1 20?C 7 control 64 . 2 67 . 0 67 . 0 68 . 6 66 . 7 1 . 8 heated 60 . 1 60 . 6 59 . 6 - 60 . 1 0 . 5 4 control 63 . 9 6 3 . 0 6 2 . 5 6 1 . 4 62 . 7 1 . 0 heated 5 3 . 3 55 . 4 56 . 1 54 . 8 54 . 9 1 . 2 9 control 60 . 3 60 . 4 59 . 4 - 60 . 0 0 . 6 heated 49 . 6 49 . 7 49 . 6 - 49 . 6 0 . 1 2 control 66 . 0 65 . 5 64 . 2 - 65 . 2 0 . 9 heated 49 . 1 48 . 9 5 1 . 7 50 . 8 50 . 1 1 . 4 - - 1 29?C 6 control 7 2 . 0 68 . 0 70 . 3 - 70 . 1 2 . 0 heated 56 . 8 56 . 3 57 . 9 - 57 . 0 0 . 8 1 control 7 1 . 5 7 3 . 5 72 . 4 7 2 . 2 7 2 . 4 0 . 8 heated 57 . 5 57 . 3 57 . 0 - 5 7 . 3 0 . 3 8 control 66 . 8 69 . 4 66 . 1 - 67 . 4 1 . 7 heated 5 1 . 2 52 . 8 53 . 3 - 52 . 4 1 . 1 5 control 64 . 4 6 3 . 2 65 . 3 - 64 . 3 1 . 1 heated 49 . 5 49 . 2 47 . 6 - 48 . 8 1 . 0 10 control 76 . 5 75 . 6 74 . 8 - 75 . 6 0 . 9 heated 56 . 0 55 . 3 55 . 5 - 55 . 6 0 . 4 SO $ Q P T = 1 o u o o o u so l O O O?H E y ? f u N T < 1 ? ' 1 5 ? , T H C 1 5 ' 1 ? ) , ? 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F f l ? TDt.L/0?_/ I.J_X ____ _ _ ________ __ _ _ _____ _____ ____ _ _ _ _ _ - --- -- - -8 g8l ??-8-8 -- ? 1 1 1 0 0 I f C C f .., X ? L f . O . u 3 l G u T O 1 ? ? O u 0 1 1 1 0 0 l i 1 8 8 8 C L T u ? ? ? C c F O X , C Y L , C I X > g ? g l l 1 8 8 tl?88 ? 14' tifE*E???g?cF-?>c .. cvL;o:x, c x? > ? ? H< ? - ? .... w ..... -.. ... ?=-??-? ----- ??nglt??gg- -- il l,&8 ? ?- ,._ l S S tf ? ?fZ?_L.J_? Q. ?Jt.tLG_Q J_p __ J 65 ___ ,.:t.:."??:c?? ___ _ ?-'""' '- ? ??= --- ? . -? - - - , 828 1 1 ?88 ; ?lis ss . ... . L ?5 D!Ft?t?j}=?i?????!t . . . . . - - -? ?? s?gi?ss? i ; o ? ? .? ?.- ?.f:?:i\ -e ? L I ?I L Nu u c; v c , a , s R A .. x J o ? , x J I e , ?? ' ? ; -:: ? - Q o 1 2 1 0 0 ? ' '.4>. '<. GO 0 . - 7 5 ,. . ?? .. - OQ0 1 2 1 0 0 ' 2 200 '::;;; , ,_,.::!,:(: \ ? 6 5 ! .f C l? ? ?T ? 0 ? 1 ) G O ,TO 1 85 ' 7 ? ?- .. ' . . 0 00 1 22 0 0 I ?- R?DC t C - ---- - --?? - ?- - - -.:--?---'-- -?-&-1-2--l-66-1 2 4 0 0 C A L L L ? 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E S , L T I M E O u 0 1 7 J O O 17460? .302 , f:i?H4?T" " Hf;A llN? t1?C4LC l-:'+f*2? ??-4.1 . . . -- - ___,....,.. . QF...,... .......,.- - -- -gm -7-? --1 750 0 - * C O N U T I'IE < S t:.. C a " , f l c: , 1 , / / ) , . - . 0 0 7 S O O 1 76 0 0 .W R I ?t ? f 6 , 2 2 ? ( R E T EN N L ) , RA T I O C NL ) , R K ( N L. ) I EA < N L ) , N L.? l , NL E V?L ) 8 o o 7 6 00 1 7 7 0 0 2Z FORMA t n Rl.TE N T I ON C O N C E N T H AT I O N ?: " , f 1 2 ? S , /7 - O u 0 1 7 ;7 0 0 . ?1?