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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
(Massey University, 1980) Taimmanenate, Kalaya
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 experimental 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 was best described by a first order reaction. For riboflavin, different 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 quality retention calculation in unsteady-state was confirmed experimentally. For colour and viscosity changes in processing, the method of kinetic parameter determination in unsteady-state heating procedure was used assuming first order kinetics. It was concluded in this food system for the temperature ranges of 60-139°C, the kinetic reaction rate at 129°C and the activation energy were 0.42-0.44 x 10-4 s-1 and 77-85 kJ mole-1, 0.11-0.25 x 10-4 s-1 and 84-105 kJ mole-1, 1.20 x 10-4 s-1 and 122 kJ mole-1 and 1.65 x 10-4 s-1 and 151 kJ mole-1 for ascorbic acid, riboflavin, colour and viscosity respectively
Heat transfer during freezing of foods and prediction of freezing times : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Biotechnology at Massey University
(Massey University, 1977) Cleland, Andrew Charles
A study of methods for predicting the freezing time of foods was made. Four shapes - finite slabs, cylinders, spheres and rectangular bricks were considered. For each shape experimental measurements of the freezing time were made over a wide range of conditions using Karlsruhe test substance, a defined analogue material. Experiments with slabs of minced lean beef and mashed potato were also conducted. Practical food freezing problems, where the material is initially superheated above its freezing point and the third kind of boundary condition (convective cooling) is applied, have not been solved analytically because of the non-linear boundary conditions. Food materials when freezing release latent heat over a range of temperature which further complicates any attempt at solution. The accuracy of the various solutions to the freezing problem proposed in the literature was evaluated by comparison of the various calculated freezing times with the experimentally determined values over a total of 187 freezing experiments. For those solutions requiring numerical evaluation, the best was found to be a three-level finite difference scheme which generally gave a prediction of the freezing time to within ±9% of the experimental values with 95% confidence. With the regular geometric shapes investigated finite elements have no advantage over finite differences and were not considered. For the existing exact and approximate analytical solutions, it is shown that these do not give accurate prediction of the freezing time for any of the four shapes, mainly because all but two of these solutions do not take account of initial superheat in the material to be frozen, and these two solutions are for initial superheat in a semi-infinite slab, not a finite slab. For the existing empirically modified solutions and empirical relationships, it is shown that they do not give accurate prediction of freezing time; at best the 95% confidence limits of the percentage difference between the calculated and experimental freezing times are 0% to +20% for slabs, cylinders and spheres. All solutions for freezing of rectangular bricks with the third kind of boundary condition use the geometric factors derived by Plank. These factors are shown to be subject to error, the error increasing as the ratios of the two larger dimensions to the smallest increase. A group of formulae is proposed which are simple to use and give accurate prediction of freezing time. They modify the geometric factors in Plank's equation, taking initial superheat into account, and in the case of rectangular bricks correct the errors inherent in these geometric factors. This group of simple formulae are shown to predict the freezing time with 95% confidence to within 5% of the experimental values for slabs, to within 7% for cylinders and spheres, and to within 10% for rectangular bricks. The prediction accuracy of the simple formulae and the three level finite difference scheme are similar but the simple formulae can be calculated quickly without the use of a computer which is a big advantage. In addition to simplicity and accuracy the simple formulae are also versatile, and by use of suitable approximations can handle some practical problems in which conditions change with time.
Depletion and harvesting thermal energy from actuator arm electronics in hard disk drives : a thesis presented in partial fulfillment of the requirements for the degree of Master of Engineering in Mechatronics at Massey University, Albany, New Zealand
(Massey University, 2011) Wu, Di
In recent years, thermally assistive magnetic recording (TAMR) has been applied on actuator arm electronics (AE) in hard disk drive (HDD). When HDD operates, temperature of the AE chip inside enclosure can be as high as 80-100 ºC, primary caused by processing and conditioning of magnetic signals and heated by wasted mechanical energy in form of thermal energy. To guarantee reliability of electronic device, AE chip junction temperature should be maintained at a relatively low level, which requires novel depletion of thermal energy. There are generally two methods to manage the thermal dissipation of chips. One is to follow existing approaches that conduct the thermal energy from the topside of the chip to a heat sink through a conductive paste, or other mediums. The other way is to dissipate the heat from the inner surface of the chip to a heat sink through silicon substrate. In this thesis, thermal analysis of AE chip junction temperature is presented and discussed. Depletion of thermal energy generated by the AE chip will be characterized among several thermal management configurations. Then, a thermal resistance network model is established for AE chip junction temperature to ambient. The thermal resistance network is based on heat transfer paths from the chip to ambient. Every thermal resistance in the network can be calculated by analytical expression. The accuracy of the presented model will be also proven through comparing the results of mathematic model and simulation. Finally, based on the thermal analysis and managements, design of a novel active thermal energy harvester to transform the wasted energy into electrical energy will be presented. Finite element analysis (FEA) software is used to simulate piezoelectric characteristics of the thermal energy harvester.
