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 
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MODELING HEAT TRANSFER IN BUTTER 
PRODUCTS 
A thesis presented in partial fulfilment of 
the requirements for the degree of 
Doctor of Philosophy (PhD) 
In 
Bioprocess Engineering 
Institute of Technology and Engineering 
Massey University 
Palmerston North, New Zealand 
AMSHA NAHID 
2007 
ABSTRACT 
Butter keeping qual i ty and pal let physical stabi l ity during transport and storage are dependent on 
the temperature distribution through the product. Understanding these temperature changes are of 
vital importance for the dairy industry with regard to butter manufacture, storage and shipping. 
Three dimensional mathematical models of heat transfer were developed to predict thawing and 
freezing in butter products. These models require accurate thermophysical data as an input. Specific 
heat capacity and enthalpy of butter with different composition was measured using Differential 
Scanning Calorimetry. The specific heat capacity of butter differs for cool ing and heating 
operations due to significant supercooling and delayed crystal l ization of the fat fraction of butter at 
temperatures wel l  below the equil ibrium phase change temperature during cooling. This reduces the 
heat capacity for cooling relative to that for heating. 
Thawing of individual blocks of butter was accurately predicted by the conduction only model (no 
mass transfer l imitations) with equilibrium thermal properties giving accurate predictions when the 
butter was completely frozen before thawing. For partial ly frozen butter the conduction model with 
the measured temperature dependent specific heat capacity data for unfrozen butter including 
melting of some of the fat fraction gave accurate predictions. 
For freezing it was observed that water in the butter supercools  many degrees below its initial 
freezing point before freezing due to its water in oil structure. Experiments suggested that duri ng 
freezing release of latent heat observed as a temperature rebound is controlled as much by the rate 
of crystal l isation of water in  each of the water droplets as by the rate of heat transfer. A conduction 
only model including water crystal lization kinetics based on the Avrami Model predicted freezing 
i n  butter successfu l ly. Simple models with equi librium thermal properties and nucleation only 
kinetics (based on homogenous nucleation theory) or the sensible heat only model (no release of 
latent heat) gave poor predictions. 
The models for i ndividual blocks were extended to predict heat transfer in  butter pal lets. A butter 
pallet contains product, packaging material and the air entrapped between the packaging and butter 
cartons. Measurements were made for freezing and thawing of ful l  and half pal lets at a commercial 
storage fac i lity and in the University laboratory. Thawing and freezing in wrapped tightly stacked 
pallets was predicted accurately by the conduction only model with effective thermal properties 
(incorporating butter, packaging and air) estimated by the paral lel model .  
For unwrapped tightly stacked or loosely stacked pallets there is  potential for air flow between the 
adjacent cartons of butter. An alternative approach was developed which consisted of modeling the 
pallet on block by block basis using effective heat transfer coefficients for each surface. Different 
heat transfer coefficients were used on different faces of the blocks depending on the location of the 
block in the pallet. This approach gave good predictions for both unwrapped tightly stacked and 
loosely stacked pallets using the estimated effective heat transfer coefficients from the measured 
data. Further experimental and/or model l ing work is required in order to develop guidel ines for 
estimating effective heat transfer coefficient values for internal block face for i ndustrial scenarios. 
11 
ACKNOWLEDGEMENTS 
It has been said by a wise person, "Preserve your knowledge by writing it". This PhD thesis consists 
of knowledge I gained during the last several years of my study at Massey University. Gaining this 
knowledge and i ts preservation would have not been possible without the help (and patience) of a 
number of people. I would l ike to thank to these people for a huge variety of reasons. 
Firstly I l ike to thank my supervisors Associate Prof. John Bronlund, Professor Don Cleland 
(Massey University) and Bruce Philpott (Fonterra Co-operative Group Limited) for their 
continuous support, guidance and constructive criticism while supervising this work. I could not 
have imagined having a better supervising team for my PhD. 
My special thanks to Or. Ashraf Choudhary (Member of New Zealand Parliament) for helpi ng me 
to come and study in  Massey University and advising me to pursue Doctoral research. 
I am grateful to The New Zealand Foundation for Research, Science and Technology (FRST) 
for Enterprise scholarship funding and Fonterra Co-operative Group Ltd for funding the project 
costs. 
Lot of thanks goes to the administrati ve staff of ITE, special ly Joan Brookes, Gayle Leader, Trish 
O'Grady, Alisha Anan and John Hayward for their help and support throughout the project. 
Thanks to Susan Lane for assisting me with the use of DSC and sample preparation and to Or. 
David Oldfield and Chris Ballentyne for their help during the early stage of the project. 
I appreciate Grant Gilbert at Whareroa site for his great help and time in conducting experiments 
at the dairy factory, Garry Radford for keeping tons of butter in freezers and then disposing off i t, 
John Edwards who was always there for me whenever I needed a hand in experimental work, 
Humphrey O'Hagan for cutting, chopping and dri l l ing my butter, Bruce Collins and Craig 
Bellhouse for giving me a hand in understanding data logging equipment. 
III 
Huge thanks to Dr. Tehseen Aslam and Muhammad AIi (my Pakistani friends and colleagues at 
Massey University) for their support and help during my stay in  New Zealand especially  Dr. 
Zulfiqar Butt and Dr. Zaker Hussain, who always supported me as my real brothers. 
I won' t  be able to forget the support, understanding and encouragement given by the Pakistani 
community in Palmerston North and Wel l ington specially  Or Khalid Sandhu, Dr. Razia Sandhu 
and Aunty Salima Bibi for thei r moral support and prayers. 
A very sincere gratitude to my friends Misbah Akhar, Asifa Butt, Shazia AIi, Samina Zakir, 
Erum Tariq, Nasreen Bhali, Rizwana Tehseen and Robina Babar for their help and support that 
made the last stage of my PhD a bit easier. 
I am forever indebted to my father Professor Abdul Hamid ( late), my mother Nasim Akhtar, my 
father in law Choudhary Nazir Ahamad ( late) and my mother in law Khurshid Bibi for their 
prayers and support without which I would have never been able to complete this task. Thanks to 
my brothers Mumtaz, Abbas, I1yas, Usman, and Suleman, my sister Uzma, my sisters and 
brothers in law and al l  other fami ly  members for their encouragement. 
Lastly my hubby Tahir, my daughter Bazal and son Hashim for their love, understanding, endless 
patience and encouragement when it was most required. 