&?8 ?? ? " HW? yt ?t ??? ? T-; 1 , 11 ? - ?? ?? ?- - ? OJLO 1 i r?o ' t ? ' ... . p *""? .. .. "','? .?,,. ? I N A ( 17 fC )i1fll:T2 ? s?/7 -- . ?- ?-..- ---?-ouO'T71HJcr ? . 17 ? 00 0 .. . r?- ? ... "*._. " ? . A. C T ? V A ! 0 N E. N 1: R G . C A L I M U L E ) :a? .. " , E 1 2 ? 5 ; / I > , ? . . , . . 8 0 0 11 67 9 0 0 t' 8 0 .: : ?i T O P ? . \- .-? ' ? ? " ., ?, 0 0 0.00 . " il OQ "': ' , NO ?-"-- --- . . . . -'- . ?c .. - -- ? -????!? ?? --?-?-?-__ ._, _ .. -- ---?""-- -L--- ,_ ?i, 0 00 1 ?. 1.0 0_ . N 1--' ""' ?....----.-- ""f!'ii t'-Sllt!l"U'ii" " .... ?" -P:'C ??? - ?:?"""" .-. ? ? ' -? g 8 f g 18 g I 0 0 0 1 8 8 0 0 . -'OVOI"B? ou O u 0 1 6 J O O 0 0 0 1 8 4 0 0 o u o 1 8 5 0 0 't q r ? !:' ? ? '"4 ? ,1, ? ? ? '!: .. " ,. , , --- -? ?- ? -- 888 lSZ&8-J 0 0 0 1 9 1 0 0 ------? )PO::;;; no!?- N ...... V1 2 2 4 0 0 S U b R U U T l ? E L S L ? B ( F u , Y L , u X 1 X L ) O u 0 2 2 4 0 0 ? ???g? _,.,,??,h .ata:j?ai2f!?4!?o'''Fo.s ? , "? ? ,! ? * ?* .. *"*"_., ""??+ ?-? ? , -i881?'8t. 22aoo N? I ? 1 '1 ? ---HHo22aoo ? ??98o -????P'*N?t??sx?xL>???s? ?ru . _ .. . 2?Q_Q U 0 2 : .:: * ? + * ;< + X L J ' ? I F u . - --- u 0 "Jl)()'U-2 3 1 0 0 1 0 2 Y L = Y L ? C ( ? l ) * * I ? * C E k t N C 'fl ) + t. f< f N C Y 2 ) ) ) u 0 2 3 1 0 0 ? ? ? 8 8 ? ? J U R t t - 8 ? 8 ? ? j 8 8 ???;gg ? ,,. } 'tXV?'J!?i'????l??A??:?? to."3 2is9?""i? o . ??2*s4 a??9;?, -o=:2a;?????7'"4 , ?? -? ... _,,. . .. .... ?-g?J?g -? ? ' g g ? ? !J ? tJ ! ! 1 ? a ? a ? ? ? 5ta !) f g 3 ' 1 ' 0 6 1 4 0 ? 4 3 1 8 8 8 ? 1 ? 8 8 2 3 o O O - - - X = C ? U * x ? - ? - - -- -- - - -- ?- -? - O v 0 2 3 8 0 0 ?3jOO 13 Tl?ttul< 1+t??XJ - ?- -- -?-3-9-Qu ? 4 0 0 0 T 2 ? * T 1 ooo24000 24 1 0 8 ???t2 *f l - 0 ? 02 4 1 0 0 ?2?8o T :?::? t - - - -- --- ? -- - ---- - -U&?:?gg -2 4 ? 0 8 E R f N =? x p C ? x ? X ? * ( A 1 ? T 1 + A 2 * T 2 + A J ? T 3 + A 4 * T 4 + A S * T 5 ) O u 0 2 4 ? 0 0 224 ? 0 RE T \J R . ? O u 0 2 4 !:1 0 0 4 6 0 0 E N D 0 0 0 2 4 6 0 0 I ? N ? 0\ 2 1 7 APPENDIX 5 . 3 An Example o f the Kinetic Parameters Calculation (a) Calculated (c/c0) at each k 1 29 o C and Ea Level Temper- ? O o 335?4 O o 335?4 O o 487?4 O o 487?4 O o 4 1 1?4 O o 4 1 1? 4 O o 4 1 1? 4 O o 258?4 O o 564_!4 Experi- ature n X 10 X 10 X 10 X 10 X 10 X 10 X 10 X 10 X 10 mental oc a 93 7 3 9 3 73 83 103 63 83 83 c/c0 129 6 O o 94988 O o 94369 O o 92803 O o 9 1922 O o 93540 O o 94 192 O o 92656 O o 95879 0 . 