Computational Methods in Food Processing

Computational methods in food processing:

Applications in heat transfer

S. Yanniotis

Department of Food Science and Technology Agricultural University of Athens, Greece

Abstract

Calculation of heat transfer rates in processing of foods is essential in order to design optimum processing conditions and the required equipment. The use of computational methods in food processing heat transfer applications that has been published in recent years is briefly presented in this paper.

Introduction

The aim of the food industry today is to provide safe, nutritious and of high sensory quality food to the consumers. This aim is achieved by applying basic concepts of chemistry, microbiology and engineering to food processing. One of the most important and more common engineering disciplines in food processing is heat transfer. There are many unit operations in the food industry where steady or unsteady state heat transfer is taking place e.g. pasteurization, sterilization, blanching, dehydration, evaporation, cooling, freezing etc. Heat transfer in these operations is of primary importance and affects the hygienic, nutritional and sensory quality of the product. In applying heat transfer knowledge to food processing, one must take into account that food industry usually deals with difficult raw materials. As biological materials, in many cases they are non-uniform and of variable consistency. The shape of the products is often irregular and some times changes during processing. Many food products undergo physical property changes during heating and some even composition changes. Some, are shear- dependant, others are time-dependant. In some cases, the materials are anisotropic. In addition, very often heat transfer is combined with mass transfer and/or momentum transfer. The effect of heat treatment on the food product

596 Advanced Computational Methods in Heat Transfer VI depends on the combination time-temperature because, in addition to temperature changes during processing, biochemical and microbiological changes take place. Heat transfer and reaction kinetics considerations must be taken into account in designing thermal processes of foods. Overprocessing, by applying high heat treatment, has a negative effect on the product quality and its nutritional value. Underprocessing may result in spoilage of the product.

Because of these complexities, the unsteady state heat transfer partial differential equation can be solved analytically only with several simplifying assumptions. Numerical solutions by finite differences and finite elements methods in canning, freezing, drying and other food processing operations have been used. There are several publications on simple shape bodies using the finite difference method, while in more irregular geometries, the finite element method has been used. Recently, Computational Fluid Dynamics (CFD) codes have been applied to food engineering problems. The present paper attempts to outline the recent scientific activity on the applications of computational methods in heat transfer research in the field of food processing and preservation.

Current State

Sterilization

The required processing time in commercial canning is usually calculated with semi-empirical methods. It can be calculated also by analytical solutions of the heat conduction equation for simple cases. For more complicated situations, numerical solutions have been applied. Most of the existing work with numerical solutions applied earlier is focussed on solid foods or very viscous foods like purees and concentrates which are usually assumed to be heated by pure conduction. One of the earliest applications of numerical methods to thermal processing of foods, was that of Teixeira et al.[l]. Recently, Welt et al. [2] compared the time step restrictions in a heat transfer simulation in a cylindrical can with an explicit finite difference approach using both the capacitance and the non-capacitance surface approaches. Akterian [3] developed a mathematical model for conduction heating of cans with convective boundary condition. He solved the problem with finite differences. Banga et al. [4] developed a model for the thermal processing of anisotropic and non- homogeneous conduction-heated canned foods and applied it to canned tuna fish. The mathematical analysis in sterilization of stationary cans containing liquid foods is more difficult because in this case the heat is transferred inside the can by natural convention. Since the fluid motion is due to the buoyancy force, the velocity in the momentum equations is coupled with the temperature in the energy equation. Therefore, the momentum equations must be solved simultaneously with the energy equation in order to calculate the temperature profile, the velocity profile and the slowest heating zone of the can. Numerical solution of this problem has attracted the interest of some researches. Datta and

Texeira [5] numerically predicted transient temperature and velocity profiles during natural convection heating of canned liquid foods. Yang et al. [6] used a CFD code for the simulation of natural convection heating of starch dispersions in a cylindrical still can. Ghani et al. [7] have applied CFD to calculate transient temperature and velocity profiles in sterilization of canned liquid foods in a still- retort. Quarini and Scott [8] used a CFD package to predict the thermal- hydraulic behaviour of a non-Newtonian liquid food heated in a vertical still can.

Aseptic processing and filling has been developed in recent years primarily to improve the quality of products conventionally heated in autoclaves. High temperature-short time heating of the product is applied before the container is filled and sealed aseptically. This method is applied to liquid foods and to liquid foods that contain particulates, which can be pumped through heat exchangers.

Residence time distribution in holding tubes, where the product stays for certain time at a predetermined temperature in order to receive the required heat treatment, and in heat exchangers is an important processing parameter not only for liquids that contain paticulates but in continuous flow systems in general.

