Review of effective thermal conductivity models for foods

The literature associated with modelling and predicting the thermal conductivities of food products has been reviewed. The uncertainty involved in thermal conductivity prediction increases as the differences between the food components' thermal conductivities increase, which means that there is greater uncertainty involved with predicting the thermal conductivity of foods which are porous and/or frozen, than with unfrozen, non-porous foods. For unfrozen, non-porous foods, a number of simple effective thermal conductivity models that are functions only of the components' thermal conductivities and volume fractions may be used to provide predictions to within ±10%. For frozen and/or porous foods, the prediction procedure is more complicated, and usually requires the prediction of porosity and/or ice fraction, which introduces another source of error. The effective thermal conductivity model for these foods may require an extra parameter (in addition to the components' thermal conductivities and volume fractions) whose value must often be determined empirically. Recommendations for selecting models for different classes of foods are provided. There is scope for more research to be done in this area.     

Extension of soil thermal conductivity models to frozen meats with low and high fat content

Thermal conductivity models of frozen soils were analyzed and compared with similar models developed for frozen foods. In total, eight thermal conductivity models and 54 model versions were tested against experimental data of 13 meat products in the temperature range from 0 to −40 °C. The model by deVries, with water+ice (wi) as the continuous phase, showed overall the best predictions. The use of wi leads generally to improved predictions in comparison to ice; water as the continuous phase is beneficial only to deVries model, mostly from −1 to −20 °C; fat is advantageous only to meats with high fat content. The results of this work suggest that the more sophisticated way of estimating the thermal conductivity for a disperse phase in the deVries model might be more appropriate than the use of basic multi-phase models (geometric mean, parallel, and series). Overall, relatively small differences in predictions were observed between the best model versions by deVries, Levy, Mascheroni, Maxwell or Gori as applied to frozen meats with low content of fat. These differences could also be generated by uncertainty in meat composition, temperature dependence of thermal conductivity of ice, measurement errors, and limitation of predictive models.     

A numerical model for thermal mapping in a hermetically sealed reciprocating refrigerant compressor

In a refrigerant compressor, improvement in performance such as reduction of various electrical and mechanical losses, reduction of gas leakage, better lubrication, reduction of suction gas heating etc. can be achieved by maintaining a low temperature rise inside the compressor. Proper selection and location of an internal over load protector relay, estimation of heat transfer coefficient and winding insulation coefficient are also vital in enhancing the performance. In this context it is necessary to understand the temperature distribution inside a compressor for an optimal design. In this paper, a numerical model has been created and a heat transfer analysis for a hermetically sealed reciprocating refrigerant compressor is presented. The temperature distribution inside the compressor has been obtained taking into consideration the various heat sources and sinks and compared with experimental results. The maximum temperature was observed at the rotor which was 427.5 K. The deviation of the predicted rotor temperature from that of experimental value is 5.5% only. A good agreement was found between experimental results and that predicted in the numerical analysis.     

Numerical modelling of the temperature increase in frozen food packaged in pallets in the distribution chainModélisation numérique de l'augmentation de température des produits alimentaires congelés palettisés dans la chaîne de distribution

Frozen food can undergo temperature rise essentially during handling processes which are the weakest links of the cold chain: delivery, loading or unloading operations and temporary storage where pallets are generally handled in an ambience above 0°C. In this study, the temperature rise in a pallet is investigated numerically and experimentally. A three-dimensional finite-volume heat transfer model is developed using Phoenics Computational Fluid Dynamics (CFD) software. Food temperature within the pallet is predicted as a function of time of exposure, ambient conditions, product initial temperature, palletization and thermal characteristics of products and packaging. The experiments are carried out with packaged frozen fish pallets placed on a closed or open dock. The temperatures are recorded, at different levels in pallets over 25- to 85-min periods. The model shows good agreement with experimental results.     

A review of numerical models of airflow in refrigerated food applications

Temperature homogeneity in most food refrigeration systems is directly governed by the airflow patterns in the system. Numerical modelling of airflow provides an opportunity to develop improved understanding of the underlying phenomena influencing system performance, which can lead to reduced temperature heterogeneity and increased effectiveness and efficiency of refrigeration systems. With the rapid advances in computational power of recent years, the use of Computational Fluid Dynamics (CFD) techniques in this application has become popular. This paper reviews the application of CFD and other numerical modelling techniques to the prediction of airflow in refrigerated food applications including cool stores, transport equipments and retail display cabinets.     

Generalized model for the simulation of food refrigeration. Development and validation of the predictive numerical method

A generalized mathematical model was developed to simulate food refrigeration in air. The model takes into account surface water evaporation. It allows food physical properties to be considered as functions of temperature and/or composition, while providing means for including internal heat generation, composite materials (for instance, flesh and skin) and time-varying external temperature and humidity. Wetted surfaces and packaging can also be accounted for by the model, which can be used for spheres, infinite or finite cylinders, slabs. The numerical method was developed using the Crank-Nicolson scheme, and compared with exact analytical solutions as well as with experimental data on the refrigeration of various foods.     