Prediction of chilling times of foods subject to both convective and evaporative cooling at the product surface : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Biotechnology and Bioprocess Engineering at Massey University
(Massey University, 1995) Chuntranuluck, Sawitri
No published chilling time prediction method which covers a wide range of practical conditions, and which can be applied using only simple algebraic calculations for chilling with evaporation at the product surface has been proven accurate. The objective of the present work was to develop and test a simple chilling time prediction method with wide application for situations where significant evaporation as well as convective cooling occurs from the product surface. A numerical method (finite differences) was used to simulate convection and evaporation at the product surface in cooling of solid products of simple shape (infinite slab, infinite cylinder, and sphere) with constant surface water activity. Semi-log plots relating temperature change to be accomplished to time were linearised by appropriate scale transformations based on die Lewis relationship. The effect of evaporation on cooling rate was measured by considering the slope and intercept of such plots, and comparing these to the slope and intercept that would arise in convection-only cooling. The enhancement of cooling rate due to the evaporative effect depended on six parameters; initial product temperature, cooling medium temperature, Biot number, relative humidity, product shape factor, and surface water activity. Four simple algebraic equations were curved-fitted to the numerically simulated data for predicting temperature-time profiles at centre and mass average positions in the product. The numerically generated results and the simple algebraic equations agreed well with a mean difference close to 0% for all three shapes, and 95% confidence bounds of about ±3% for the infinite cylinder, and ±5% for the infinite slab and the sphere geometries. To test the simple models, chilling experim ents were conducted in a controlled air flow tunnel across a range of conditions likely to occur in industrial practice. Trials were conducted using infinite cylinders of a food analogue as an idealised product (with saturated salt solutions percolating over a wet cloth on the product surface to maintain constant surface water activity), and carrots (both peeled and unpeeled) as examples of real food products. Measured centre temperatures for both the idealised products and peeled carrots were predicted by the proposed method, assuming a constant surface water activity, within a range of differences which was almost totally explainable by experimental uncertainty. For unpeeled carrots, predictions mode using three different surface water activities in the model (one to represent the initial condition, one to represent the active chilling phase, and one to represent the quasi-equilibrium state at the end of chilling) agreed sufficiently well with experimental centre temperature data for the lack of fit to be largely attributable to experimental uncertainty. No experimental verification for prediction of mass-average temperatures was attempted. The proposed method is recommended for predicting chilling times of food products of infinite slab, infinite cylinder or sphere shapes, across a wide range of commonly occurring chilling conditions provided the product has constant surface water activity. The establishment of bounds on a theoretical basis for limiting the ranges in which surface water activity values are selected for making predictions for products with non-constant surface water activity is proposed, and some guidance on application of these bounds established. Further work to refine the use of these bounds for a range of food products, to consider a wider range of shapes, to test the ability of the proposed method to predict mass-average temperatures is recommended.
