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.     

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 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.     

Effective thermal conductivity of a high porosity model food at above and sub-freezing temperatures

The modelling of heat transfer within materials with high porosity is complicated by evaporation-condensation phenomena. The aim of this work is to develop a model for apparent thermal conductivity in these products. The effective thermal conductivity of a porous food model (sponge) having 0–60% moisture contents and 0.59–0.94 porosity was measured by a line-source heat probe system in the range −35 to 25 °C. Two predictive models of the effective thermal conductivity of porous food were developed (Krischer and Maxwell models). The effective thermal conductivity predicted by Krischer model were in good agreement with the experimental data. Also, it was shown that the model including the effect of evaporation-condensation phenomena in addition to heat conduction was useful to predict the effective thermal conductivity of sponges.     

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.     

Measurement of thermal conductivity of ice slurry made from solution by transient line heat-source technique (analytical discussion on influence of latent heat of fusion)

We have been studying on ice slurry in a dynamic type ice storage system. The ice slurry has many good characteristics. The ice slurry can be made from a solution. When designing the ice storage system using this ice slurry, thermal conductivity of the ice slurry is essential.When thermal conductivity of the ice slurry made from a solution is measured by a transient line heat-source technique, a measurement value of thermal conductivity is affected by a latent heat of fusion of ice. Therefore, the thermal conductivity measured is apparent thermal conductivity. In this study, influences of Stefan number, initial concentration of the solution, initial solid fraction (initial IPF) and Fourier number on the thermal conductivity was analytically discussed to improve measurement accuracy of the thermal conductivity of ice slurry in the transient line heat-source technique.     

Introduction to the field of cryobiology and overview of selected papers

The article is a synopsis of the 9 papers in the field of cryobiology, particularly regarding the use of modern cryopreservation and related techniques for conservation of genetic resources of endangered species and economically important breeds of wild and domesticated animals and plants published in this issue of the International Journal of Refrigeration. The papers are related to vitrification, primarily of reproductive and progenitor cells as a swiftly expanding and effective approach of biostabilization, as well as to cryopreservation of spermatozoa, leucocytes, and other cells of the humans, sturgeon species, European mink, marine invertebrates, and plants. A brief introduction to cryobiology and related fields is also provided.     

Modeling the thawing of frozen foods using air impingement technology

With the continual growth in the use of frozen foods both in retail and in food service, there is a need to develop improved thawing methods. Current methods are often undesirably slow (still air) or are very expensive and cause uneven thawing (microwave). Air impingement technology is one possible method to improve the thawing of frozen foods. The objectives of this research were to develop a two-dimensional model for air impingement thawing frozen foods and to verify the model experimentally. Frozen products were thawed using a laboratory impingement system with a single impingement jet. A simulated meat product (Tylose gel) was used as the test material. Thawing of a Tylose disk (12.7 cm diameter, 1.98 cm thickness) with air at 6 °C without impingement required more than 12 h, while thawing under a single impingement jet took less than 3 h, over four times faster. Results from the finite difference model gave good agreement with experimental data. Moisture loss during thawing was typically over-predicted because moisture gain due to condensation was not modeled.     

Development and validation of “grey-box” models for refrigeration applications: A review of key concepts

“Grey-box” modelling combines the use of first-principle based “white-box” models and empirical “black-box” models, offering particular benefits when: (a) there is a lack of fundamental theory to describe the system or process modelled; (b) there is a scarcity of suitable experimental data for validation or (c) there is a need to decrease the complexity of the model. The grey-box approach has been used, for example, to create mathematical models to predict the shelf life of chilled products or the thermal behaviour of imperfectly mixed fluids, or to create models that combine artificial neural networks and dynamic differential equations for control-related applications. This paper discusses the main characteristics of white-box, black-box and their integration into grey-box models, the requirements and sourcing of accurate data for model development and important validation concepts and measures.     

