Freezing Time Modeling for Small Finite Cylindrical Shaped Foodstuff

A model was developed consisting of a modified Plank's equation to estimate phase change time and two unsteady state cross-product heat transfer equations for estimating precooling and tempering times. It accurately predicted total time to proceed from an initial temperature above the freezing point to a final temperature of ?18°C. A correction factor was developed and incorporated in the P term in Plank's equation to correct for the effect of initial and freezer medium temperatures and heat transfer coefficients. The model, tested over a broad range of freezing conditions, had a mean absolute error of 5.9% in predicted values relative to experimental values.     

Simplified Equations for Transient Temperatures in Conductive Foods with Convective Heat Transfer at the Surface

Simple equations were developed to predict the values of some characteristic transcendental and Bessel functions, and hence the temperature history in regular solid foods of finite and infinite dimensions under unsteady state conduction with convective heat transfer at the surface. For various combinations of Biot (0.02- 200) and Fourier (>0.2) numbers, the mean error involved in predicting the unsteady temperature ratio using the developed equations was less than 0.1% as compared to the original models. Equations were presented for temperature at any location as well as the mass average temperature. The characteristic functions were related to the f and j parameters from heating and cooling curves.     

Average and center temperature vs time evaluation for freezing and thawing rectangular foods

A numerical solution of the heat transfer partial differential equation and equations for predicting effective heat capacities, enthalpies and thermal conductivity were used to determine the thermal response of objects placed in cooled air freezing units. Central temperatures of a rectangular meat patty for one and two dimensional heat transfer were predicted and compared with experimental results. Times to reach an enthalpy average temperature were calculated by the program. Differences between the times obtained with the same average and central temperature depend on heat transfer rate and can represent 12% of the time involved.     

柱状胡萝卜样品热风微波耦合干燥数学模型

利用热风微波耦合干燥装置研究了柱状胡萝卜样品的干燥特性,一个实验室规模的热风微波耦合干燥装置用来实现此实验目的。基于干燥过程中同时具有传热传质现象,建立了一个数学模型以此来预测干燥过程中样品内温度和含水量的分布。考虑到柱状样品的半径和微波的穿透深度,假定微波中的电场强度在样品内均匀分布。由于表面水分的蒸发而造成的热损失被考虑在内并将其作为模型的一个边界条件,利用数值方法中的隐式有限差分法对模型进行求解。通过干燥尺寸不同的柱状胡萝卜样品得到的实验值和模型的预测值进行比较来对模型进行验证,探讨了微波功率密度和热风温度的影响作用。      

TEMPERATURE PROFILES IN DOUGH HEATED WITH A SUSCEPTOR IN THE MICROWAVE OVEN

A model based on energy considerations for predicting temperature profiles in a microwaved dough placed in contact with a susceptor was developed. Using a commercial finite element software ("Ansys 5.01"), for an axisymmetric and transient heat transfer problem, the temperatures at the dough/susceptor interface and in the whole dough were calculated. The calculated temperatures at the susceptor/dough interface were superimposed on previously published curves (based on a correlation relating temperatures at the interface with heating time, dough and susceptor parameters) and compared to experimentally determined values. A very good agreement between the experimentally determined temperatures and the values predicted from this model and from the previously described correlation was obtained. In the dough, an uneven temperature distribution in the radial direction, caused mainly by evaporative cooling at the surface, was predicted. The calculated temperatures for different susceptors, heating times and various locations in the dough correlated well with experimentally determined values.     

Coupled 3D heat and mass transfer model for numerical analysis of drying process in papaya slices

An experimental and numerical study for the drying process of a solid food, Chilean papaya slices, was carried out in a range of air temperatures from 40 to 80 °C. The unsteady temperature and moisture distributions results inside the sample were predicted by using an unsteady tri-dimensional coupled heat conduction and mass diffusion mathematical model. The validation procedure includes a comparison with experimental and numerical temperature and moisture content results obtained from experimental data. The samples thermophysical properties as density, specific heat, and thermal conductivity are assumed to vary non-linearly with temperature. The convective heat and mass transfer coefficients were found by the analytical model. The water effective diffusion coefficient, the drying curves and the center temperature were measured by physical experiments. It was found from the experimental results that slices of papaya present an isotropic behavior with an uncertainty between 6.0% and 9.0%. According to statistical test results (RE%), the finite volume method based calculations gave a very good fit quality.     