9 1 266 O o 9 3884 1 O o 94072 O o 93389 O o 9 1505 O o 90538 O o 92394 O o 9 3 1 19 O o 9 1432 O o 95 1 37 0 0 89 738 O o 9 1 440 8 O o 9385 1 O o 93 157 O o 9 1 193 O o 90 103 O o 92031 O o 92857 O o 9 1049 O o 94960 O o 89254 O o 9 1 1 16 5 O o 9286 1 O o 92 1 7 7 O o 89798 0 0 88834 O o 90930 O o 9 1657 O o 89973 O o 94 185 O o 87796 O o 909 16 10 O o 92703 O o 920 19 O o 89576 O o 886 1 2 0 0 907 39 O o 9 1467 O o 89783 O o 9406 1 O o 87545 0 0 89939 120 7 O o 9 5886 O o 94861 O o 94074 O o 92 6 1 5 O o 94398 O o 95480 O o 92949 O o 96435 O o 92407 O o 9 1667 4 O o 94 109 O o 92754 O o 9 1547 O o 89636 O o 92052 O o 93498 O o 90 180 O o 94921 O o 89274 0 . 9 1 1 50 9 0 0 93644 O o 92269 O o 90890 O o 88955 O o 9 1471 O o 92951 O o 89589 O o 94547 O o 88510 O o 90942 2 O o 92 334 O o 90754 O o 89046 O o 86838 O o 89778 O o 9 1479 0 . 87637 0 0 93438 0 . 86265 O o 89839 (b) Calculated Absolute Residuals Temper- ? O o 335? 4 O o 335?4 O o 487?4 O o 487?4 O o 4 1 1?4 O o 4 1 124 O o 4 1 1?4 O o 258?4 O o 564_!4 ature X 10 X 10 X 10 X 1Q X 10 X 10 X 10 X 10 X 10 oc 93 73 93 73 83 103 63 83 83 129 6 O o 0 1 144 O o 00525 O o 0 104 1 O o 0 1922 O o 00 304 O o 00348 O o 0 1 188 O o 02035 O o 02578 1 O o 02632 O o 0 1949 O o 00065 O o 00902 O o 00954 O o 0 1679 O o 00008 O o 03697 O o 0 1 702 8 O o 02 7 35 O o 0204 1 O o 00077 O o 0 10 1 3 O o 009 1 5 O o 0 1 74 1 O o 00067 O o 03844 O o 0 1862 5 O o 0 1945 O o 01 261- O o 01 1 1 8 O o 02082 O o 000 14 0 . 0074 1 O o 00943 O o 03269 O o 0 3 1 20 10 O o 02764 O o 02080 O o 00363 O o 0 1 327 O o 00800 O o 0 1 528 O o 00 1 56 O o 04 122 O o02394 Average absolute residua l s O o 02244 O o 0 1 5 7 1 O o 00533 O o 0 1449 O o 00597 O o 0 1 207 O o 00472 O o 0339 3 0 . 0233 1 S tandard deviation O o 00700 O o 00673 O o 00514 O o 0053 1 O o 004 1 7 O o 00626 O o 0055 1 O o 00820 O o 0057 1 1 20 7 O o 04219 O o 03194 O o 02407 O o 00948 O o 02 73 1 O o 03813 O o 0 1 282 O o 04768 O o 00 740 4 O o 02959 O o 0 1604 O o 00397 O o 0 1 5 1 4 O o 00902 O o 02348 O o 00970 O o 037 7 1 O o 0 1876 9 O o 02702 O o 0 1 327 O o 00052 O o 0 1988 O o 00535 O o 02009 O o 0 1 353 O o 03605 O o 02432 2 O o 02495 O o 009 15 O o 00793 O o 0300 1 O o 00061 O o 0 1640 O o 02202 O o 03599 O o 03574 Average absolute residua1s O o 03093 O o 0 1 760 O o 009 1 2 O o 0 1863 O o 01057 0 . 