iv  
TABLE OF CONTENTS 
ABSTRACT .................................................................. i 
A C KN 0 WLEDG EMENTS .................................................. iii 
TABLE OF CONTENTS ...................................................... v 
LIST OF TABLES ...................... ....................................... xii 
LIST OF FIGURES ............................................................. xv 
LIST OF APPENDICES .................................................. xxvii 
CHAPTER 1 :  PROJECT OVERVIEW 
1.1 Background and Project Definition . .. . .. . .... . .. . . .. . .. . ... ..... 1-1 
1.2 Project Objectives ...... ..... ... . ... .. .. ... . . . . .. ......... . . . . ...... 1-2 
CHAPTER 2: LITERATURE REVIEW 
2.1 Introduction .... . .. .. . . . . .. . . . . . . .......... .. . . . .. .. . . .. . .... . . ..... .. 2-1 
2.2 Butter Composition and Structure . . . .. . . . . .. ..... . ....... . . . . . ... . ... 2-1 
2.3 Milkfat Composition . . . ... ..... . ... . . .. .. .. . . .. . .... . .. .... .. . .. . . . 2-2 
2.4 Crystallisation of Fat. .. . ..... . .. . ......... . .. ... . .. . . .. . . . . ........ 2-3 
2.5 Aqueous Phase of Butter. . ... . .... ............ .. . . . . . . . .. . . . .. .. .. 2-6 
2.6 Crystallisation of Aqueous Droplets . .......... . . . . . . .... . ... . . . .  2-6 
2.7 Manufacturing Process .. . ............... .. ... . . . . . .. .. .... . . . ...... 2-9 
2.7.1 Fritz Buttermaking Process . . . . . . . . .. . . . . . . . .......... . . . ...... 2-9 
2.7. 2 Ammix Buttermaking Process .. . . ... . . . . . .... .. . .... . . . . .. ... 2-10 
2.7. 3 Difference Due to Manufacturing processes ... ...... . . .. . . . .. 2-11 
2.8 Thermophysical Properties .. . .. . .. . . ... ..... . .... . . . .. .. . . . . .. . 2-11 
v 
2.8.1 Initial Freezing Point. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  2-1 2 
2.8.2 Density ........................................................ 2-14 
2.8.3 Thermal Conductivity ......................................... 2-16 
2.8.4 Specific Heat Capacity and Enthalpy ............................ 2-19 
2.9 Heat Transfer Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. .. . . . .2-24 
2.9.1 General Heat Conduction Equation ........................... 2-24 
2.9.2 Initial and Boundary Conditions .............................. 2-25 
2.9.3 Analytical Solution for Conduction Problems ................ 2-27 
2.9.4 Numerical Solutions for Heat Transfer ........................ 2-27 
2.9.5 Freezing Models for Water - enriched foods .................... 2-2 8 
2.10 Literature Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . 2-30 
CHAPTER 3: ESTIMATION AND MEASUREMENT OF 
THERMAL PROPERTIES OF BUTTER 
3.1 Introduction ......................................................... 3-1 
3.2 Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  3-1 
3.3 Initial Freezing Point. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  3-7 
3.3.1 Measurement Methods ......................................... 3-7 
3.3 . 1 .1 Extrapolation Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  3-8 
3 .3 . 1 .2 Cal ibration with the Standard Solution . . . . . . . . . . . . . . . . . . . . .  3-9 
3.3.2 Measurement of Initial freezing Point of Butter. ................... 3-9 
3.3.3 Alternative Approaches . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  3-12 
3 .3 .3 . 1 Empirical Curve Fitting Models . . . . . . . . . . . . . . . . . . . . . . . . .  3-12 
3 .3 .3 .2  Theoretical Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  3-13 
VI 
3.3.4 Estimation of Initial freezing Point of Salted Butter. . . . . . . . . . . .  3-16 
3.4 Density ..................................................... , ....... 3-17 
3.5 Specific Heat Capacity and Enthalpy ........................... 3-20 
3.5.1 Measurement Techniques ..................................... 3-20 
3.5.2 Measurement of Specific heat Capacity and Enthalpy of 
Butter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  3-28 
3.5 .2.1 Generic Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  3-28 
3.5 .2.2 Measurement Technique . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . 3-29 
3.5 .2.3 Scanning Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . .  3-32 
3.5.2.4 Phase Separation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  3-33 
3.5 .2.5 Sample Homogeneity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-34 
3.5 .2.6 Variation in Frozen Water Contents . . . . . . . . . . . . . . . . . . . . . .  3-35 
3.5 .2.7 Equilibrium Versu Supercooling of the Water Phase . . . . . .  3-36 
3 .5 .2.8 Equilibrium versus Supercooling of the Bulk Fat Phase . . . . .  3-39 
3.5.2.9 Hysteresis Effects Brought About by Microstructure . . . . . . .  3-40 
3.5.2. 1 0  Method Summary . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-41 
3.5.2. 1 1  Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  3-42 
3 .5.2. 1 2  Adjusting and Modeling the Measured Data . . . . . . . . . . . . . .  3-44 
3.5 .2.13 Comparison With Literature Data . . . . . . . . . . . . . . . . . . . . . . .  3-51 
3.5.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  3-52 
3.6 Thermal Conductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  3-52 
3.6.1 Estimation of Thermal Conductivity of Butter. .............. 3-55 
3.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  3-57 
VII 
CHAPTER 4:  HEAT TRANSFER IN BUTTER BLOCKS 
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . ... 4-1 
4.2 Material and Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. .4-1 
4. 2.1 B utter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  4-1 
4. 2.2 Tempe rature Measurements .. . . . . . . . . . . . . . . . . . . . . . .. . . . . . . ... . .  .4-2 
4. 2.3 Posit ion of Thermocouples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  .4-2 
4.2.3 . 1 Salted Pat (B 1 8) . . .. ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  .4-3 
4.2.3 .2 Unsalted Pat (B  1 6) ..................................... .4-3 
4.2.3 .3 Salted Block (B  1 5) .. . . .. . . . .. .. . . .. . . . . . . . . . . . . . . . . . . . . .4-4 
4.2.3 .4 Unsalted Block (B 1 9) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  .4-5 
4.2.4 Initial and Ambient Conditions .. . . ... ... . . . . . .... .... . . . . . . . . . .. . .  .4-5 
4.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . .. . . .. .4-7 
4.3 . 1 Hea t  Transfer  in Salted B utter Pats . . . . . . . . . . . . . . . . . . . . . . . . . . .  .4-7 
4.3 . 2 Heat Transfer  in Unsalted B utter Pats . . . . . . . . .. . . . . . . . . . . . . . .  4-10 
4.3 .3  Hea t  Transfer in Salted B utter B locks . . . . . . . . .. . . . . . . .. . . . . . .  4-15 
4.3.4 Heat T ransfer in Unsal ted B utter B locks . . . . . . . .. . . . . . . . . . . . .  4-21 
4.4 Conclusions . .. . . . . .. . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . .  .4-26 
CHAPTER 5 - MODELING HEAT TRANSFER IN BUTTER 
5.1 Introduction . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  5-1 
5.2 Model Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  5-1 
5.2. 1 Conceptual Model . . . . . . . . .. . . . . . . . . . . . . . . . . .. . . . .. . . . . . . . .. . . .  5-1 
5 . 2. 2  Validit y o f  Assumptions . .. . . . . .. . . . . . . . . . . . . . . . . . . . .. . . . . . . . . .  5-2 
5 . 2.3 Mathematical Formulation . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . .  5-4 
V 111 
5.3 System Input Parameters . . .. . . . . . . . .. . . . . . . . . . .. . . . . . . . . . . . . . . . . . .  5-6 
5.4 Numerical Solution of the Heat Transfer ModeL .............. 5-6 
5.5 Maths Checking .................................................... 5-7 
5 .5  . 1  Numerical Error Checking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  5 -7 
5 .5 . 2 Checks against Previousl y Val idated Solution . . . . . . . . . . . . . . . . .  5-8 
5.6 Evaluation of Mathematical Model . . . . . . . . .. . . . . . . . . . . . . . . . . . . . .  5-9 
5 .6. 1 Sensitivity  Anal ysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  5-9 