A SIMPLIFIED ANALYTICAL MODEL FOR FREEZING TIME CALCULATION IN FOODS

A simplified analytical model for the freezing time prediction of simple-shaped foodstuffs was developed. It was assumed in the model that the solution to the unsteady state, unidirectional heat conduction equation with constant thermophysical properties was valid during cooling and freezing. the latent heat effects during freezing were incorporated into an effective diffusivity term. the predictions of the model were compared to the available experimental data on freezing of infinite slabs, infinite cyliners and spheres, and to the experimental data obtained in this research for the freezing of apples. the level of agreement between the predictions and the experimental data was quite satisfactory.     

非稳态自然对流换热系数计算方法及其在防护服隔热预报中的运用

为得到相对精确的热防护服非稳态隔热性能预测数值,基于传热系统的非稳态传热模型,在防护服材料外表面分别为恒温边界条件和Howard模型对流边界条件下,利用有限差分法分别计算了2种边界条件下模拟皮肤处温度的时程曲线,所得结果均与实验测量值差别较大。在细致分析传热过程的基础上,综合运用傅里叶定律、牛顿冷却定律、以及Howard模型对流边界条件,在线化假设下提出了一种自然对流换热系数计算方法,代入非稳态模型后利用有限差分法进行了求解,随着时间步长的加密,计算结果迅速向实验测量值收敛,当时间步长为0.001 s时,计算结果与测量结果误差小于0.1 ℃。     

Mathematical Models for Nonsymmetric Freezing of Beef

A microscopic balance with simultaneous change of phase together with equations for predicting the thermal properties as a function of the ice content and a cryoscopic descent model are used to simulate the nonsymmetric freezing of a beef slab. The equations are solved numerically to obtain temperature profiles as well as freezing times. Comparison with experimental results shows good agreement. A variation of the thermal center position throughout the freezing process is detected and assumptions to predict its position in the different periods of freezing are supplied. On the basis of these assumptions a simplified model for calculating processing times in plate freezers is proposed, showing good agreement with experimental freezing times and with predictions obtained from the numerical model.     

Prediction of Freezing and Thawing Times of Foods Using a Numerical Method Based on Enthalpy Formulation

An explicit numerical method, involving enthalpy formulation, to predict temperature distribution in foods during freezing and thawing was developed. The accuracy of the proposed method was validated using published experimental data obtained for freezing and thawing of Tylose. The enthalpy formulation avoids the problems of strong discontinuity experienced when the apparent specific heat formulation is used in predicting temperatures for situations involving phase change. The proposed method predicts temperatures in good agreement with experimental data. The computer code can be easily programmed on a desk-top computer for use in teaching and research on predicting freezing and thawing rates in foods.     

Growth of Salmonella serovars, Escherichia coli O157:H7, and Staphylococcus aureus during thawing of whole chicken and retail ground beef portions at 22 and 30 degrees C

Food regulatory agencies advise against thawing frozen meat and poultry at room temperature. In this study, whole chickens (1,670 g) and ground beef (453 and 1,359 g) were inoculated with Salmonella serovars, Escherichia coli O157:H7, and Staphylococcus aureus on the surface (all products) and in the center (ground beef). After freezing at -20 degrees C for 24 h, products were thawed at 22 or 30 degrees C for 9 h. Pathogen growth was predicted using product time and temperature data and growth values from the U.S. Department of Agriculture Agricultural Research Service Pathogen Modeling Program 7.0 predictive models of pathogen growth. No pathogen growth was predicted for whole chicken or 1,359 g of ground beef thawed at 30 degrees C or 453 g of ground beef thawed at 22 degrees C. Growth (< or = 5 generations) was predicted for 453 g of ground beef at 30 degrees C. Inoculation study data corroborated the predictions. No growth occurred on whole chickens or 1,359-g portions of ground beef thawed at 30 degrees C for 9 h. Pathogen numbers increased an average of 0.2 to 0.5 log on the surface of 453-g ground beef portions thawed for 9 h at 22 or 30 degrees C. Our results suggest that thawing > or = 1,670 g of whole chicken at < or = 30 degrees C for < or = 9 h and thawing >453 g ground beef portions at < or = 22 degrees C for < or = 9 h are not particularly hazardous practices. Thawing smaller portions at higher temperatures and/or for longer times cannot be recommended, however. Use of values derived from the Pathogen Modeling Program 7.0 model provided realistic predictions of pathogen growth during thawing of frozen ground beef and chicken.     

