Modeling Flow and Heat Transfer During Freezing of Foods in Forced Airstreams

ABSTRACT: Mathematical modeling of food freezing has been limited to the modeling of the internal heat transfer where the external convective heat-transfer coefficients are assumed or empirically estimated. Previous procedures followed to solve the external boundary layer in tandem with the internal heat transfer were constrained by numerical complexities due to the transient nature of the heat transfer, requiring unsteady formulation for the flow. In this article, attempts have been made to decouple the flow and heat transfer equations for the external boundary layer flow over a food product being frozen. The flow equations have been solved as a steady-state problem using Falker-Skan transformations of the boundary layer equation. The heat-transfer equation for fluid flow is solved as an unsteady-state problem in conjunction with the internal heat transfer and phase change inside the product undergoing freezing. The model is validated for a case of air-impingement freezing.     

COMPUTER SIMULATION of MICROBIAL GROWTH DURING FREEZING and FROZEN FOOD STORAGE

A computer simulation model was developed to predict the time for temperature equilibration as well as microbial growth within a food product during freezing and the equilibration to frozen storage conditions. Theoretical results indicate that freezing medium temperature, surface heat transfer coefficient and product size influence the equilibration time significantly. Storage conditions influenced the equilibration time during storage and significantly influenced the growth of microorganisms. Microbial growth is a function of the freezing time. Slow freezing of a food product from a high initial temperature and stored at a relatively high temperature can provide conditions for microbial growth as compared to very rapid freezing processes. the model is a useful tool for approximate indications of effects of freezing conditions on microbial growth within a food product.     

Numerical modelling of conjugate heat and mass transfer during hydrofluidisation food freezing in different water solutions

A novel method of hydrofluidisation food freezing is numerically investigated in this paper. This technique is based on freezing small food products in a liquid medium under highly turbulent flow conditions when the heat transfer coefficient is higher than 1 000 W⋅m⁻²⋅K⁻¹, which depends on the operating and flow conditions. A numerical model was developed to characterise the freezing process in terms of the heat transfer and diffusion of liquid solution components into the food product. The study investigates the freezing process of spherical samples in binary solutions of ethanol (30%) and glycerol (40%) and ternary solution of ethanol and glucose (15%/25%). The developed model was employed to determine the concentration of the liquid solution in food samples and to quantify the effect of sample size, heat transfer coefficient, solution temperature and concentration on the process. The food sample size varied from 5 to 30 mm, and the heat transfer coefficients varied from 1 000 to 4 000 W⋅ m⁻²⋅ K⁻¹. The results confirm that a freezing time of 15 min for 30 mm diameter samples or less than 1 min for 5 mm diameter samples can be achieved with the hydrofluidisation method. The solution uptake was influenced by the solution type, sample size and process parameters and varied from 8.9 to 35 g of solute per kg of product for ethanol-glucose and glycerol solutions, respectively. This paper quantifies the advantages and possible limitations of hydrofluidisation, which has not yet been entirely studied, especially in terms of the mass absorption of different solutes.     

A model for heat transfer in cryogenic food freezing

An experimental study of the heat transfer between liquid nitrogen sprays and a model food (a gelatine slab) was carried out under conditions similar to those in a cryogenic freezer. Measurements of heat flux and local mass flow rates of the spray were made at various liquid N₂ pressures and various temperature differences between the spray and the food surface.
At higher spray pressures, the heat transfer coefficient increases with the mass flux density of the liquid available at the food surface. The quantity of liquid nitrogen sprayed onto the solid surface, the mean droplet size, spray velocity, surface coverage and the mean temperature difference between the boiling nitrogen and the food surface are major factors influencing the rate of heat transfer during the freezing process. Although the heat transfer coefficients at the food surface are much less than those obtained for individual droplets, the model provides useful data.
The results are critically discussed in relation to cryogenic freezing of foods.     