The minimization of residence time scattering from the mean value is desirable in process optimization. The more narrow the residence time distribution, the more uniform will be the heat treatment and the better the nutritional and organoleptic quality of the product. The number of surviving microorganisms in a heat treated product is determined by the least heated part of the product. To be on the safe side, processors usually base the heat treatment on the center temperature of the fastest moving part through the system, but this results in overprocessing of the main percentage of the product which induces quality decrease. Yang et al. [9] calculated the lethality distribution within particles in the holding section of an aseptic processing system using a finite difference method. Sandeep et al. [10] wrote a three-dimensional finite difference program to compute the liquid and particulate velocities in a suspension passed through a holding tube. The program incorporated the effect of particulates on the liquid velocity, the interactions between particulates, the non-Newtonian behavior of the liquid and the effect of particulate concentration and temperature on the viscosity of the suspension. A finite element program was used to determine the temperature distribution within the particulates in the heat exchanger, the holding tube and the cooling section of an aseptic processing system.

Electroheating methods

Electroheating methods, mainly microwave heating and ohrmc heating, are volumetric heating methods and thus, they do not depend on heat transfer from 'the surface to the center but all the mass of the product heats simultaneously. Microwave heating of foods is a well-established heating method on domestic scale. However, on industrial scale the use of microwave heating is limited. It is being used mainly for tempering of meat, fish and butter. The main concern in microwave heating of foods in industrial scale is the uniform temperature distribution in the food. For safety reasons, all the points of the heated products must reach certain temperature. The temperature profile in the

product depends on the absorption of microwave energy and on heat transfer by conduction, convention and evaporation. The absorption of microwave energy is controlled by a number of factors such as food and packaging composition and geometry as well as microwave field distribution in the oven and the resulting field in the food [11]. Research is concentrated on understanding these interacting factors. Ohlsoon and Risman [12] developed a finite difference numerical program to simulate the electromagnetic field distribution and the heat distribution in food pieces in a tubular microwave heater in order to find microwave field patterns that give uniform in-flow heating. Datta et al. [13] developed a finite element model to predict temperature distribution inside a cylindrical container of liquid in a microwave oven. Datta and Peyre [14] studied the effect of dielectric property variations on the detailed heating patterns in the food heated in a microwave cavity. Shamchong and Datta [15] studied the effect of power cycling, power level and dielectric properties on the non-uniformity of temperature during the thawing of foods. Zeng and Fagri [16] also studied the microwave thawing of cylindrically shaped samples and developed a two-dimensional model which solved numerically to deal with the thawing process including the frozen, mushy and thawed phases, and the evaporation of water. Ohmic heating generates heat inside the food due to the electrical resistance of the food when electric current passes through the food. Ohmic heating was developed for heat treatment of liquids that contain solid particulates because the solid phase can be heated at a similar rate as the liquid and thus the heat treatment is more uniform. Research on ohmic heating is focussed on optimization of process conditions. Sastry [17] developed a mathematical model for the prediction of particle and fluid temperatures during ohmic heating of solid-liquid mixtures. The model was solved for a cubical shaped particle using 3-dimensional finite element in space, finite difference in time.

Cooling, Freezing and Thawing

Freezing and thawing are common operations in the food industry. The rate of heat removal affects the energy consumption, the weight loss, and the product quality. Engineering aspects, which are of interest, deal mainly with the computation of refrigeration requirements and the time-temperature history of the product. Accurate predictions in food freezing are difficult because the physical properties of foodstuffs change with temperature during freezing and in some cases, they are also direction dependent e.g. in meat freezing, heat will transfer in parallel to the muscle fibers at a different rate than in perpendicular direction

(Sun and Zhu [18]). Moraga and Salinas [19] described the fluid mechanics and heat transfer in the freezing process of a plate-shaped portion of salmon meat inside a refrigeration chamber. The finite volume method was used to solve the model. Moraga and Medina [20] used a finite volume method to solve the equations that describe unsteady forced convection and heat conduction in a meat plate during freezing. External fluid mechanics and internal solidification

Advanced Computational Methods in Heat Transfer VI 599 of water content in the meat are predicted from the model which includes continuity, Navier-Stokes and energy equations for air around the food and the heat diffusion equation inside the meat. Sheen and Hayakawa [21] developed a mathematical model which includes the volumetric change for the food freezing or thawing time estimation and process simulation. The model was solved using a finite difference method for an irregular domain (mushroom shape or spheroidal shape). Sanz et al. [22] used a mathematical model to simulate different cooling rates at the surface of a pork muscle with the aim to find the freezing rates that led to a good quality product with respect to the optimum distribution of small ice crystals located inside and outside the tissue fibres. The model was solved with a finite element method. Saad and Scott [23] presented a technique to assess the accuracy of the Crank-Nicolson and the two-step finite difference methods in solving the non-linear simulation of food freezing. Tocci and Mascheroni [24] developed a mathematical model for the simulation of heat and mass transfer during freezing and storage of foods. They solved the model numerically.