Temperature and water content influence on thermophysical properties of coffee extract

Specific heat, thermal conductivity, thermal diffusivity, and density of coffee extract were experimentally determined in the range of 0.49 to 0.90 (wet basis) water content and at temperatures varying from 30 to 82°C. Thermal conductivity and specific heat were measured by means of the same apparatus‐ a cell constituted of two concentric cylinders ‐ operating at steady and unsteady state, respectively. The thermal diffusivity was measured by the well‐known Dickerson's method and density was determined by picnometry. The results obtained were used to derive mathematical models for predicting these properties as a function of concentration and temperature.     

鲍鱼浸入式快速冷冻理论及实验验证

计算流体力学(CFD)可准确预测鲍鱼冷冻过程中的传热传质变化,鲍鱼冷冻过程中内部温度变化和冷冻所需时间的预测对品质研究具有重要意义。本文以鲍鱼为研究对象,研究鲍鱼的浸入式快速冷冻,基于计算流体力学建立鲍鱼的三维非稳态数值计算模型,选用冻结计算模式,建立鲍鱼热物性的多项式计算方法,提高鲍鱼冷冻过程的计算精度,利用CFD计算获得鲍鱼冷冻过程的温度分布状态,获得鲍鱼质量与冷冻时间的关系,并开展了实验验证,结果表明鲍鱼的数值计算结果是可信的,能够较为准确的预测鲍鱼快速冷冻过程中温度的变化与冷冻所需时间。     

Dynamic modeling of Listeria monocytogenes growth in pasteurized vanilla cream after postprocessing contamination

A product-specific model was developed and validated under dynamic temperature conditions for predicting the growth of Listeria monocytogenes in pasteurized vanilla cream, a traditional milk-based product. Model performance was also compared with Growth Predictor and Sym'Previus predictive microbiology software packages. Commercially prepared vanilla cream samples were artificially inoculated with a five-strain cocktail of L. monocytogenes, with an initial concentration of 102 CFU g(-1), and stored at 3, 5, 10, and 15 degrees C for 36 days. The growth kinetic parameters at each temperature were determined by the primary model of Baranyi and Roberts. The maximum specific growth rate (mu(max)) was further modeled as a function of temperature by means of a square root-type model. The performance of the model in predicting the growth of the pathogen under dynamic temperature conditions was based on two different temperature scenarios with periodic changes from 4 to 15 degrees C. Growth prediction for dynamic temperature profiles was based on the square root model and the differential equations of the Baranyi and Roberts model, which were numerically integrated with respect to time. Model performance was based on the bias factor (B(f)), the accuracy factor (A(f)), the goodness-of-fit index (GoF), and the percent relative errors between observed and predicted growth. The product-specific model developed in the present study accurately predicted the growth of L. monocytogenes under dynamic temperature conditions. The average values for the performance indices were 1.038, 1.068, and 0.397 for B(f), A(f), and GoF, respectively for both temperature scenarios assayed. Predictions from Growth Predictor and Sym'Previus overestimated pathogen growth. The average values of B(f), A(f), and GoF were 1.173, 1.174, and 1.162, and 1.267, 1.281, and 1.756 from Growth Predictor and Sym'Previus, respectively.     