5 .6 . 2 Model Predictions - Thawing . . . . . .. . . . .. . . . . . . . . . . . . . . . ... . . .  5-11 
5 .6.2 . 1 Predicting Thawing of Pats . .. . . . . . . . . . . . . . . . . . . . . . . . . . .  5-12 
5 .6.2.2 Predicting Thawing of Blocks .. . . . . . . . . . . . . . . . . . . . . . . . . .  5-18 
5 .6 . 3 Model Predictions - Freezing .. . . . .. . . . . . . . . . . . . . . . . . . . . . . ... .  5-25 
5.6.3. 1 Predicting Freezing of Pats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  5-25 
5.6.3 .2 Predicting Freezing of Blocks . . . . . . . . . . . . . . . . . . . . . . . . . . .  5-30 
5.7 Conclusions ........................................................ 5-36 
5.7. 1 Thawing of  B utter . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  5-36 
5 .7.2 Freezing of B utter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  5-36 
CHAPTER 6 - MODELING FREEZING OF BUTTER 
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  6-1 
6.2 Model Formulation ................................................ 6-2 
6.3 Model Freezing Kinetics ........................................... 6-4 
6.4 Measurement and Estimation of Input Data .................... 6-9 
6.4. 1 Measurement o f  Nucleation Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  6-10 
6.4. 2 S peci fic Heat Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  6-16 
IX 
6.4. 3 Equilibrium Freezing Temperature . . . . . . . ... . . ... . . ..... . . . . . .  6-19 
6.4.4 Latent Heat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..... . . . . . . . . . . .... 6-21 
6.4.5 Thermal Conducti vity . . . . . . . . . . . . . . . . . . . . . . . . ... . . . . . . . . . . . .. 6-21 
6.4.6 Model Solution ............................................................ 6-21 
6.5 Nucleation Only Model Predictions ........ . . . . . . . . . . . . . . . . ... ... 6-21 
6.6 Avrami Model Predictions . . . .. . ... . . . .. . . ... . . . . . . . . . ... . . . . . . . . 6-23 
6.6. 1 Unsalted Butter B lock (BI9) .................................. 6-23 
6.6. 2 Sensiti vity  Anal ysis .......................................... 6-25 
6.6.3 Salted and Un salted Pats ...................................... 6-26 
6.6.3 . 1 Salted Pat CB 1 8) . . . . . . . . .... . . .... . . . . . . . . . . . . ... . . . . ..... 6-26 
6.6 .3 .2 Unsalted Pat CB 1 6) .. . . . . . . . . . . ... . . . . . . . . . . ... . ... . . . .... 6-29 
6.6.4 Predictions fo r Salted Butter Block ........................... 6-30 
6.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . ....... . . . . . . . . . . . . . . . . . . . . . .. 6-31 
CHAPTER 7 :  HEAT TRANSFER IN PALLETIZED BUTTER 
7.1 Introduction . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... . . . . . .... 7-1 
7.2 Data Collection . . . . . . . . . . ... . . ... . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . ... 7-1 
7. 2.1 Full Pallet Trials ................................................ 7 -3 
7. 2. 2 Hal f  Pal let Trials ................................................. 7-6 
7.3 Experimental Results . . . . . ... . . . . ... . . . ... . . . . . . . . . . . . . . . . . . . . .... 7-11 
7. 3.1 Trial 1- Wrapped Ful l Pallet . ................................. 7-11 
7.3 . 2 Trial 2 - Unwrapped Full Pallet . .............................. 7-17 
7.3 . 3 Trial 3 - Wrapped Loosely Stacked Half Pallet .............. 7-25 
7. 3 .4 Trial 4 - unwrapped Tightl y Stacked Hal f  Pallet ............ 7-33 
x 
7.3 .S Trial S - Unwrapped Loosely Stacked Hal f  Pallet . . . ........ 7-41 
7.4 Conclusions ........................................................ 7-50 
CHAPTER 8 :  MODELING HEAT TRANSFER IN 
PALLETISED BUTTER 
8.1 Introduction ......................................................... 8-1 
8.2 Modeling Approaches .............................................. 8-2 
8.2.1 Modeling Heat Transfer  in Pallets With No Internal Ai r 
Flow ....................................... ....... ....... . ...... 8-3 
8 .2 . 1 . 1  Calculation of the Volume of Air Gaps .................... 8-3 
8.2 . 1 .2 Effective Thermal Conductivity Model. ....... ............ 8-4 
8 .2 . 1 .3 Effective Density . . .................................. . ... 8-5 
8.2 . 1 .4 Effective Specific Heat Capacity and Enthalpy .............. 8-5 
8.2. 1 .5 Effective Heat Transfer Coefficients, Ambient and Initial 
Conditions ........................................................... 8-7 
8.2 . 1 .6 Results and Discussion . . ....... . . ..................... 8-9 
8.2.2 Modeling Heat Transfer  in Pal lets With Inte rnal Air Flow .... 8-15 
8.3 Conclusions ........................................................ 8-29 
CHAPTER 9:  CONCLUSIONS AND RECOMMENDATIONS 
9 .1 Conclusions ............................................................................ 9-1 
9.2 Recommendations .................................................................. 9-2 
REFERENCES .............................................................................. R-1 
APPENDICES ... ......... ................... . ....... . . ....... .......... .................... A-1 
XI 
Table 2 . 1 
Table 2 .2  
Table 2 .3  
Table 2 .4 
Table 2 .5  
Table 2 .6  
Table 2 .7 
Table 2 .8 
Table 2 .9  
LIST OF TABLES 
Fatty acids composition  of spring and summer rnilkfat. . . . . . . . . . . . . . . . . . . . . . . . . . . . .  2-3 
Composition of butter used by Pham ( 1 994) and Lindsay & 
Lovatt ( 1 993). . . . . . . . . . . . .  . . . . . .  . . . . . .  . . .  . . . . . .  . . . . . . . . . . . . . . .  . . . . . . . . .  . . .  . . .  . . .  . . .  . . . . . .  . . .  . . .  . . . . . .  . . . . . .  2 - 1 3  
Freezing point depression of salted and unsalted butters. . . . . . . . . . . . . . . . . . . . . . . . . . .  2- 1 3  
Density of butters as a function of temperature and air contents . . . . .  . . .  . . . . . . .  2 - 1 4  
Composition of butter and fitted parameters for the thermal conductivity 
mode1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  2 - 1 6  
Thermal conductivity of butter (Olenew, 1 959) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  2- 1 7  
Specific heat capacity of butter for different composi tion 
(Houska et a1. 1 953). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . .. 2 - 1 9  
Average specific heat capacity of unsalted butter as a function of 
Temperature (McDowell ,  1 953). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  2-20 
Enthalpy of butter for different composition Houska et a1 . 
( 1 994) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  2-2 1 
Table 2 . 1 0  Parameters fitted to enthalpy equations for different compositions of 
Table 3 . 1 
Table 3 .2  
Table 3 .3  
Table 3 .4 
Table 3 .5  
Table 3 .6  
Table 3 .7  
Table 3 .8  
Table 3 .9 
Table 3 . 1 0  
Table 3 . 1 1  
Table 3 . 1 2  
butter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  2-22 
Butter samples collected from different seasons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  . 
Composition of butters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  . 
Sol id  fat contents of butter at different temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  . 
Measured initial freezing point of unsalted butters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  . 
Solute concentration in the aqueous phase of butter compared with TiJ· .... . 
Element analysis of salted, unsalted and lactic butter.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  . 
Initial freezing point  estimated using salt solution and empirical curve 
3-2 
3-3 
3-4 
3- 1 0  
3- 1 1 
3- 1 5  
fi tti ng. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  3- 1 7  
Density of butter measured at 1 2°C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  3- 1 8  
Density of butter measured at 20°C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  . 
Cal ibration standards for the DSC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  . 
Constants for speci fic heat capacity of sapphire . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  . 
Comparison of measured and DSC derived initial freezing point . . .  . . . . . . . . . .  . 