A Response Surface Method for the Estimation of Convective and Radiative Heat Transfer Coefficients during Freezing and Thawing of Foods

A procedure was developed to determine simultaneously convective and radiative heat transfer coefficients applicable to the nonsymmetric freezing or thawing of planar food. The transient state temperature distribution and transient state locations of thermal centers in a sample were used for this development together with computer programs for simulating heat transfer in the food. The coefficients were determined by minimizing squared residuals related to the temperature distributions and thermal centers. The developed method was used to determine the boundary coefficients of slabs made from a crystallized methyl cellulose gel subjected to freezing and thawing. The influence of thermophysical characteristics of the sample material on the determined coefficients was examined qualitatively.     

Non-uniform Heat Transfer During Air-Blast Freezing of a Fruit Pulp Model in Multilayer Boxes

Effective heat transfer coefficients were measured using an aluminum test body and compared with the results obtained from a Gnielinski correlation for air-blast freezing of a fruit pulp model in multilayer boxes, with the internal airflow through rectangular ducts and the hydraulic diameter as characteristic dimensions. The quantities of products inside the boxes were varied, and the inlet air velocities and temperature profiles during freezing were measured. The inlet air velocities were applied in dimensionless Gnielinski correlations to estimate the local heat transfer coefficient values. The experimental and predicted heat transfer coefficient values were used to determine an average convective heat transfer coefficient weighted by the heat transfer area. The results from this methodology were used in an analytically derived procedure for freezing-time estimates and then compared with experimental results. The average effective heat transfer coefficient underestimated freezing times and demonstrated a higher level of accuracy than the Gnielinski correlation when applied to boxes containing smaller product amounts. For experiments with greater quantity of products, the use of average heat transfer coefficients from the Gnielinski correlation yielded errors lower than 20%. Based on boundary layer theory, the Gnielinski correlation can be used to explain the isotherm behaviors observed during freezing. Many of the results satisfy the standards of accuracy used in engineering, and the procedure does not require extra computational effort.     

Estimation of Heat and Mass Transfer Coefficients During Air-Freezing of Cucumber

Freezing of foods involves coupled heat and mass transfer. It is essential to optimally design the freezing equipment and maximise the efficiency of the freezing process. Therefore, it is necessary to estimate the heat and mass transfer coefficients. In this study, the surface heat and mass transfer coefficients were estimated employing the Hilbert equation as well as the corresponding thermal and diffusive boundary layers during freezing of unpeeled cucumber at low air temperatures (?10 to??18 and??25°C). The estimated mean heat transfer coefficients ranged from 10.99 W m^?2 K^?1 for 0.5 m s^?1 up to 40.07 W m^?2 K^?1 for 5.0 m s^?1. The respective mass transfer coefficients ranged from 8.98 up to 32.40 m s^?1. The estimated heat transfer coefficients were compared with the respective ones calculated from Dincer and Dincer and Cengeli during air-cooling (22 to 2°C) of unpeeled cucumbers of similar size as well as other agricultural cylindrical products.     

Heat transfer coefficient for nitrogen droplets film-boiling on a food surface

A method of measuring heat transfer rates from a solid food surface to liquid nitrogen droplets on it has been developed using 0.5 sec repeat-shot photography. Droplet diameters were varied from 0.1 to 2.5 mm and food surface temperatures from +30 to -100°C. All measurements were carried out at atmospheric pressure. The mean heat transfer coefficients were determined using an energy balance for the droplets. An empirical dimensionless correlation equation was established, and the significance of the results for food freezing by liquid nitrogen sprays is critically discussed.     

Stability of n-3 fatty acids in fish particles during processing by impingement jet

Impingement jet systems have been identified as an alternative to conventional drying and freezing methods. Due to a high gas-particle relative velocity, which enhance heat transfer, product quality is improved. Surface heat transfer coefficients, drying and freezing times of fish particles (mackerel, Trachurus murphyi) were determined under several operation conditions (gas velocity and temperature, particle geometry, material load) using impingement jet. Heat transfer coefficients were estimated in the range of 100–300 W/m² K and a correlation of Nusselt and Reynolds numbers were established. Drying and freezing time was significantly influenced by gas temperature and particle geometry. The susceptibility of n-3 fatty acids of fish particles to oxidation during drying and freezing was determined by GC analyses of methyl esters of fatty acids, and results were compared with those obtained by alternative conventional methods. As freezing and drying time increased, n-3 fatty acids losses increased. This suggests that a lower gas temperature with short freezing time would yield a higher quality of fish particle (i.e. with minimal n-3 fatty acids losses) and a higher gas temperature with short drying time would yield a higher quality of product.     