02453 O o 0 1452 O o03936 O o 02 156 Standard deviation O o 00774 O o 00997 O o 0 1040 O o 00870 O o 01 1 70 O o 00952 O o 00527 O o 0056 1 O o 0 1 180 Overall average absolute residuals O o 0262 1 O o0 1655 O o 00701 O o 0 1633 O o 00802 0 .0 1 7 6 1 O o 00908 O o0 36 34 0 .02253 Standard deviation O o 00819 O o 00781 O o 00761 O o 00687 O o 0081 1 O o 00983 O o 00732 O o 00732 O o 00832 2 1 8 (c ) Multiple Regression Analysis (c) . 1 Using average absolute residual at each processing temperature : regression of residuals (Q) to X 1 , X2 , X 1 2 , x22 , X1X2 : Variable X1 X2 X 1 2 X22 X1X2 Coefficient 0 . 00985 -0 . 00400 0 . 00 1 5 1 0 . 00502 0 . 00 1 1 3 -0 . 00484 R2 = 85 . 1% , degree of freedom = 1 2 . t-ratio 4 . 1 1 -4 . 3 1 1 . 62 5 . 59 1 . 25 -3 . 0 1 As x22 was lower than 80% significance , therefore , the regression was repeated using only X1 , X2 , x1 2 , X 1X2 : Variable Coefficient t-ratio 0 . 0 1 225 8 . 34 X 1 -0 . 00400 -4 . 22 X2 0 . 00 1 5 1 1 . 59 X 12 0 . 00435 5 . 9 2 X 1X2 -0 . 00484 -2 . 95 R2 = 83 . 1 % , degree of freedom = 1 3 . 0 . (c ) . 2 Using individual residuals : regression of residuals (Q) to X 1 , X2 , x12 , X22 , X 1X2 : Variable X1 X2 X1 2 x22 X1X2 Coefficient 0 . 00964 -0 . 00392 0 . 00 145 0 . 00505 0 . 00103 -0 . 00475 R2 = 57 . 2% , degree of freedom = 75 . t-ratio 4 . 87 - 5 . 1 1 1 . 89 6 . 80 1 . 38 -3 . 5 7 2 1 9 As X22 was lower than 80% significance , therefore , the regression was repeated using only X1 , X2 , x1 2 , X 1X2 : Variable Coefficient t-ratio 0 . 0 1 183 9 . 90 X 1 -0 . 00392 -5 . 08 X2 0 . 00 145 1 . 88 X 1 2 0 . 00444 7 . 42 X1X2 -0 . 00475 -3 . 55 R2 = 56 . 1% , degree of freedom = 76 . (d) Decoding the Regression Equation and Minimization of Residual From equation : Q = j 0 . 0 1 225 - 0 . 00400X 1 + 0 . 00 1 5 1X2 + 0 . 00435X1 2 - 0 . 00484X1X2 j substitute X1 by X2 by giving k1 29oC - 0 . 4 1 1 5 x 10 -4 0 . 763 X 10-5 Ea - 83 10 and 220 I -3 -3 7 Q = -0 . 065 1 - 1 . 4904x10 k1 29oc + 2 . 699x10 Ea + 7 . 4652x10 k1 29oc -62 . 0238 k1 29oC Ea j Minimization of Q was done by : - 1 . 4904x103 + 1 4 . 9304x107 k1 29oc - 62 . 0238 Ea = 0 E.Q_ - -3 dEa - 2 . 6995x10 - 62 . 0238 k1 29oC Ea 0 = 0 . 4352x10-4 s- 1 - 1 80 . 7 kJ mole l O O R E A D ( 5 1 / ) X H I , X L?, Y H I , Y L O 0 0000 1 0 0 200 69 FORI1AT( 4F6 t 2 __,..0-0-0-().Q.Z{)O 3 U O W R I T E ( 6 , 1 ) ? H l , X L U , Y H l , Y L U 0 0 0 0 0 3 0 0 4 0 0 1 F O R M A T C T l O ' ' X = t , 2 ? 1 2 e ? / T 1 0 , t Y = ' ' 2 G 1 2 ? S > 0 0 0 00 4 0 0 ? 0 0 C A LL C O ? T C X H I , X L O , Y H I , Y L O ) 0 0 0 0 0 ? 0 0 ?08 r;?? 0088 8 Q _()_() ? c:u C T I ON FCTC X 1 , X 2 > _ 7 0 0 b O O F C T =?BS ( - 0 ? 