3- 1 9  
3-29 
3-30 
3-43 
XII 
Table 3 . 1 3  
Table 3 . 1 4  
Table 4. 1 
Table 4 .2 
Table 4 .3 
Table 5 . 1 
Table 5 .2  
Table 5 .3  
Table 5 .4 
Table 5 .5  
Table 5 .6 
Table 5 .7 
Table 5 .8  
Table 5 .9 
Table 5 . 1 0  
Table 5 . 1 1 
Table 6 . 1 
Table 6.2 
Enthalpy equations parameters for all  butters . . . . . . . . . . . .. . . ... . . . . . . . . . . . . . . . . . . . . . . . . . . .  3-47 
Thermal conductivi ty of butter components in frozen and unfrozen range 
using Chio & Okos ( 1 986) models . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . .  3-56 
Dimensions and type of butter used in experiments (without 
packaging).. . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . .. . .. . . . . . . . . . . . .. .. . . . . . . . . . . . . . . . . . . . .. .. . . . . ..... . . . . . . . . . .  4- 1 
Thermocouple position in the butter block with the origin as shown 
in Figure 4.3 . . . . . . . . . . . . . . . . . . . . . . . . . .. .. . .. . . . ... . . .. .. . . ... . . . . . . . . . . . . . . . . . . . .. . . . . . . . . ... . . . . .. . . .. . . . . .  4-5 
Experimental conditions for the trial on butter pats and blocks . .. .. .. . . . . . .. . . .  . 
Sensitivity analysis of the heat transfer models . . . . .. . .. .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  . 
Input data for salted butter pat (B 1 8) heat transfer predictions 
(Trial SPH - I) . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . .. . . . .. . . .. . . . . . . . . . . . . . . . . . . . . . . . . .. . . . .. . . . . . . . . . . . .. . . . . .  . 
Input data for unsalted butter pat (B 1 6) heat transfer predictions 
(Trial UPH - 1 ) . . .. . . . . . .. . . . . . .. . . .. . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . .. . . .. .. .... . . .. . . . . . . . . . . . . . . . . . . . . .  . 
I nput data for unsalted butter pat (B I S) heat transfer predictions 
4-6 
5 - 1 0  
5 - 1 2  
5 - 1 4  
(Trial SBH -I a). . . .. . . . .. . . . .  .. . .  . . . . .  . . . . . . . . . . .  . . . . . . . .  . . . . . . . . .  . . . .. .. . . . . . . . . .  . . . . .  . . . . . . . . . . . .  . . . . . . .  5 - 1 7  
Input data for unsalted butter pat (B  1 6) heat transfer predictions 
(Trial UPH - 3 ). . . . . . . . ... . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .... . . .. . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . .  5 - 1 8  
Input data for u nsalted butter pat (B IS) heat transfer predictions 
(Trial SBH - 2a). . . . . . . . .. . . . . . .. .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . ... . .. . . ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  5 -22 
Input data for u nsalted butter block (B 1 9) heat transfer predictions 
(Trial UBH - I a). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  5-24 
Input data for salted butter pat (B 1 8) heat transfer predictions 
(Trial SPC - I ) . . . .. . . . .. . .. . .. . .. . . .. . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. .. . .. . . . . . . . . . . . . . . . . . . . . . . .  5 -26 
Input data for unsalted butter block (B 1 6) heat transfer predictions 
(Trial UPC - ]). . . . . . .  . . .  . . . . . .  . . .  . . .. . .  . .. .. . . . .  . . .. .. . . . . . . . . . . . . . . .  . . . . . . . . . . . . .  . .. . .. .. . . . . . . . . ... . . . . .  5-28 
Input data for salted butter block (B 1 5) heat transfer predictions 
(Trial SBC - 1 a) . ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. ' "  . . . . . . . .. ... . . . . . . . . . . . . . . . . . . . . . . . . . . . .  . 
Input data for unsalted butter block (B 1 8) heat transfer predictions 
(Trial UBC - 1 a) . .. . . . . ... . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... . .. . .. . . . . . . . . .. . . . . . . . . . . . . . . . . . . . .  . 
Theoretical values of A vrami constants . .. . .. . . . . . . . . . . . . . . . . . . . . . . . . . .. ' "  .. . . ... ... . . . . .. .  . 
Measured kinetics constants 'a' and 'b' for different emulsions .... . . . .... . . .. . 
5 -3 1 
5 -34 
6-8 
6- 1 2  
x i i i  
Table 6 .3  
Table 6 .4 
Table 7 . 1 
Table 8 . 1 
Table 8 .2 
Table 8 .3 
Table 8 .4 
Table 8 .5  
Table 8 .6 
Table 8 .7 
Calculation of the nucleation rate J from the experimental data. . . .  . . . . . . . . . . . . .  6- 1 5  
Enthalpy equation parameters for experimental butters . . . . . . . . . . . . . .  . . . . . .  . . .  . . . . . . .  6- 1 8  
Experiment plan for half and ful l  pallet trials. . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  7-3 
Pal let component thermal properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  8-3 
Summary of the effective properties for butter half and full pallet 
used in model predictions. . . . . .  . . .  . . . . .  . . . . . . .  . . . . . .  . . . . . . . . .  . . .  . . .  . . .  . . . . . .  . . .  . . . . . .  . . .  . . . . . . . .  . . . . .  8-6 
Input data for the full pal let and half pallet trials. . . . . .  . . . . . . .  . . . . . . . .  . . . . . .  . . . . . . . .  . . . . .  8-8 
Effective heat transfer coefficients (W m-2 K') used in the model 
to predict freezing in trial PC - 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  8- \ 8  
Effective heat transfer coefficients (W m-2 K') used in the model 
to predict thawing in trial PH - 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  8-20 
Input data for unwrapped loosely stacked triaL. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  8-20 
Input data for unwrapped tight packed ful l  pallet triaL. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  8-24 
xiv 
LIST OF FIGURES 
Figure 2 . 1 
Figure 2 .2  
Figure 2 .3  
Figure 2.4 
Figure 2 .5  
Figure 2.6 
Figure 2.7 
Figure 2 .8  
Structure of  butter . . .... .. . . . . . ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... . . . . . . . . . . . . . . ... ... ... ... . . . .... . . . . . .  2-2 
Most extreme differences between New Zealand summer and spring 
milkfat (MacGibbon, 1 993) . . . .. . . . . . . . . .. .. . . . . .. . . . . . . . . . . . .. .. . . . . . . . . . . . . . . . . . . .  2-5 
The temperature transition of the five stages of freezing for water and 
aqueous solution .. ..... . . . . ... . . . . . .... .. . . . . . . ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... . . . .. . . . .. .. . . ... . . .. . . . . . .  2-7 
The Fritz butter making process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... . . . ... . . .. . . . . . . . . . . . . . . . . .. . .. 2-9 
The Ammix butter making process . ..... . . .. . .. . . ... .... . .. . ... . . ............ . . .. . .. .... . . .... ... 2- 1 0  
Schematic diagram of temperature-ice fraction relationship . . . . . . . . . . . . . . . . . . . . . . . .  2- 1 2  
Density of butter as a function of temperature . . . . . . . . . . . . . . . . . . . . . . ... . . . . . . . . . . . . . . . . . . . . 2- 1 5  
Thermal conductivity of butter as a function of temperature . . . . . . . . . . . . . . . . . . . . . . .  2- 1 8  
Figure 2 .9 Specific heat capacity of butter as a function of temperature ............. . ........ . 2-20 
Figure 2 . 1 0  Enthalpy of butter as a function of temperature . .. . . . . .... ..... . . . . . .. ..... . . ... . . . ... . . . . 2-23 
Figure 2 . 1 1  Enthalpy - Temperature relationship ... . . .. . . . . ...... .. . . . . . ... . . . . .. . . .... .... .. . . . ... .... . ... . 2-30 
Figure 3 . 1 
Figure 3.2 
Figure 3.3 
Figure 3.4 
Figure 3 .5  
Figure 3 .6 
Figure 3.7 
Figure 3.8 
Solid fat contents of Summer, Spring and Autumn milk fat . . .  . . . . . . . . . . . . . . . . . . . . .  3-5 
Sol id fat contents of butter (a ) Summer (b) Spring (C) Autumn ... . . . . . . . ....... . . 3-5 
Thermal history of a sample during  ceroscopy measurements . . . . . . . . . . . . . . . . . . . . . . .  3-8 
Extrapolation method for determining the initial freezing point. . . . . . . . . . . . . . . . . . . .  3-8 
Initial freezing point of unsalted butters as a function of solute 
concentration in the aqueous phase .. ... . ... . . . . . . . . . . ..... ... . . . . . . . . ..... . . . . . . . . ... . . . .. ......  3 - 1 1 