Modelling of food transportation systems – a review

In 2002, over a million refrigerated road vehicles, 400,000 refrigerated containers and many thousands of other forms of refrigerated transport systems are used to distribute chilled and frozen foods throughout the world. All these transportation systems are expected to maintain the temperature of the food within close limits to ensure its optimum safety and high quality shelf life.Increasingly, modelling is being used to aid the design and optimisation of food refrigeration systems. Much of this effort has concentrated on the modelling of refrigeration processes that change the temperature of the food such as chilling, freezing and thawing. The purpose of a refrigerated transport system is to maintain the temperature of the food and appears to have attracted less attention from modellers. This paper reviews the work that has been carried out specifically on the modelling of food temperature, microbial growth and other parameters in the transportation of food.     

Evaluation of the mean ice ratio as a function of temperature in a heterogeneous food: Application to the determination of the target temperature at the end of freezing

The freezing process is widely used in the food industry. In the 70s, French regulation authorities have created in collaboration with the food industry the concept of «surgélation» process with the objective of improving the image of high quality frozen foods. The process of “surgélation” which could be translated as “super freezing” corresponds to a freezing process for which a final temperature of −18 °C must be reached “as fast as possible”. This concept was proposed in opposition to a conventionally “freezing” process for which no specific freezing rate is expected and the final storage temperature can be of −12 °C only. The objective of this work is to propose a methodology to evaluate the mean amount of frozen ice in a complex food as a function of temperature and to deduce a target temperature that must be considered as the temperature for which the food may be considered as “frozen”. Based on the definition proposed by the IIF-IIR red book, this target temperature has been defined as the temperature for which 80% of the freezable water is frozen. A case study is proposed with a model food made of two constituents.     

Modeling and performance analyses of evaporators in frozen-food supermarket display cabinets at low temperatures

This paper presents modeling and experimental analyses of evaporators in “in situ” frozen-food display cabinets at low temperatures in the supermarket industry. Extensive experiments were conducted to measure store and display cabinet relative humidities and temperatures, and pressures, temperatures and mass flow rates of the refrigerant. The mathematical model adopts various empirical correlations of heat transfer coefficients and frost properties in a fin-tube heat exchanger in order to investigate the influence of indoor conditions on the performance of the display cabinets. The model is validated with the experimental data of “in situ” cabinets. The model would be a good guide tool to the design engineers to evaluate the performance of supermarket display cabinet heat exchangers under various store conditions.     

Modelling heat and mass transfer in frozen foods: a review

This paper reviews mathematical methods for modelling heat and mass transfer during the freezing, thawing and frozen storage of foods. It starts by considering the problems in modelling heat transfer controlled freezing (the Stefan problem): release of latent heat, sudden changes in thermal conductivity. The author gives a unified overview of the common numerical methods: finite difference, finite element and finite volume. Mass transfer is then considered, involving different phenomena and approaches for dense and porous foods. Supercooling, nucleation and trans-membrane diffusion effects during freezing, and recrystallization during frozen storage are considered next. High pressure thawing and thawing are considered in view of their recent popularity. Finally, the paper offers a brief look at mechanical stresses during freezing, a much neglected area. It is concluded that while modelling heat transferred controlled freezing is a settled problem, much work remains to be done in modelling associated phenomena in order to gain the ability to predict changes in food quality at the micro-level.     

Quantitative prediction of microbial behaviour during food processing using an integrated modelling approach: a review

Microbiological safety of food relies on microbial examination of raw materials and final products, coupled with monitoring process parameters and hygiene standards. The concept of predictive microbiology was developed to evaluate the effect of processing, distribution and storage operations on food safety. The objective of this paper is to review the approaches proposed by researchers to quantify the effect of competitiveness or fluctuating conditions on bacterial behaviour. The main microbial models that quantify the effects of various hurdles on microbial kinetics are presented. To provide complementary information for microbial models, three areas have to be considered: process engineering that characterises and models mass and heat transfer; microbiology that characterises and models bacterial behaviour and metabolite production, and; applied thermodynamics that characterises and models the physico-chemical properties of a food product. Global modelling approaches, developed by integrating the previous models, are illustrated with recent results.     

A generalised mathematical modelling methodology for design of horticultural food packages exposed to refrigerated conditions: Part 3, mass transfer modelling and testing

A modelling methodology developed to simulate a wide range of heat and mass transfer processes in refrigerated storage of horticultural foods was used for prediction of mass transfer of water vapour in packaged horticultural products. The mass transfer pathways, which are considered the most significant in industrial practice for a range of products and packaging systems, were modelled. Experimental testing was conducted for 10 product-package systems. Even though the model supports multi-zone package representation, a single zone was found to be adequate for all test data. Agreement between prediction and measurement was within likely data uncertainties for mass loss, packaging moisture uptake and relative humidity difference to the external environment. Sub-models for which further development may be justified are identified. Coupled with the heat transfer results presented in Part 2, the present work verifies the validity of the overall model structure presented in Part 1.     