0 6 5 l : i 4 9 0 * X l+2 : 6 9 9 5E - 3*X2+7 , 4 ? 5 2 E ? * X l *X l - 6 2 . 0 2 3 8 *X l *X 2 } 0 0 0 0 0 ? 0 0 9 0 0 R E T URN 0 0 0 00 9 0 0 1 ooo E t?O - ?---- 000 0 1 .0 ..0 0 1 1 0 0 S U 13 R 0 U T I N E C 0 ,?4 T ( X t I I , X L 0 , Y H I , Y L U ) 0 0 0 0 1 1 0 0 1 2 0 0 D I M E N S I O N Z C 4 1 , 4 1 ) , 1 P T C 4 1 ) 0 0 0 0 1 ? 0 0 1 J O O O X = C X H I - X L 0 ) / 4 0 ? 0 0 0 0 1 J O O 14 u 0 2 'l' = C Y HI ? Y L ? J I M 0 ? _o_o 0.0 t? 0_0 1 ? 0 0 M A x =? 1 ? E + o ( o o o o1 5 o o 1 ? 0 0 Z M I N = l ? E + 2 0 0 0 0 0 1 ? 0 0 1 7 0 0 Y = Y H I + O Y . 0 0 0 0 1 / 0 o 1 U 00 DO 1 I -1 ,4 {. ------- --- ---??- ---- ? ----- - - -- .-??-? -- - ??-? - ?-- - - ?- - --4>0-0 0 .1 d 0 0 1 9 0 0 Y = Y ? O Y ' 0 0 0 0 1 ? 0 0 2 0 0 0 X = X L O ? D X 0 0 0 0 2 0 0 0 2 1 0 0 D U 2 J = 1 , 4 1 0 0 0 0 2 1 0 0 26UC x-x+ox ouo022?o 2 3 0 0 I ' I ' I > = f ? T ( X , Y ) 0 0 0 0 2 ) 0 0 .2 4 0 0 f ( Z I , J . L T ? Z ?H N l G O T O 3 0 0 0 0 2 4 0 0 2 5 0 0 f C Z J , J , G T ? l ? A X ) GO T O 4 . 0 0 0 0 2 5 0 0 2600 ?0 TO 2 00002600- 2 7 0 0 ? Z M I N = l C l , J ) 0 000 2 7 0 0 2 6 0 0 X M I N= X 0 0 0 0 2 ? 0 0 2 9 0 0 Y MIN = Y 0 0 0 0 2 9 0 0 ?ooo 3H w-1 oaao?ooo ? 1 0 0 M N? J 0 0 00 l O O 2 0 0 0 0 G O T O 2 , 0 0 0 0 3 2 0 0 3 3 0 0 4 Z M A X ? Z C I , J ) 1' 0 0 0 0 3 3 0 0 -a-4oo )04Ax:ax oooo.3?.o..o . , 3 ? 0 0 Y H A X = Y 0 U 0 0 3 ? 0 0 3 b 0 0 I M A X = I 0 0 0 0 3 ? 0 0 31 0 0 J : 1 A X = J 0 0 0 0 3 7 0 0 , bOQ GO TO 2 ooog 3 ? QO 3 'i 0 0 2 C O N T I N U E I ouo 1 3 9 0 0 4 0 0 0 1 C O N T I N U E I 0 0 0 0 4 0 00 4 1 0 0 C * S C A LE THE l V A L U E S ? 0 0 00 4 1 00 -4 :t! 0 0 0 0 2 1 I ? 1 ' 4 1 ? 0 0 0 0 A ? 0.0 4 3 0 0 D O 2 1 J a 1 , 4 1 0 0 0 0 4 3 0 0 4 4 0 0 Z C I , J ) : C ( Z ( l , ? ) ? Z M I N l / C Z M A X ? Z H I N ) ) * l O . 0 0 0 0 4 ? 0 0 4 ? 0 0 2 1 C O N T I N U E 0 0 0 0 4 5 0 0 AbOQ ZZ=ZHI N+ C [I QAT C t?l ) lt' ZMA X?lMI N l /1 ?b..OO ,...... (1) ...._, CJ 0 ::l rt 0 c ., '1::1 f-' 0 rt '1::1 ., 0 )Q ., Ql El N N ? 4 7 0 0 Z Z 1 i Z Z + \2-M A X ?t i? l N ) / 1 0 ? 0 0 0 0 4 7 0 0 4 0 0 0 W R I TE C 6 -' 1 2 1 ) 0 0 0 04 ? 0 0 4 9 0 0 1 2 1 F O R ? A T C ' l ? , T 1 0 , ' X 2 V A L U E S ' ) 0 0 0 0 4 9 0 0 -5-UOu DO 122 1.<=1,.41 QuQ05UJ)0 5 1 0 0 Y = Y H I ? C F L O A T ?< K ? l ) ) ? D Y 0 0 0 0 5 1 0 0 5 ? 0 0 D O 3 8 2 I A N = 1 , ? 1 O u 0 0 5 2 0 0 S l U O 3 6 2 I P T C I A ? > = Z C K , I A N ) 0 0 0 0 5 3 0 0 s 4 o o w e 1 r r c 6 t1 2 4 l v ,c I e 1 c ' >. 