食品冷冻理论和技术的进展

冷冻贮藏对食品保藏和运输具有重要意义,冷冻食品加工行业发展势头良好,与食品冷冻相关的理论与技术也有长足的进展。本文介绍了与食品冷冻过程相关的传递、玻璃化转变和冰结晶理论的现状和进展,指出由食品物料及其在冷冻过程变化的特殊性所引起的建立系统的食品冷冻理论的复杂性;综述了超声强化冷冻、高压冷冻、冷冻蛋白技术、CAS冻结系统和冰温技术的简要原理,及其在食品行业的应用进展。     

Numerical simulations of chilling and freezing processes applied to bakery products in irregularly 3D geometries

Finite element algorithms implemented in numerical codes were developed by the authors for irregular 3D food systems, to simulate: (i) the chilling process considering domains of different thermo-physical properties, and (ii) the freezing operation using a combined enthalpy and Kirchhoff transformation. The specific heat of the food materials were measured using Differential Scanning Calorimetry and the heat transfer coefficients of the low temperature equipments were determined; this information was further used as inputs in the model.     

GAS PARTICLE HEAT TRANSFER COEFFICIENT IN FLUIDIZED PEA BEDS

Individually Quick Frozen food production has led to the development of fluidized bed freezing equipment, where the previously cooled fluidizing air freezes the food by direct heat transfer. The operating conditions of these beds, as well as their design characteristics, are consequently related to the gas-particle heat exchange including the fluid dynamic complexity of aggregative fluidization. The purpose of this paper is the experimental determination of gasparticle heat transfer coefficients for fluidized pea beds and their extension to conditions prevailing in industrial processing. Heat transfer coefficients were determined for both, peas and porous alumina pellets, in a system where particles were dryed by the fluidizing air. Transfer coefficients were evaluated for various gas velocities and bed depths. The results obtained for alumina pellets and those for peas can be satisfactorily correlated by using the Archimides number, and show good agreement with correlations obtained by other authors.     

COLLECTION of ACCURATE EXPERIMENTAL DATA FOR TESTING the PERFORMANCE of SIMPLE METHODS FOR FOOD FREEZING TIME PREDICTION

Objective testing of the accuracy of food freezing time prediction formulae requires experimental data to be of high quality. It is shown that there are shortcomings in commonly used experimental methods, particularly relating to minimizing heat transfer in all but the required dimensions in experiments with the slab and infinite cylinder shapes, in maintaining uniformity of surface heat transfer coefficients across a sample, and in measurement of surface heat transfer coefficients. Broad guidelines to ensure that the errors introduced by experimental techniques are negligibly small are proposed. Major published experimental data sets are compared to these guidelines and comments made on their likely accuracy.     

Parametric Analysis for the Freezing of Spheroidal or Finitely Cylindrical Objects with Volumetric Changes

Parametric analyses were performed to examine heat transfer in freezing of spheroidal (including prolates and oblates) and finitely cylindrical foods through computerized simulation which considered volumetric changes. The boundary conditions included convective surface heat and moisture transfer and radiative surface heat transfer. Regression equations for freezing time estimation were developed through screening and central composite analyses and verified experimentally using a food simulator with physical properties similar to lean beef. Sensitivity analysis showed the convective surface heat transfer coefficient was the most significant factor affecting accuracy of calculated freezing time followed by operational temperatures, ther-mophysical properties and food dimensions. Effect of volumetric expansion on freezing time estimation was not significant.     