Mathematical modelling of heat transfer and water vapour transport in apple coolstores : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Biotechnology and Bioprocess Engineering at Massey University
(Massey University, 1995) Amos, Nevin David; Amos, Nevin David
A study of heat transfer and water vapour transport in a large industrial apple coolstore was undertaken. A set of measurements was made including product cooling rates in both pre-cooling units and the bulk-storage area, evaporator and fan performance, floor and building shell temperatures, door opening frequency and air temperature, relative humidity (RH) and velocity variation with both position and time. Measurements within pallet pre-coolers showed large variations in product cooling rate, between apple cartons but this could not be attributed to any positional factor studied. The spread of data was probably due to widely differing airflows through and around each apple carton. A staggered pallet pre-cooler configuration had a 30% faster cooling rate on average than an in-line pallet arrangement. Measurements of cooling rates within single cartons showed large variation of cooling rate with position within a carton, probably resulting from non-uniform airflow within the carton. Existing heat conduction-based models were unable to predict the level of variability of cooling rate within cartons. A multi-zoned conduction and convection model was developed which predicts apple temperature and weight loss, air temperature, enthalpy and humidity, and packaging temperature with position within the carton. Testing of the model against measured data showed good fit for air and apple temperatures, but insufficient data were available for comprehensive testing of the humidity and weight loss sub-models. Difficulties in developing methodology to accurately define the patterns of airflow within cartons were not adequately overcome, so measurements to determine airflow patterns would be required before predictions could be made for alternative packaging systems. Within the coolstore measured there was significant positional variation in air temperature and humidity associated with local heat sources (such as pre-coolers, doors, uninsulated floor, and warm fruit batches), and the degree of air circulation as quantified by local air velocities. In addition, temperature and humidity showed a diurnal fluctuation associated with the operation of the coolstore. These results suggested the need for a multi-zone dynamic model to enable predictions of both the time and the positional variation to be made. Such a model was developed which included component models for zone air, external surfaces, floors, heat generators, inert materials such as internal structural components, evaporators, fans, doors and product. Novel features of the model compared to existing models are that it estimates airflow between zones using fixed user defined pathways, rather than complex hydrodynamic models; it considers water vapour transport in detail as well as heat transfer; condensation on surfaces and water absorption by packaging are modelled; and the product sub-model both allows movement of product batches during the simulation and accounts for differences in cooling rate within a batch. Single-zone, 5-zone, 8-zone and 34-zone versions of the model were tested. The 1-zone model predicted mean thermal conditions for the coolstore adequately. The 5-zone model which differentiated the pre-coolers and the bulk-storage area predicted measured data well for the pre-coolers, but more time-variability was predicted for the bulk-storage area than occurred in the measured data. Separate door zones and vertical subdivision of the bulk-storage area were allowed in the 8-zone model. The pre-cooler prediction was largely unchanged and predicted vertical temperature differences were consistent with measured data, but the predicted mean temperature in the bulk-storage area was offset from the measurements. Little accuracy improvement was achieved by further subdivision (up to 34 zones), probably because of imprecision in defining and predicting interzone airflow rates. Irrespective of the number of zones, adequate air humidity predictions could only be achieved when water absorption by packaging was modelled as well as product weight loss, door infiltration and deposition of moisture on evaporators. For the industrial coolstore studied use of 5 or 8 air zones appeared to be the best trade off between accuracy and complexity. The model allows study of the effect of design and operational features on coolstore air temperature, humidity, product temperature and weight loss with better accuracy than previous models.
Prediction of chilling rates for food product packages : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Food Engineering at Massey University, Palmerston North, New Zealand
(Massey University, 2000) North, Michael Francis
Many food product packages contain significant air void fractions in which natural convection and radiation heat transfer occurs. This may significantly affect the cooling rate of the package as a whole. Voids tend to be either rectangular (at the top of the package), approximately triangular (e.g. in comers of the package), or can be represented as a combination of both shapes. For widely used meat cartons containing voids the bulk of the heat transfer can be modelled two-dimensionally, ignoring end effects. Empirical Nu vs. Ra correlations for horizontal rectangular air voids were available from the technical literature. Since corresponding published data were not obtainable for right-angled isosceles triangular air voids cooled from above with a hypotenuse-down orientation, temperature-time data were collected from twenty-eight transient chilling trials using analogue food packages that contained different sized voids (up to 50mm high) with this shape and orientation. A reliable finite element package was used to model the heat transfer as a conduction process throughout the entire analogue package. The effective thermal conductivities that best-fitted modelled and measured temperature-time profiles within each of five sequential time intervals during cooling were determined. The results were then curve-fitted to generate Nu vs. Ra correlations. New two-dimensional finite element models were developed for predicting chilling rates of food packages that contained combinations of isosceles triangular and/or horizontal rectangular air voids. The models were solved by using a customised heat conduction program called FINELX, in which the effective thermal conductivity in the voids was recalculated at the start of every time-step from the Nu vs. Ra correlations, but the