1 = 1 , 4 1 > OJ.L0.:8t 5. !t..O .O ? ? 5 5 0 0 1 2 4 F O R M A T C T 1 5 , G 1 2 ? 5 , T 3 0 , 4 1 C i l , lX ) ) 0 0 0 ??00 5 6 0 0 1 2 2 C O N T I N U E 0 0 0 0 5 6 0 0 . 5 7 0 0 C ? L A B E L X l A X I S 0 0 0 0 5 7 0 0 ? 0-_- -0 X-XJa..LX H I ? )( L 0 l 15 ? . __ Q..o.a.D_5 ti 0 0 5 Y O O Y. X 2 = X L O + D X X O U 0 0 5 Y O O 6_ 000 XX3=XX2+0x? , 000060crcr ; 6 1 0 o x x 4= X x 3+ o x . ? oo oo 6 1 o o 6 2 0 o x x s = x x 4 +?x x o o o o 6 ? o o 6?0 0 WRfi''P' 1?7? 0 0 0 0 6 3 0 0 6 0 0 1 2 0R i? T T)O , ' I ' , se 15X, t I ' )) - -.- ?--- ? - - ?-- - O \J U 0 6 4 0 0 6 5 0 0 W R I T E C 6 -' 1 2 ) X L O , X X 2 , X X 3 , X X 4 , X X S , X) H l 0 0 0 0 6 ? 0 0 6 6 0 0 1 2 7 F O I? t 1 A T ( T ? S , G 1 2 e 5 , 5 C 4 X , ? 1 2 ? 5 ) O O U0 6 o O O 6 7 0 u W R I T E C 6 , 9 9 6 ) O u 0 0 6 7 0 0 ?600 996 fORMAT OOOO?b? 6 9 0 0 C ? NOW DO T H E K E Y 0 0 0 0 6YOO 7 0 0 0 W R I T E C 6 , 1 2 8 > 0 0 0 0 7 0 0 0 7 1 0 0 1 2? f 08MAT C ' 1 ? , / t T 2 0 , t KE Y T O C O N T O U R S ' > . 0 0 0 0 7 1 00 12oo oo so I=t , lo ?or2?o 7 3 0 0 Z Z = Z t 1 I N +( C F L U A T C l ? 1 ) ) * C Z M A X .. Z M I N ) 1 1 0 ? 0 0 0 0 7 J 0 0 7 4 0 0 Z Z 1 = Z Z + Z M A X ? l M I N ) / 1 0 . 0 0 0 0 7 4 0 0 7 ? 0 0 Y. K = I ? 1 0 0 0 0 7 5 0 0 7000 WRITtC?' 129)KK1lf1ZZ1 00007600 9 70 0 -1 2 9 F ORMAT C T 1 0 , f OR S Y M B O L 1 1 l 3 , ? Y I S BE T W E EN ' , G 1 2 ? 5 , ' AN O ? , G t 2 ? 5 > 0 0 0 0 7 7 0 0 8 0 0 1 5 0 C ONT I NUt . 0 0 0 0 7 ?0 0 9 00 WRITEf6 , ?5+ ) ???X , lHtX 0 0 00 7 9 0 0 8 o o o 1 5 1 D R A C 0 , M X V A L I S A T ' , I T 3 0 , ' X 1 2 t , G 1 2 ? 5 I T 3 o , ' X 2 = ' , G 1 2 ? 5 I > --u-uuue 0 l> 0 8 1 0 0 W R I T E C 6 , 1 5 2 l Z M A X 0 0 0 0 8 1 0 0 6 ? 0 0 1 5 2 F O R M A T C T l O , ' A N D I T I S ' , G 1 2 ? 5 l 0 0 0 0 8 2 0 0 g3 ou ?ETURN o u o 0 8 3 o o 4 0 0 ? N 0 - ---o-wo-e"ll 0 0 N N N ,....._ .--1 I Cl) .--1 0 s t-") ,!G ..._, ('(j ? ( f ) Contour Plot Based on Decoded Equation Shown in ( d) 0 147 ? 0.; .9..> 1 26 105 84 + 63 0,? (;:)" (;:) " 42 0 . 25 0 . 30 0 . 35 0 . 40 0 . 45 0 . 50 0 . 55 + denotes the optimum point 223 ' . 0 . 60 APPENDIX 5 . 4 Es timation of k1 29oc for the Design for Ascorbi c Acid 224 From equation ( 5 . 4 ) , the final concentration at the end of a small time interval , ?t , was : = where fn (k 1 29oC , Ea , T) Ea 1 1 is exp (-k1 29oC exp (- Bl(T - 402) ) ?t) If T is constant , fn (k1 29oc , Ea , T) will be constant as well . So at the end of the second ?t , the f inal concentration will be : be : Therefore , at the end of the nth ?t , the final concentration will 0 0 For run no . 