Estimation of init ial freezing point  from measured enthalpy data ...... . . . . .... 3 - l 4  
Initial freezing point of salt solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . .  3- 1 6  
(a) Comparison calorimeter (b) Example of cool ing curve for use 
in method of comparison calorimeter. .......... . . .... ... . . . . ... . . .. . .. . . . .. . . .. .... .. .. . .......  3-22 
Figure 3 .9  Specific heat capacity measurement for frozen specimen . . . . . . . . . . . .. . . . . . . . . . . . . . . .  3-23 
Figure 3 . 1 0  The concept of guarded hot plate method for specific heat capacity 
measurement. . . . . . . . . . . . . . . . . . . . ....... . . . . .... . . . . . . .. . . .. . . . . . . . ...... . . . .. . .. . . .. . . . . . . . . . . ... . . . ... .... . .  3-24 
Figure 3 . 1 1  Schematic diagram of differential scanning calorimeter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-25 
Figure 3 . 1 2  Typical specific heat thermogram of food by DSC. .. . . .. . . ....... . . . . . . . . . . . .... . .. . . . .  3-27 
Figure 3 . 1 3  Measured specific heat capacity and enthalpy of sapphire 
xv  
compared with l iterature data .............. ................... . ..................................... 3-30 
Figure 3. 1 4  (a) Specific heat capacity (b) Enthalpy of unsalted butter (B 1 7) 
with two curve method compared with Mohsenin' s Method ....................... 3-3 1 
Figure 3. 1 5  (a) Specific heat capacity (b)  Enthalpy of salted butter (B 1 5) 
at different scanning rates ..................................... ........................................ 3-32 
Figure 3. 1 6  (a) Specific heat capacity (b)Enthalpy from repeated DSC trial 
with the same sample of butter (B 1 5) . .... .... . . .. .. .. .. . . . . . . .. . .... .. ..... . ..... . ...... . ... .. . 3-34 
Figure 3. 1 7  (a) Specific heat capacity (b) Enthalpy of the same kind of butter 
(B 1 7) for two samples done on the same day ... .. . .. . . . ....... .. . . . . . . . . . . . . . . . . . . . . . .. .. . .  3-34 
Figure 3. 1 8  (a) Specific  heat capacity (b) Enthalpy of unsalted butter (B 1 7) 
frozen to different temperatures ....... . ........... . .. ......... . .................... . ..... ........ 3-35 
Figure 3 . 1 9  (a) Specific heat capacity (b) Enthalpy of salted butter (B 1 5) measured 
by heating runs after cool i ng to -20°C, -40°C and at to -70°C. . . . . . . . . .... . . . .. . . .  3-36 
Figure 3.20 Cool ing of salted butter sample (B 1 5) at a rate of lOoCmin-1 to 
avoid water supercool ing problem . . . ................ ....... . . .. . . . . . . . . . . . . ... .. .. . ... .... ...... 3-36 
Figure 3.2 1  Specific heat capacity repeated heating and cooling of one 
unsalted butter sample (B 1 2) ............... ........... ... . . . ...... . . .. .. . . . . . .. .. . .................. 3-37 
Figure 3.22 Specific heat capacity measured form repeated heating and 
cool ing DSC runs for one salted butter sample (B 1 5) . . . . . . . . .. . .. . . . . . . . .. .. .... ...... 3-38 
Figure 3.23 Specific heat capacity of repeated heating and cooling of rnilkfat. . .  ............ 3-39 
Figure 3 .24 Specific heat capacity and enthalpy of milkfat compared with the 
specific heat capacity and enthalpy of salted butter (B 1 5 ) freeze 
to -40°C and unsalted butter (B 1 9) freeze to -20°C. .......... . . . . . . . . . . . . . . . . . . . . .. . . . . .  3-40 
Figure 3.25 Specific heat capacity (a) Unsalted butter (B 1 9) (b) Salted 
butter (b 1 5) measured by cooling DSC runs. Run 2 measured 
eight months later than Run 1 . .. .... ....... ... ....... . . . .. . ... . ..... .......... ....... ..... .... .. .... 3-4 1 
Figure 3.26 Measured enthalpy for (a) Salted butters 
(b) Unsalted butters using DSC. ..... . .. ........ .... . ......... . . . ............... . ..... . ............ 3-44 
Figure 3 .27 Measured and modeled enthalpy of butter. . .. ............................................... 3-46 
Figure 3 .28 Modeled data for unsalted butters ............ ......... . ........ .................................. 3-47 
Figure 3.29 Solid fat contents of butters at different temperatures ................................. 3-48 
XVI 
Figure 3 .30 (a) Adjusted enthalpy for salted butters 
(b) Sol id fat contents for salted butters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  3-49 
Figure 3 .3 1 a) Adjusted enthalpy for lactic butters 
(b) Solid fat contents for lactic butters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  3-50 
Figure 3.32 Comparison of measured enthalpy data with the li terature data . . . . . . . . . . . . . . . . . .  3-5 1 
Figure 4. 1 Position of thermocouples in the salted butter pat (B 1 8) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  .4-3 
Figure 4.2 Position of thermocouples in the unsalted butter pat (B 1 6) . . . . . . . . . . . . . . . . . . . . . . . . .  .4-4 
Figure 4.3 Position of thermocouples in the salted butter block (B I S) . . . . . . . . . . . . . . . . . . . . . . . . .  .4-4 
Figure 4.4 Position of thermocouples in the unsalted butter block (B 1 9) . . . . . . . . . . . . . . . . . . . . .  .4-5 
Figure 4.S Heat transfer in  salted butter pat (B 1 8) 
(a) Cooling (SPC - I )  with: Ti = 1 0°C, Ta = -24°C, tp= I Oh 
(b) Heating (SPH - \ ) with :Ti =-24°C, Ta = l OoC, tp= 1 3h . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  4-7 
Figure 4.6 Heat transfer in salted butter pat (B 1 8) 
(a) Cooling (SPC - 2 )  for 60 hours 
(b) :Thawing (SPH - 2 )after cooling at -2SoC for 60 hours . . . . . . . . . . . . . . . . . . . . . . . . . . .  .4-9 
Figure 4.7 Heat transfer in unsa1ted butter pat (B 1 6) 
(a)Cooling (UPC - I )  with: Ti = 1 5°C, Ta = - I SoC, tp= 1 0h 
(b) Heating(UPH - I  )wi th: Ti = I SoC, Ta = 20°C, tp= 1 2h . . . . . . . . . . . . . . . . . . . . . . . . . . .  .4- 1 1 
Figure 4 .8 Heat transfer in  unsalted butter pat (B 1 6) 
(a) Cooling (UPC - 2 )  with: Ti = 20oC,Ta = -70°C, tp= 1 0h 
(b) Heating (UPH - 2)  with: Ti = -70°C, Ta = 20°C, tp= 1 2h . . . . . . . . . . . . . . . . . . . . . .  .4- 1 2  
Figure 4.9 Heating of unsalted butter pat (UPH - 3) 
with : Ti = - l SoC, Ta = 20°C, tp= 1 2h ............................................................ .4- 1 3  
Figure 4 . 1 0  Comparison of thawing time for an unsalted pat 
with (UPH - 3) and without(UPH - I )  complete prior water freezi ng . . . . . . .  .4- 1 4  
Figure 4. 1 1  Heat transfer i n  butter block (B 1 5 ) with cardboard packaging 
(a) Cooling (SBC - 1 a) with : Ti = 4°C, Ta = - 1 8°C, tp= 3days 
(b) Heating (SBH - I a) with : Ti = - 1 8°C, Ta = 2°C, tp= 3days . . . . . . . . . . . . . . . . . . .  .4- 1 5  
Figure 4 . 1 2  Heat transfer in butter block (B \ 5 ) without cardboard packaging 
(a) Cooling (SBC - I b) with: Ti = 4°C, Ta = - 1 8°C, tp= 3days 
(b) Heating (SBH - 2b) with : Ti = - 1 8°C, Ta = 2°C, tp= 3days . . . . . . . . . . . . . . . . . . .  .4- 1 7  
xvi i  
Figure 4 .13 Comparison of with box and without packaging trails for 
salted butter (B I 5) (a) Cooling (b) Heating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  .4- 1 8  
Figure 4 .14 Position of the thermocouples i n  the plan view of 
frozen salted block (B 15) . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . .  .4-19 
Figure 4.15 Thawing of frozen salted butter block (SBH - 2a) with 
Ti = _lOoC, Ta = l OoC, tp= I year . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . ... . . . . . . . . .  .4-20 
Figure 4 .16 Comparison of two independent thawing trials (SBH - 2a) and 
(SBH - 2b) of salted butter blocks (B 15) with 
Ti = -10°C, Ta = 1 0°C, tp= I year . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  .4-21 
Figure 4 .17 Heating of a frozen unsalted butter block (UBH - I a) 
with :Ti = _l OoC, Ta = l OoC, tp= 6 months . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  .4-22 
Figure 4 .18 Compari son of heating times for salted (SBH - 2a) and 
unsalted (UBH - I a) butter blocks . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . .  .4-23 
Figure 4 .19 Cooling of unsalted butter block (UBC - 1 a) 