High pressure freezing and thawing of foods: a review

The phase diagram of water shows that the melting temperature of water decreases with pressure down to −21°C at 210 MPa while the opposite effect is observed above this pressure. This phenomenon allows the achievement of rapid freezing and thawing of foods that mainly contain water. In addition, pressure-assisted thawing has the advantage of inducing a reduction in drip loss which tends to be a function of process parameters and nature of the product. Concerning pressure shift freezing, this process permits the significant preservation of the microstructure of biological substances. The current status of high pressure freezing and thawing applications in foods is reviewed in this paper. Concepts and principles underlying the application of these technologies are firstly developed. Available literature on the applications of high pressure freezing and thawing is then presented and discussed. Finally, the modelling aspects of theses processes are dealt with.     

Analysis of stresses during the freezing of solid spherical foods

An analytical model is presented to calculate thermal stresses and strains during the freezing of a spherical food, taking into account both the expansion during phase change and subsequent thermal contraction due to temperature decrease. The Young modulus and Poisson ratio are assumed to undergo a step change at the freezing point. The expansion due to phase change cause a uniform and virtually constant isotropic tensile stress in the unfrozen core. In the frozen shell, this expansion gives rise to tensile radial stress and compressive tangential stress. The thermal contraction subsequent to phase change causes reverse effects, i.e. uniform compressive stress in the unfrozen core and compressive radial stress in the frozen shell, while tangential stress is tensile on the outside and compressive on the inside of the frozen shell. The effect of thermal contraction is noticeable only at cryogenic temperatures.     

Modelling transport phenomena in refrigerated food bulks, packages and stacks: basics and advances

Transport phenomena, comprising airflow, heat and mass transfer, are key processes in refrigerated storage. This paper gives a review of approaches to modelling transport phenomena in food bulks, packages and stacks. Darcy–Forchheimer porous media models have been successfully used. Ergun theory was found not directly applicable when foods are stored in packages, which cause flow confinement and vent hole resistance, invalidating traditional theory. Heat and mass transfer in food bulks has been modelled using single- and two-phase models. Suggested modifications were demonstrated to not be generally valid, leaving much scope for further development of models for refrigerated system design. Direct CFD approaches were shown to be successful alternatives to achieve this goal.     

Modeling of frosting behavior on a cold plate

This paper proposes a mathematical model to predict the frost properties and heat and mass transfer within the frost layer formed on a cold plate. Laminar flow equations for moist air and empirical correlations for local frost properties are employed to predict the frost layer growth. Correlations for local frost density and effective thermal conductivity of the frost layer, derived from various experimental data, are expressed as a function of the various frosting parameters: the Reynolds number, frost surface temperature, absolute humidity and temperature of the moist air, cooling plate temperature, and frost density. The numerical results are compared with experimental data to validate the proposed model, and those agree well with the experimental data within a maximum error of 10%. Heat and mass transfer coefficients obtained from the numerical analyses are also presented. The results show that the model for the frost growth using the correlation of the heat transfer coefficient without considering the air flow has a limitation in its application.     

Recent developments in simulation techniques for vapour-compression refrigeration systems

Simulation has been widely used for performance prediction and optimum design of refrigeration systems. A brief review on history of simulation for vapour-compression refrigeration systems is done. The models for evaporator, condenser, compressor, capillary tube and envelop structure are summarized. Some developing simulation techniques, including implicit regression and explicit calculation method for refrigerant thermodynamic properties, model-based intelligent simulation methodology and graph-theory based simulation method, are presented. Prospective methods for future simulation of refrigeration systems, such as noise-field simulation, simulation with knowledge engineering methodology and calculation methods for nanofluid properties, are introduced briefly.     

The primary chilling of poultry carcasses—a review

This paper reviews the published scientific studies that have been carried out on the chilling of poultry carcasses. The prime purpose of chilling is to limit the growth of both pathogenic and food spoilage microorganisms. There are a wide range of publications that show that, in general, the numbers of both types of microorganism, on the surface of poultry carcasses, is reduced during the chilling process. Immersion or spin chilling is not used in the production of ‘fresh’ chilled poultry in Europe, ‘dry’ air chilling being the preferred chilling method. Many people believe that there is some clear microbiologically based reason behind the selection of air chilling. However, the published data do not appear to support this belief, and if anything point to a microbial advantage of immersion systems. The rate of chilling has some influence on the taste, texture and appearance of poultry meat. Very rapid chilling can result in tougher chicken meat, while very slow chilling can produce pale soft exudative (PSE) muscle. However, in both cases the effect is not as marked as with red meat. No comprehensive published data has been found on the effect of a range of chilling systems, chilling conditions, carcass weight and shape on the rate of chilling, weight loss and heat loss. Without such data it is impossible to optimise the design of a poultry chilling system.     