Recent developments in numerical modelling of heating and cooling processes in the food industry—a review

Numerical modelling technology offers an efficient and powerful tool for simulating the heating/cooling processes in the food industry. The use of numerical methods such as finite difference, finite element and finite volume analysis to describe the heating/cooling processes in the food industry has produced a large number of models. However, the accuracy of numerical models can further be improved by more information about the surface heat and mass transfer coefficients, food properties, volume change during processes and sensitivity analysis for justifying the acceptability of assumptions in modelling. More research should also be stressed on incorporation of numerical heat and mass transfer models with other models for directly evaluating the safety and quality of a food product during heating/cooling processes. It is expected that more research will be carried out on the heat and mass transfer through porous foods, microwave heating and turbulence flow in heating/cooling processes.     

Prediction of freezing time for food products using a neural network

An artificial neural network (ANN) was developed to predict the freezing time of food products of any shape. The Pham model was used to generate freezing time data and to train ANN based on Wardnets. The product thickness (a), width (b), length (c), convective heat transfer coefficient (h_c), thermal conductivity of frozen product (k), product density (ρ), specific heat of unfrozen product (C_pu), moisture content of the product (m), initial product temperature (Ti), and ambient temperature (T_∞) were taken as input variables of the ANN to predict freezing time. The effects of the number of hidden layer nodes, learning rate, momentum on prediction accuracy were analyzed. The performance of the ANN was checked using experimental data. Predicted freezing time using the ANN was proved a simple, convenient and accurate method. Selection of hidden nodes, learning rate and momentum were important to ANN predictions.     

速冻设备流场优化研究进展

速冻是食品保鲜的重要技术之一,冻结速率越快,速冻食品解冻后品质越好。冻品表面风速越高,换热强度越大,冻结速率则越快。若只增加风机转速会导致风机效率降低,流场不均匀度增加,因此需要对流场进行优化。对风机设置锥形口等引导流体设施,可以增加风机效率;在流场中设置导流板,可以消除流场中的涡流;增加冷冻区域流速,可以加强食品表面的对流换热;隔断设备内外的空气交换,可以减少蒸发器结霜,降低设备的冷负荷。文章指出将多种措施结合,减少制造与维护的成本、节省运行费用与提高冻品质量是未来速冻设备优化的方向。     

食品真空贮藏过程中温度变化的数值模拟与有限元分析

食品真空贮藏过程是复杂的传热传质过程，该过程涉及到扩散、传热、传质等机理。在能量守衡基础上建立数学模型，通过数值求解得到不同真空压力下食品温度随时间的变化曲线，并通过有限元分析，与数值模拟的结果进行对比分析，为下一步的实验验证及食品冷冻冷藏工程的实践提供理论依据。     

Generalization of a method for the characterization of quick frozen beef

The lack of standardized tests for determining if a product can be defined as 'quick frozen' is a source of difficulty in the commercialization of foods. An even greater difficulty is the fact that there is no one definition of a quick frozen food. With the aim of partially filling this gap, a previous paper developed a simple physical method of characterizing quick frozen beef. The study was carried out with meat cuts cooled by means of heat transfer perpendicular, in a sense, to the meat fibres with 'quick frozen' being defined by a minimum average freezing rate. In the present paper the characterization method is generalized for either heat transfer perpendicular with, or parallel to, beef fibres, 'quick frozen' being defined either by a maximum freezing time or a minimum freezing rate.     

Simulation and experimental validation of simultaneous heat and mass transfer for cooking process of Mortadella Bologna PGI

In this study, Protected Geographical Indication (PGI) Mortadella Bologna cooking process was investigated for heat and mass transfer. Apparent mass and heat transfer coefficient functions as well as apparent thermal diffusivity and mass diffusion coefficients were experimentally estimated. These thermo‐physical properties were used to develop a mathematical model for the simulation of simultaneous heat and mass transfer during Mortadella Bologna PGI cooking. The developed method was successfully validated for both heat and mass transfer by means of experimental cooking tests: maximum errors of about 3.5% and 4% were found for final product temperature and cooking time experimentally obtained respectively. Simulated weight loss values were also found not to differ significantly from those experimentally obtained. In addition, the developed model was successfully validated during a Mortadella cooking process carried out in an industrial plant proposing itself as a predictive tool to forecast and optimise cooking time and weight loss of this type of meat product. The proposed approach may be also used to design air cooking processes of other food products.