with: Ti = lOoC, Ta =- 23°C, tp= 3 weeks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  .4-24 
Figure 4.20 Comparison of two cooling trial in  the same unsalted butter 
block (B 19) under identical cooling conditions as 
Ti = 10°C, Ta = -23°C, tp= 3 weeks . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  . .4-25 
Figure 4.21 Cooling of unsalted butter block (UBC - 2) 
with :  Ti = lOoC, Ta = - l OoC, tp= 3 weeks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  .4-26 
Figure 5 . 1 A block of butter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  5-2 
Figure 5 .2  Comparison of measured data for thawing of salted butter 
pat (B 18, Trial SPH - I )  with equilibrium property model 
and sensible heat only model predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  5- 1 3  
Figure 5 .3 Compari son of measured data for thawing of unsalted butter 
pat (B 16, Trial UPH - I )  with equilibrium properties model 
and sensible heat only Model predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 5-15 
Figure 5 .4 Compari son of measured data for unsalted butter pat 
(B 16, Trial UPH -I) with sensible heat only model using 
temperature dependent specific heat capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  5- 1 6  
Figure 5 .5 Comparison of thawing data of a fully frozen butter pat 
XVIII 
(B 1 6, Trial UPH - 3 )  with equilibrium properties mode1 . . .  . . . . . . . . . . . . . . . . . . . . . . . . .  5 - 1 7  
Figure 5 .6 (a) Comparison of the measured data for the salted block 
(B 1 5 , Trial SBH - l a) with equilibrium property model and 
sensible heat only predictions for surface and centre 
(b) Comparison of the measured data for the salted block using 
equilibrium properties model predictions for all the positions . . . . . . . . . . . . . . . . . . . . .  5-20 
Figure 5 .7 Comparison of measured data for salted butter block without 
packaging (B 1 5 , Trial SBH - I b) with predictions using sensible heat 
only model predictions with temperature dependent heat capacity . . . . . . . . . . . . . .  5-2 1 
Figure 5 .8  Measured data for thawing of fully frozen salted butter block 
(B 1 5 , Trial SBH - 2a) compared with the equilibrium thermal 
properties model predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . .  5-23 
Figure 5 .9 Measured data for thawing of fully frozen unsalted butter block 
(B 1 9, Trial UBH - I a) compared with the equilibrium 
thermal properties model predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  5-24 
Figure 5 . 1 0  (a): Comparison of measured data for the freezing of the salted pat 
(B 1 8 , Trial SPC - 1 )  with Equilibrium thermal properties 
model predictions and the sensible heat only model predictions 
(b) Measured data for the salted pat(B 1 8) w ith the sensible heat only 
model for all the positions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 5-27 
Figure 5 . 1 I a) Measured data for the unsalted butter pat (B 1 6, Trial UPC - I )  
compared wi th the sensible heat only model and the equilibrium 
property model predictions(b) Measured data compared with the 
sensible heat only model predictions for all the position . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  5-29 
Figure 5 . 1 2  (a) Measured data for the salted butter block (B 1 5 , Trial SBC- I a) 
compared with the sensible heat only model and the equilibrium 
property model predictions(b) Measured data with the sensible 
heat only model for all the positions in the salted block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  5-32 
Figure 5 . 1 3  Measured data for the salted butter block (B 1 5 , Trial SBC - I b) 
compared with the sensible heat only model for all the positions 
in  the salted block ........................................................................................ 5-33 
XIX 
Figure 5 . 1 4  Measured data for the unsalted butter block (B 1 9) compared 
with the sensible heat only model and the equilibrium property 
model predictions (a) Freezing with an air temperature of -23°C 
Figure 6. 1 
Figure 6.2 
Figure 6.3 
Figure 6.4 
Figure 6.5 
Figure 6.6 
Figure 6.7 
Figure 6.8 
(UBC- I a)(b) Freezing with an air temperature of - l OoC (UBC-2) . . . . . . . . . . . . . . .  5-35 
DSC thermogram for Fritz and Amrnix butter. . . . . . . . ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  6- 1 0  
DSC thermogram for the Fritz unsalted butter wi th a constant 
cooling rate of 1 .25°C rnin-I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  6- 1 2  
InJ as a function of super cooling for both Fritz butter and 
the AmrrUx butter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  6- 1 3  
Nucleation rate as a function of temperature for the Fritz and 
Amrnix butters .............................................................................................. 6- 1 4  
InJ as a function of super cooling calculated from the experimental 
freezing data and the DSC measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  6- 1 5  
Nucleation rate J as a function of temperature calculated from two 
freezing experiments on a butter block (B 1 9) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  6- 1 6  
Specific heat capacity of butter (B 1 9) measured by DSC in 
heating and cooling modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  6- 1 8  
(a) Equilibrium enthalpy-temperature diagram for butter (B 1 9) 
showing specific heat capacity values used for different 
temperature ranges. (b) Enthalpy-temperature diagram for the 
calculation of equilibrium freezing temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  6-20 
Figure 6.9 Comparison of the measured data (B 1 9) with the prediction using 
the nucleation-only model. (a) Freezing of butter block (UBC - I a) 
with an ambient temperature of -23°C. (b) Freezing of butter 
block (UBC - 2) with an ambient temperature of - I  1 °C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  6-22 
Figure 6 . 1 0  Comparison of the measured data for unsalted butter (B 1 9) with 
the predictions using the A vrami model. (a) Freezing with an 
ambient of -23°C (UBC - l a,UBC - I b)(b)Freezing with an 
ambient of - 1 1 °C (UBC - 2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  6-24 
Figure 6 . 1 1  Comparison of the measured data (UBC - 2)  for unsalted butter (B 1 9) 
with the Avrami model using a U value of 0.0 1 2  rather than 0.0 1 4  . . . . . . . . . . . . . 6-25 
xx  
Figure 6 . 1 2  Effect of U and b values on the model prediction  using the 
Avrami Model with Ta= -23DC, T j= I I DC,  U =0.0 1 4, b = -0.00 1 8  . . . . . . . . . . . . . .  6-26 
Figure 6 . 1 3  Comparison of the measured data (SPC - 1 )  for the salted butter 
pat (B 1 8) with the prediction using various freezing models 
(a) For 1 0  Hours (b) For 70 hours . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  6-27 
Fi gure 6 . 1 4  Comparison of the measured data(SPC-2) for the salted butter 
pat (B 1 8) )with the prediction using A vrami Model predictions for I 
onger period of time(b) Comparison of measured data (SPH-2) for 
the thawing of salted butter pat (B 1 8)with the equilibrium properties 
models and sensible heat only model predictions after cooling 
at -25DC for 60 hours . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  6-28 
Fi gure 6 . 1 5  Comparison of the measured data (UPC - I )  for the unsalted butter 
pat (B 1 6)with the prediction using various freezing models predictions 
(a) For to hours (b) For 80 hours . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  6-29 
Figure 6. 1 6  Comparison of the measured data (SBC - I  a) for the salted butter 
block(B 1 5) with the prediction using various freezing models 
(a) For 70 hours (b) For 200 hours . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  6-3 1 
Figure 6. 1 7  Comparison of the measured data for the salted block freeze to -23DC 
with all the freezing models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  6-32 
Figure 7. 1 Plan and elevation view of the full butter pallet configuration  
(approximate outer dimensions in  mm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  7-2 