6 ? assuming the average temperature was 1 10 C or 383 K over the processing time of 2952 + 2400 seconds , k could be calculated from the measured initial and f inal concentration of ascorbic acid of -2 -2 -1 25 . 68 x 10 and 24 . 10 x 10 mg g using ?t of 72 seconds and assuming that Ea was 84 . 2 kJ mole- 1 (Chit taporn , 1 9 77 ) . As n?t = 2952 + 2400 n = 2952 + 2400 7 2 ? 74 So 74 24 . 10 X lQ-Z fn (k1 29oc , 84 . 2 , 383) = -----25 . 68 X 10-Z fn (k 1 29oC ' 84 . 2 , 383) ? 0 . 999 196 84 . 2 1 1 exp (-k 129oC exp (0 . 0083 (383 - 402) ) x 72 ) = 0 . 999 196 10-4 8- 1 k 1 29oC = 0 . 4 1 15 x 225 226 APPENDIX 5 . 5 De termination of k1 29oc and Ea for Riboflavin, Colour Y , and Viscosity Using Equivalent Processing Time (a) Riboflavin The equivalent processing time at specified temperatures can be calculated if the kinetic reaction rate at that temperature is known by : ln .?.__ -k t c r r 0 1 c t - k ( ln -) r c r 0 where t is an equivalent processing time a t reference temperature , r . r -4 - 1 Knowing that the k1 29oC o f ascorbic acid was 0 . 435 x 1 0 s , the equivalent processing time at 1 29?C , t 1 29 o C , could be calculated f rom - the experimental of c/c of ascorbic acid . 0 Run no . 6 1 8 5 10 ( c /c ) ascorbic acid o exp , 0 . 9 3844 0 . 9 1 440 0 . 9 1 1 1 6 0 . 909 1 6 0 . 89939 24 . 3 34 . 3 35 . 6 36 . 5 40 . 6 As t 1 29oC for ascorbic acid and riboflavin should be the same , c /c0 for riboflavin corresponding to t 1 29 oC was calculated : Run no . t 1 29?C , min ( c /c ) exp , riboflavin 0 6 24 . 3 0 . 9 7844 1 34 . 3 0 . 9 58 1 3 8 35 . 6 0 . 94745 5 36 . 5 0 . 94025 10 40 . 6 0 . 93537 m in 227 Regression of ln c /c0 with t 1 29oC resul ted in k1 29oC of 0 . 2459 -4 - 1 x 10 s with 99 . 9% significance and 0 . 9 73 correlation coefficien t . - 1 As the Ea o f ascorbic acid was 8 1 kJ mole , the k1 20oC could be calculated from : k Ea (Tr - T) kTr exp (- RTTr ) -4 -81 ( 1 29- 1 20) 0 ? 435 x 10 exp <0 . 0083 ( 1 29+273) ( 1 20+273) ) 0 . 2495 x 10-4 s- 1 The equivalent processing time a t 120?C was again calculated based on the experimental c/c resulted from 1 20?C processing temperature 0 experiments . These calculated equivalent processing t imes were corres- ponded to experimental c /c of riboflavin resulted from 1 20?C processing 0 temperature experiments as shown below . Run no . t 1 20?C ' m in ( c /c ) , riboflavin 0 exp 7 58 . 