heat transfer was otherwise modelled as conduction. The finite element model was tested against twenty independent transient chilling trials using an analogue food package that contained rectangular and triangular voids of various heights. Predictions from the finite element model agreed to within ±7% and ±12% (at the 95% level of confidence) of the measured data for packages containing rectangular voids and packages containing combined rectangular and triangular voids respectively. This indicated that the model was an accurate simulator of the overall heat transfer occurring in packages that contained significant air void fractions. Previously available simple methods for the prediction of chilling rates of such packages assumed that the contents were homogeneous solids with 'effective' thermal properties based upon the packaging arrangement and the relative amounts of solid and air. These methods were shown to be inaccurate. A simple model based on the semi-infinite slab shape was developed for predicting chilling rates of food packages that contained combinations of isosceles triangular and/or horizontal rectangular void shapes. The simple model accounted for the presence of air voids by the use of effective heat transfer coefficients. Several types of solution method were possible: from analytical methods to simple numerical methods with a run-time of only a few seconds on a 350MHz Pentium II computer, which was significantly less than the 3 hours preparation and 5 hours run-time for the finite element model. Testing of the simple model against measured data from forty-eight transient chilling trials yielded 95% confidence intervals of (-6, +12)%, (-15, +11)%, and (-9, +17)% for packages containing rectangular voids, triangular voids, and combined voids respectively. The quality of prediction indicated that the assumptions employed during the development of the simple model did not worsen its accuracy beyond a level that was likely to be acceptable in industry. Although the simple model gave relatively accurate results for much less computational effort, the customised finite element approach would allow researchers to extend the applicability of the model to any void shape, provided that natural convection and radiation heat transfer data within that particular void shape were available.
A CFD modelling system for air flow and heat transfer in ventilated packing systems during forced-air cooling of fresh produce : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Food Engineering at Massey University
(Massey University, 2002) Zou, Qian
Forced-air cooling is the common method for precooling horticultural produce. Ventilated packaging systems are often used to facilitate cooling efficiency. A computational fluid dynamics (CFD) modelling system was developed to simulate airflow and heat transfer processes in the layered and bulk packaging systems during the forced-air cooling of fresh produce. Airflow and heat transfer models were developed using a porous media approach. The areas inside the packaging systems were categorised as solid, plain air, and produce-air regions. The produce-air regions inside the bulk packages or between trays in the layered packages were treated as porous media, in which the volume-average transport equations were employed. This approach avoids dealing with the situation-specific and complex geometries inside the packaging systems, and therefore enables the development of a general modelling system suitable for a wide range of packaging designs and produce. The calculation domains were discretised with a block-structured mesh system that was referenced by global and local grid systems. The global grid system specifies the positions of individual packages in a stack, and the local grid system describes the structural details inside individual package. The solution methods for airflow and heat transfer models were based on SIMPLER (Semi-Implicit Method for Pressure-Linked equations Revised) method schemes, and the systems of linear algebraic equations were solved with GMRES (Generalised Minimum Residual) method. A prototype software package CoolSimu was developed to implement the solution methods. The software package hid the core components (airflow and heat solvers) from user, so that the users without any knowledge of CFD and heat transfer can utilise the software to study cooling operations and package designs. The user interaction components in CoolSimu enable users to specify packaging systems and cooling conditions, control the simulation processes, and visualise the predicted airflow patterns and temperature profiles. When the predicted and measured product centre temperatures were compared during the forced-air cooling of fresh fruit in several layered and bulk packaging systems, good agreements between the model predictions and experimental data were obtained. Overall, the developed CFD modelling system predicted airflow patterns and temperature profiles with satisfactory accuracy.
Modeling heat transfer in butter products : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy (Ph. D.) in Bioprocess Engineering, Institute of Technology and Engineering, Massey University, Palmerston North, New Zealand
(Massey University, 2007) Nahid, Amsha
Butter keeping quality and pallet physical stability 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 cooling and heating operations due to significant supercooling and delayed crystallization of the fat fraction of butter at temperatures well below the equilibrium 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 limitations) with equilibrium thermal properties giving accurate predictions when the butter was completely frozen before thawing. For partially 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 during freezing release of latent heat observed as a temperature rebound is controlled as much by the rate of crystallisation of water in each of the water droplets as by the rate of heat transfer. A conduction only model including water crystallization kinetics based on the Avrami Model predicted freezing in butter successfully. Simple models with equilibrium 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 individual blocks were extended to predict heat transfer in butter pallets. 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 full and half pallets at a commercial storage facility 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 parallel 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 modelling work is required in order to develop guidelines for estimating effective heat transfer coefficient values for internal block face for industrial scenarios.

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