Fi gure 7.2 Wrapped full pallet used for Trial I (PC - \ ,  PH - 1 ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  7-5 
Figure 7.3 Unwrapped full pallet used for Trial 2 (PC - 2, PH - 2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  7-5 
Figure 7.4 Plan views « a) and (b)) and front elevation (c) of half pallet 
trails (Trials 3-5) . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  7-8 
Figure 7.5 Position and code numbers of thermocouples in  the mjddle layer of the 
three layered half pallet trials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  7-9 
Figure 7 .6 Position of the thermocouples in cartons \ , 2 , 7  and 8 in  half 
pallet Trials 3-5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  7 - \  0 
Figure 7.7 Direction of air flows in the experimental room 
(a): Plan view ( freezing) (b) :  Plan view (thawing) 
XXI 
(c) :  Elevation (freezing) (d) :  Elevation (thawing) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7- 1 O  
Figure 7 .8  Experimental temperature profiles measured for trial PC - I 
(a) pallet faces (b) across the pallet diagonal from bottom LHS front 
corner to top RHS back corner - positions in mm indicated are relative 
to bottom LHS of pallet as in  Figure 7 . 1  (c) across layer 4 . . . . . . . . . . . . . . . . . . . . . . . .  7 - 1 2  
Figure 7 .9 Experimental temperature profiles measured for trial PC - 1 at centre 
of the blocks (one on each layer) from top to bottom of the pallet. . .  . . . . . . . . . . . .  7- 1 4  
Figure 7 . 1 0  Experimental temperature profiles measured for trial P H  - I 
(a). pallet faces (b). across the pallet diagonal from bottom LHS front 
corner to top RHS back corner - positions in  mm indicated are relative 
to bottom LHS of pallet as in  Figure 7. 1 (c). across layer 4 . . . . . . . . . . . . . . . . . . . . . . . . . .  6- 1 5  
Figure 7 . 1 1  Experimental temperature profiles measured for tri al PH - I at the centres 
of the blocks (one on each layer) from top to bottom of the pallet. . .  . . . . . . . . . . . .  6- 1 7  
Figure 7 . 1 2  Experimental temperature profiles measured for trial PC - 2 
(a). pallet faces (b). across the pallet diagonal from bottom LHS front 
corner to top RHS back corner - positions in  mm i ndicated are relative 
to bottom LHS of pallet as in  Figure 7 . 1  (c). across layer 4 . . . . . . . . . . . . . . . . . . . . . . . . . .  7 - 1 8  
Figure 7 . 1 3  Experimental temperature profiles measured for tri al PC - 2 at centers 
of the blocks (one on each layer ) from top to bottom of the pallet.. . . . . . . . . . . . .  7-20 
Figure 7 . 1 4  Compari son of the slowest cooling position ( 1 6) in the wrapped (PC - I )  
and unwrapped (PC - 2)  full pallet trials . . . . .. . . . . . . . . . . . . . . . . ... . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 7-2 1 
Figure 7 . 1 5  Experimental temperature profile measured for trial PC - 2 (a)Centre 
of all the faces of the Block 3 1  (b). posi tions inside the Block 3 1 . . . . . . . . . . . . . . .  3-22 
Figure 7 . 1 6  Experimental temperature profiles measured for trial PH - 2 at the centre 
of all the faces of the Block 38 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... . . . . .  7-23 
Figure 7 . 1 7  Experimental temperature profiles measured for trial PH - 2 at positions 
inside the Block 38 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-24 
Figure 7 . 1 8  Comparison of thawing of wrapped (PH - I )  and unwrapped (PH - 2)  
in  the full pallet trials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  7-24 
Figure 7 . 1 9  Experimental temperature profiles measured for trial PC - 3 
(a). Temperature profile at the centre of the faces exposed to ambient 
xx i i  
(b). Temperature profile at the centre of each block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-25 
Figure 7 .20 Temperature readings (between the blocks and corresponding butter 
surfaces) after 50 hours in Trial PC - 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-27 
Figure 7 .2 1 Experimental temperature profiles measured for the wrapped loosely 
stacked half pallet trial (PC - 3)(a) Comparison of block 1 & 8 
(b) Comparison of block 2 & 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  7-28 
Figure 7.22 Experimental temperature profiles measured for the wrapped loosely 
stacked half pallet trial (PC - 3) (a) :  Temperature profiles of the 
slowest freezing position along with the other positions around the centre 
of the half pallet. (b) :  Schematic diagram of the centre of the pallet. . .  . . . . . . . . . .  7-29 
Figure 7.23 Experimental temperature profiles measured for trial PH - 3 
(a).  Temperature profile at the centre of the faces exposed to ambient 
(b). Temperature profile at the centre of each block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  7-30 
Figure 7 .24 Temperature readings (between the blocks and corresponding butter 
surfaces) after 50 hours in Trial PH - 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  7-3 1 
Figure 7 .25 Experimental temperature profiles measured for the wrapped loosely 
stacked half pallet trial (PH - 3)(a) Comparison of block I &8 
(b) Compari son of block 2 & 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  7-32 
Figure 7 .26 Experimental temperature profile measured for the slowest thawing 
position along with other positions around the centre of the 
half pallet (PH - 3 )  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  7-33 
Figure 7.27 Experimental temperature profiles measured for Trial PC - 4 
(a). Temperature profile at the centre of each block along with the 
average ambient temperature on four sides of the half pallet 
(b). Temperature profile for the centres of all the blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-34 
Figure 7.28 Temperature readings (between the blocks and corresponding 
butter surfaces) after 50 hours for Trial PC - 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  7-35 
Figure 7 .29 Experimental temperature profiles measured for the unwrapped half 
pallet trial (PC - 4) (a) Comparison of block 1 and 8 
(b) Comparison of block 2 and 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  7-36 
Figure 7 .30 Experimental temperature profiles measured for the slowest freezing 
XXIII 
position along with other positions around the centre of the half 
pallet (PC - 4r . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  7-37 
Figure 7.3 1 Experimental temperature profiles measured for Trial PH - 4 
(a) : Centre of all the faces exposed to ambient (the position 1 2  on block 1 
i s  missing)(b ) :  Centres of all the blocks in the ntiddle layer.. . . . . . . . . . . . . . . . . . . . . . .  7 -38 
Figure 7 .32 Temperature readings (between the blocks and corresponding butter 
surfaces) after 50 hours for Trial PH - 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  7-39 
Figure 7.33 Experimental temperature profiles measured for Trial PH - 4 
(a) Comparison of Blocks I & 8 (b) Comparison of Blocks 2 & 7 . . . . . . . . . . . . . .  7 -40 
Figure 7.34 Experimental temperature profiles measured for the slowest thawing 
position along with the other position around the centre of the half 
pallet Trial PH - 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  7-4 1 
Figure 7.35 Experimental temperature profi les measured for the half pallet loosely 
stacked trial PC - 5 at the centre of all the blocks along with the 
ambient temperature on four sides of the half . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  7-42 
Figure 7.36 Experimental temperature profile measured for the positions at the 
surfaces of the blocks (PC - 5a) (a) Block I (b ) Block 2 (c) Block 8 
(d) Block 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  7-43 
Figure 7.37 Temperature readings (between the blocks and corresponding 
butter surfaces )  after50 hour for Trial PC - 5a . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  7-44 
Figure 7 .38 Experimental temperature profile measured for trial PC - 5a at the 
positions i nside the blocks along with the average ambient temperature. 