1 0 . 9 7006 4 6 1 . 9 0 . 95 1 59 9 63 . 4 0 . 94575 2 7 1 . 6 0 . 93428 Again , regression of ln c/c to t 1 20oc was done ; k1 20oc for riboflavin - -4 -? was found to be 0 . 1357 x 10 s wi th 99 . 9% level of significance and 0 . 964 correlation coefficient . Then , the activation energy of riboflavin was calculated from : Ea ln ln k 0 ( 1 29 C) (RTTr k 1 20oC Tr - ( 0 . 2459 X 10 -4 0 . 1 357 10-4 X 87 kJ mole-1 T) ) ( 0 . 0083 X 402 X 393) 402 - 393 228 (b) Colour, Y Same as riboflavin , the t 1 29oc for ascorbic acid and colour Y should be the same . The c/c0 for colour , Y , corresponding to t1 29oc was calcu? lated from the analytical results : Run no . t 1 29?C ' min (c/c ) exp ' colour Y 0 6 24 . 3 0 . 8 1 30 1 34 . 3 0 . 79 16 8 35 . 6 0 . 7 782 52 36 . 5 0 . 7578 10 40 . 6 0 . 7 352 Regression analysis gave k 129oc of 1 . 0633 x 10 -4 s- 1 with 99 . 9% significance and 0 . 989 correlation coefficient . At 1 20?C processing temperature : Run no . t 1 20?C ' min (c/c ) exp ' colour Y 0 7 57 . 8 0 . 90 1 0 4 6 1 . 6 0 . 8753 9 63 . 1 0 . 8269 2 7 1 . 2 0 . 7684 Regression analysis gave k1 20oc of 0 . 4660 x 10 -4 s- 1 with 99 . 9% s ignificance and 0 . 9 7 3 correlation coefficient . The activation energy was 1 20 . 9 kJ mole- 1 for colour Y . ( c ) Viscosity The method as in riboflavin was used . At 1 29?C processing temperature : Run no . t 1 29?C ' min (c/c ) exp ' viscosity 0 6 24 . 3 0 . 8 1 30 1 34 . 3 0 . 7 9 16 8 35 . 7 o . 7 782 5 36 . 5 0 . 7578 10 40 . 6 0 . 7352 Regression analysls gave k1 29oC of 1 . 2348 x 10 -4 s- 1 with 99 . 9% significance and 0 . 996 correlation coefficient . 0 At 1 20 C processing temperature : Run no . t 1 20?C ' min (c/c ) exp' viscosity 0 7 5 7 . 8 0 . 90 10 4 6 1 . 6 0 . 8753 9 6 3 . 1 0 . 8269 2 7 1 . 2 0 . 7684 4 - 1 Regression analysis gave k1 20oc of 0 . 4633 x 10 - s with 99 . 9% significance and 0 . 932 correlation coefficient . - 1 The activation energy was 143 . 6 kJ mole for viscosity . 22-9 5 0 $ 0 P T = 1 . 0 0 0 0 0 0 5 0 1 1 0 0 D I M t ? ? ?? N T C 1 ? , 1 s > , T H < 1 ? , 1 ? ) , b C 1 0 > I X J l B C 1 o > , B R A < l v > , x J u b C 1 o > , o o o o o 1 o o I ?-z-u- o -? ? -en :n . , q 0 ) , TA V E ( 2 0 , 2 0 > ? m f-t-211 2 0 ) , V \1-5 rt-5 ) l'-'t rtt: it C 2 u-, 2"0- ) -, ------------e?a-ro-e-- I ? u o * F ? 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