A generalised mathematical modelling methodology for the design of horticultural food packages exposed to refrigerated conditions Part 2. Heat transfer modelling and testing

Sub-models required to implement the generalised simulation system, described in Part 1 for predicting in-package cooling rates of horticultural produce, are presented. These are based on heat transfer principles, but their derivation also involved application of heuristics derived by engineering judgement. Testing used two different products, eight package designs and data from four independent sources. Lack of fit between experiment and prediction was no larger than could be explained by likely data uncertainties so there is confidence that the simulation system will be accurate for a wide range of products and package designs. The object-oriented design of the simulation package allows individual sub-models to be updated without affecting any other sub-model, thereby ensuring the simulation package can remain up-to-date. In Part 3 the mass transfer sub-models are presented and test results reported.     

Thermal stresses during freezing of a two-layer food

Thermal stresses during freezing of a two-layer material, that can contribute to crack formation, are studied. A 3D numerical model of a two-layer food with food analog Tylose^® and chocolate is presented. An apparent specific heat formulation was used to model the heat transfer with phase change over a temperature range. The mechanics model considered viscoelasticity in Tylose^®; thermal strains were imposed due to the increase in volume from ice formation in Tylose^® and the decrease in volume from freezing of the chocolate. Results show that complex evolution of stresses, that include compressive and tensile values, occur during freezing. Sensitivity analysis showed that the Poisson's ratio was a very important parameter that affects the magnitude of stress. Variations in calculated stresses were found to be proportional to variations in Young's modulus. Knowing the stresses, the possibilities of undesired cracking of a chocolate coating applied onto another material such as ice cream could be evaluated.     

A physical model to predict climate dynamics in ventilated bulk-storage of agricultural produce

This paper presents a physical model for predicting climate dynamics in ventilated bulk-storage of agricultural produce. A well-ordered model presentation was obtained by combining an object-oriented zonal decomposition with a process-oriented decomposition through matrix–vector notation. The objective of this paper is twofold: (1) to present the modelling procedure and (2) to present the resulting model, validated with real data. The model is a suitable simulator to assess potential effects of changes in ambient climate, design, and controller tunings. The model predictions fit well to extensive real data from three different cases. The good fit for all three cases was achieved with the five calibration parameters calibrated on the basis of data from one case only.     

Viscosity and thermal conductivity of halogenated methane and ethane refrigerantsViscosité et conductivité thermique des frigorigènes à base de méthane ou d'éthane halogénés

Viscosity and thermal conductivity of liquid halogenated methane and ethane refrigerants from about 200 K to near the critical temperature, at saturation and also at pressures up to 50 MPa, are shown to be satisfactorily correlated on the basis of a scheme developed by Dymond and Assael from consideration of hard-sphere theory. For the 31 refrigerants considered here, from the 1445 viscosity and 1226 thermal conductivity measurements examined only 5.2% were found to deviate by more than 5% from the proposed scheme.     

CFD simulation of coupled heat and mass transfer through porous foods during vacuum cooling process

A numerical simulation by using a computational fluid dynamics (CFD) code is carried out to predict heat and mass transfer during vacuum cooling of porous foods on the basis of mathematical models of unsteady heat and mass transfer. The simulations allow the simultaneous prediction of temperature distribution, weight loss and moisture content of the meats at low saturation pressure throughout the chilling process. The simulations are also capable of accounting for the effects of the dependent variables such as pressure, temperature, density and water content, thermal shrinkage, and anisotropy of the food. The model is verified by vacuum cooling of cooked meats with cylindrical shape within an experimental vacuum cooler. A data file for pressure history was created from the experimental pressure values, which were applied in the simulations as the boundary condition of the surface temperature.     

A study of accurate latent heat measurement for a PCM with a low melting temperature using T-history method

When the latent heat of a phase change material (PCM) with a lower melting point than ambient temperature was assessed according to the standard T-history method using a vertically oriented test tube, a temperature gradient occurred in the longitudinal direction of the tube due to natural convection. This led to a decrease in the accuracy of the latent heat of fusion measurement. In this study, the accuracy of the measurement with the original T-history method was improved without decreasing the test's simplicity and convenience by setting the test tube horizontally. The heat transfer to the vapor-layer of the tube under volume change during melting was assumed to be negligible and the results were calculated using the two inflection points of temperature as the start and end of latent heat period. Under these assumptions, the results agree closely with other reference data. And, the new method proposed in this study showed a remarkable reduction in data scattering.     

Computation of the airflow in a pilot scale clean room using K- turbulence models

This work deals with the assessment of the airflow in a food-processing clean room. The flow pattern inside the working area of a pilot scale clean room was numerically investigated using a computational fluid dynamics code based on a finite volume formulation. Two versions of the k- turbulence model were tested: the standard and the RNG version. The analysis of the velocity magnitude does not reveal sensitive differences between them. Moreover, both models well predict the main features of the flow and numerical results agree with experimental measurements. However, a further examination shows that the RNG k- turbulence model predicts more swirls and more complex trajectories. As the standard k- model overestimates the turbulent diffusion, the RNG version seems to be more suitable to calculate the airflow in clean rooms. The influence of initial turbulence intensity is also pointed out. Finally, the study of the airflow below a laminar flow unit confirms that the design of clean rooms can benefit from the numerical approach.