The temperature profile during cooling is of interest in designing optimum cooling procedures and the required cooling equipment. The cooling of fruits and vegetables, besides the heat conduction inside the product and convection and radiation at the surface, must take into account the internal heat generation due to respiration, moisture loss due to transpiration and the evaporative cooling that transpiration causes. Numerical models for the prediction of cooling rates under these conditions have been developed [25]. Temperatures in the cooling tunnels in the chocolate manufacturing industry must be controlled effectively, since during solidification the chocolate must be cooled slowly, both for maximum contraction and to avoid quality deterioration. Tewkesbury et al. [26] used a CFD software package to predict the temperature distribution in a chocolate bar from the tempered molten chocolate stage to the finished confectionery item with ultimate aim to use the model for optimizing process conditions.

Simultaneous Heat and Mass Transfer

Simultaneous heat and mass transfer is found in some food processing applications e.g. dehydration, oven cooking, deep fat frying etc. In these cases, heat is transferred from the surface to the center, while moisture diffuses outward toward the product surface, where it is vaporized. In deep fat frying, in addition to heat and moisture, fat may also being transferred. Numerical solution of the transient heat conduction equation and the transient mass transfer equation has been applied to solve such problems. Chen et al. [27] developed a two-dimensional axisymmetric finite element model to simulate coupled heat and mass transfer during convection cooking of regularly shaped chicken patties, for given actual transient oven air conditions. Ikediala et al. [28] modeled the heat transfer in meat patties during single-sided pan-frying with and without turn-over using the finite element method. Ngadi [29] developed a mathematical model to describe heat, moisture and fat transfer in chicken drum-

600 Advanced Computational Methods in Heat Transfer VI sticks during deep-fat-frying. A finite element method was used to obtain solution of the mathematical equations. Mittal and Mallikarjunan [30] developed a finite element two-dimensional heat and mass transfer model for beef carcass chilling. Tsukada et al. [31] used a heat and mass transfer model combined with equations for strain-stress analysis to predict stress distribution in food during dehydration. Bowser and Wilhelm [32] developed a model for heat and mass transfer with simultaneous shrinkage of a thin non-porous film during drying. Finite elements were used to find the numerical solution. Zanoni et al. [33] set-up a computer model of bread making which describes heat and mass transfer in the product and kinetics of starch geletinization and non- enzymic browning. The equations were solved with the finite differences method. Banga et al. [34] developed a computer program for the optimization of batch processes with heat and mass transfer in food and bioproducts processing. Finite differences/finite elements were used for the solution

Other Applications

The use of modified atmospheres for insect control within unsealed grain stores is an alternative to pesticide use. Knowledge of the temperature changes, which might occur within the grain bulk, affects the choice of control strategy for this technique because they can have a profound effect on gas exchange with the outside air. Bibby [35] used a CFD code to model airflow and heat transfer inside a wheat-filled grain silo. There are many situations in which foodstuffs need to be spread over wide areas. One device for achieving this is known asfishtai ldistributor . Its purpose is to take liquid foodstuffs from a circular pipe and deliver it as a thin, uniform layer through a high-aspect-ratio rectangular exit. Rolston and Quarini [36] used a CFD code to find the velocity and temperature distributions in such a fishtail distributor with the aim to avoid recirculation spots. Sakai and Hanzawa [37] developed a model to predict two-dimensional heat transfer in food heated my far-infrared radiation. A finite element method was applied to solve the model and examine the influence of the heater temperature and surface heat conductivity on heat transfer in the food. Verboven et al. [38] calculated the local variation of heat transfer coefficient at the surface of food products heat processed by forced convection dry air using CFD codes. The effect of the variation of the local heat transfer coefficient on the product centre temperature was evaluated. Janes [39] used a CFD code to investigate the effects of various design modifications on a direct-gas-fired tunnel oven with a continuous conveyor band. Verboven et al. [40] used a CFD model to calculate the three-dimensional isothermal airflow in an industrial electrical forced-convection oven. Nicolai et al. [41] used a finite element algorithm to calculate the temperature variation inside a product heated in an oven under stochastically fluctuating oven temperature conditions.

Advanced Computational Methods in Heat Transfer VI 601

Conclusions

From the short overview that was presented in this paper it is obvious that computational methods have been applied to solve mathematical models in a wide range of food processing applications, especially in recent years. It is expected that the use of computational methods in modeling and simulation of unit operations in the food industry will be intensified in the coming years in order to allow: a) optimization related to heat transfer in food processing systems in terms of energy efficiency, equipment design, product safety and quality retention and b) on-line control of heat transfer processes which will help to handle process deviations, reduce the production cost and improve the product quality and product safety.

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