Development of computer program for simulation of an ice bank system operation, Part I: Mathematical modelling

Since the use of standard engineering methods in the process of an ice bank performance evaluation offers neither adequate flexibility nor accuracy, the aim of this research was to provide a powerful tool for an industrial design of an ice storage system allowing to account for the various design parameters and system arrangements over a wide range of time varying operating conditions. In this paper the development of a computer application for the prediction of an ice bank system operation is presented. Static, indirect, cool thermal storage systems with external ice on coil building/melting were considered. The mathematical model was developed by means of energy and mass balance relations for each component of the system and is basically divided into two parts, the model of an ice storage system and the model of a refrigeration unit. Heat transfer processes in an ice silo were modelled by use of empirical correlations while the performance of refrigeration unit components were based on manufacturers data. Programming and application design were made in Fortran 95 language standard. Input of data is enabled through drop down menus and dialog boxes, while the results are presented via figures, diagrams and data (ASCII) files. In addition, to demonstrate the necessity for development of simulation program a case study was performed. Simulation results clearly indicate that no simple engineering methods or rule of thumb principles could be utilised in order to validate performance of an ice bank system properly.     

A review on surface heat and mass transfer coefficients during air chilling and storage of food products

Heat and mass transfer coefficients are needed for the mathematical simulation of air chilling and storage of solid food products. Average transfer coefficient values and distributions around cylinders are now quite well known while it is not the case for solids of more complex shapes. CFD models are more and more often used to calculate transfer coefficient values on a single food product or packaging. Experimental knowledge is reviewed and the way it can be used by scientists and engineers to determine their own transfer coefficient values is illustrated. The potentials and limitations of present CFD models are illustrated and future improvements are also discussed.     

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.     

Detailed thermodynamic characterization of hermetic reciprocating compressors

The aim of this paper is the detailed analysis of different well-known thermodynamic efficiencies usually used to characterize hermetic compressors. Attention is focussed on the volumetric efficiency, the isentropic efficiency, and the combined mechanical–electrical efficiency. A procedure is presented to detach these efficiencies into their main components (physical sub-processes) to get deeper insight on the overall behavior.The volumetric efficiency is split into partial efficiencies related to pressure drop and heat transfer effects, supercharging effects, superdischarging effects, leakages, etc. The isentropic efficiency is detached using two different points of view: the work associated to the individual sub-processes (compression, discharge, expansion, suction), and the work associated to the underpressures, overpressures, and between the inlet and outlet mean compressor pressures. Finally, the combined mechanical–electrical efficiency is related to the heat transfer losses/gains, and to the exergy transfers and exergy destroyed.Even though some of the concepts introduced in the paper can be applied to different kinds of compressors, the discussion is specially focussed on hermetic reciprocating compressors. An advanced simulation model developed by the authors has been used to generate data to illustrate the possibilities of the detailed thermodynamic characterization proposed. The criteria developed are useful tools for comparison purposes, to characterize compressors, and to assist designers during the optimization process.     

Numerical study of electroosmotic (EO) flow in microfabricated EO pump with overlapped electrical double layer (EDL)

Micropump is an important component for the development of micro absorption heat pump systems. To study the performance of microfabricated EO pump with the dimension comparable to the electrical double layer (EDL), a model avoiding the use of the Boltzmann equation was developed to investigate the EO flow instead of using the Poisson–Boltzmann (PB) equation. Generally used Debye–Huckle approximation and symmetric condition are also not involved so this model can be applied in the more complicated EO micropumps. Numerical simulation was carried out to study the distributions of potential, ions and net charge density in the EO micropump. Comparison between the present model and the PB equation was conducted. Using the present model, the EO flow in the EO micropump with overlapped EDL was investigated. It shows that the flow is quite different from the channel with dimension much larger than the EDL, which exhibits plug-like flow characteristics. The errors induced by the PB equation for the pumps with different depths were evaluated. It shows that the accuracy of the PB equation is not good when the EO pump is very thin.