(a) Block I (b) Block 2 (c) Block 8 (d) Block 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  7-44 
Figure 7.39 Experimental temperature profiles measured at the centre of each 
block along with the ambient temperature on four sides of the 
half pallet (PH - 5) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  7-46 
Figure 7 .40 Experimental temperature profiles measured for trial PH _ 5 at the surfaces 
of the blocks(a) Block (b)  Block 2 (c) Block 8 (d) Block 7 . . . . . . . . . . . . . . . . . . . . . .  7-46 
Figure 7.4 1 Temperature readings (between the blocks and corresponding butter 
surfaces) after 50  hours for Trial PH - 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  7-47 
Figure 7.42 Experimental temperature profiles measured for trial PC - 5 inside the 
XXIV 
blocks along with the average ambient temperature. (a) B lock I 
b) Block 2 (c) B lock 8 (d) B lock 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  7-48 
Figure 7 .43 Comparison of the slowest freezing point for both the freezing runs 
of Trial S (PC - Sa and PC - Sb) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  7-S0 
Figure 7 .44 Comparison of slowest changing positions in the half pallet Trials 3-S 
(a) Freezing (b) Thawing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  7-S I 
Figure 8 . 1 Compari son of measured enthalpy with the effective enthalpy for 
the unwrapped half pallet.  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  8-7 
Figure 8 .2  Measured thawing data for the centre of the wrapped full pallet 
trial (PH - 1 )  compared with model predictions using conduction only 
model with effective thermal properties calculated by Maxwell Eucken, 
Parallel and Series models Ti =-6°C, Ta= 1 0°c. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  8-9 
Figure 8 .3 Measured freezing data for the centre of the wrapped ful l  pallet 
trial (PC - I )  compared with model predictions using conduction 
only model with effective thermal properties calculated by the 
Parallel model .  Ti = 1 0°C, T a=- I I 0c. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  8- 1 0  
Figure 8 .4 Measured data for the centre of the wrapped half pallet trial (PH - 3) 
during thawing compared with the conduction only model with effecti ve 
thermal properties calculated by the Paral lel model (Trial 3) 
with Ti =-23°C, Ta=20°C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  8- 1 1  
Figure 8 .S Predictions for the wrapped half pallet trial (PH - 3) using enthalpy for 
the fully and partially frozen butter compared with the measured data . . . . . . .  8- 1 2  
Figure 8 .6 Comparison of measured data for the freezi ng of wrapped loosely 
stacked half pallet trial (PC - 3) considering heat transfer as conduction 
only with effective thermal properties based on the parallel model.  
Ti =22°C, Ta=-23°C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  8- 1 3  
Figure 8.7 Comparison of model predictions with the measured data for the 
unwrapped half pallet trial (PH - 4) considering heat transfer as 
conduction only with effective thermal properties based on the parallel 
model .(a)Thawing with Ti =- 1 6°C, Ta=23°C 
(b) Freezing with Ti =2 1 °C, Ta=-22°C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  8- 1 4  
xxv 
Figure 8 .8 Effective heat transfer coefficient for freezing of B lock 2 and 7 in  
unwrapped half pall et trial (PC - 5)  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  8- 1 7  
Figure 8 .9 Effective heat transfer coefficient for freezing of B lock 7 and 8 in 
unwrapped half pal let trial (PH - 5) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  8- 1 9  
Figure 8 . 1 0  Measured data compared with the model prediction for freezing of 
unwrapped loosely stacked half trial with gaps (PF - 3) 
with T j= 1 1 °C,  Ta=-25°C(a) Block l (b) Block 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  8-2 1 
Figure 8 . 1 1 Measured data compared with the model prediction for thawing of 
unwrapped loosely stacked half pallet trial with gaps (PH - 5)  
with T j= -25°C, Ta=20°C(a) B lock8 (b) Block 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  8-22 
Figure 8 . 1 2  Comparison of the model predictions with measured data for the 
unwrapped full pal let trial « PH - 2 )  & (PC - 2» (a) and 
(b) Freezing in B lock 30 with T j= l OoC, Ta=- l l oC 
(c) Thawing in B lock 3 1  with T j= - 1 1 °C, Ta= 1 1  °C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  8-25 
Figure 8. 1 3  Effecti ve heat transfer coefficient for freezing of B lock 7 in 
unwrapped closely stacked half pallet trial (PC - 4) for Block 7 . . . . . . . . . . . . . . . . .  8-27 
Figure 8. 1 4  Measured freezing data compared with the model prediction for unwrapped 
closely stacked half pallet tri al (PC - 4) with Tj = 2 1 °C, Ta= -2 1 °C . . . . . . . . . . . . .  8-28 
Figure 8. 1 5  Measured data for thawing of B lock 7 in thawing of unwrapped half 
pal let trial with no gaps (Trial PH-4) with T j= - 1 8°C, Ta=22°C . . . . . . . . . . . . . . . . . .  8-29 
xxvi  
LIST OF APPENDICES 
Appendix A I :  Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  A- I 
Appendix A 2: Standard Methods Used to Measure the 
Composition of Butter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  A-4 
Appendix A3 : Numerical Formulation of ModeL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  A-6 
Appendix A4: Matlab Code for the Freezing Models for 25 kg 
Block of Butter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  A-8 
Appendix AS : Plans of Thermocouples Positions and Data for 
Pallet Trials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  A-9 
XXVl l