Prediction of frozen food properties during freezing using product composition

ABSTRACT:  Frozen water fraction (FWF), as a function of temperature, is an important parameter for use in the design of food freezing processes. An FWF-prediction model, based on concentrations and molecular weights of specific product components, has been developed. Published food composition data were used to determine the identity and composition of key components. The model proposed in this investigation had been verified using published experimental FWF data and initial freezing temperature data, and by comparison to outputs from previously published models. It was found that specific food components with significant influence on freezing temperature depression of food products included low molecular weight water-soluble compounds with molality of 50 μmol per 100 g food or higher. Based on an analysis of 200 high-moisture food products, nearly 45% of the experimental initial freezing temperature data were within an absolute difference (AD) of ± 0.15 °C and standard error (SE) of ± 0.65 °C when compared to values predicted by the proposed model. The predicted relationship between temperature and FWF for all analyzed food products provided close agreements with experimental data (± 0.06 SE). The proposed model provided similar prediction capability for high- and intermediate-moisture food products. In addition, the proposed model provided statistically better prediction of initial freezing temperature and FWF than previous published models.     

Modeling of simultaneous heat and mass transfer during convective oven ring cake baking

The convective oven ring cake baking process was investigated experimentally and numerically as a simultaneous heat and mass transfer process. The mathematical model described previously by the authors for cup cake baking was modified to simulate ring cake baking. The heat and mass transfer mechanisms were defined by Fourier’s and Fick’s second laws, respectively. The implicit alternating direction finite difference technique was used for the numerical solution of the representative model. Prior to the utilization of the developed model in predicting the temperature and moisture profiles for ring cake baking, the results of the numerical model were compared with analytical results involving only heat or mass transfer with constant thermo-physical properties. Excellent agreement was observed. The numerical temperature and moisture contents predicted by the model were compared with the experimental profiles. They agreed generally reasonably well with the experimental temperature and moisture profiles.     

A SOLUTION to the EQUATIONS GOVERNING HEAT TRANSFER IN AGITATING LIQUID/PARTICULATE CANNED FOODS

A semi-analytical (concerning the particle temperature) semi-numerical (concerning the fluid temperature) solution to the differential equations governing heat transfer to axially rotating liquid/particulate canned foods was obtained using Duhamel's theorem and a numerical 4th-order Runge-Kutta scheme. This solution avoids some of the shortcomings of earlier solutions such as the requirement for constant heating medium temperature, the need for empirical formulas, or the use of unrealistic assumptions regarding the fluid temperature. the agreement between the proposed solution and limiting case analytical results was very good. A maximum fluid temperature difference of less than 2C was momentarily observed at the beginning of heating; differences between particle surface temperatures were even smaller. Comparison between predicted values and experimental data from the literature showed good agreement only as far as the fluid temperature was concerned; particle surface temperatures deviated significantly.     

Heat Transfer Model Performance in Simulation of Process Deviations

Performance of thermal process simulation software was tested for predicting internal product temperature and lethality. Responses were tested for process deviations on canned products with a wide range of heating characteristics for computer-based on-line control of retorts. Static and agitated processes were tested with products exhibiting heating rate factors (fh) ranging from 2 to 70 min. Cans were fitted with thermocouples and subjected to deviations of various types. Center temperature profiles and lethalities predicted by the model in response to dynamic retort temperatures were compared with those measured by thermocouples. Profiles agreed, and process lethalities calculated from predicted and measured profiles agreed ±10% with the model slightly underpredicting measured lethality.     

Dry Peeling of Tomato by Infrared Radiative Heating: Part II. Model Validation and Sensitivity Analysis

In an accompanying study, a predictive mathematical model was developed to simulate heat transfer in a tomato undergoing double sided infrared (IR) heating in a dry-peeling process. The aims of the present study were to validate the developed model using experimental data and to investigate different engineering parameters that most strongly influence the rate and uniformity of IR heating. The mode was verified by comparison of the predicted temperature profiles with experimental data for tomatoes with three dimensions. Uniformity of temperature distribution at tomato surface was quantified by surface-averaged temperatures and a derived temperature uniformity index. The predicted temperatures agreed well with experimental data (r ²?>?0.9). Simulation results illustrated that IR heating induced a dramatic temperature increase on the tomato surface, which extended to 0.6 mm beneath (>90 °C) during a 60-s heating period, whereas interior temperature at the tomato center remained low (<30 °C). Sensitivity analysis suggested that strategies to enhance IR heating rate and uniformity can be implemented through varying emissive power, adjusting the distance between emitters, and presorting tomatoes according to size. The validated model provides an effective design tool for better understanding the complex IR radiation heating in developing the innovative IR dry-peeling process.     

Mathematical modeling of the heat and mass transfer in a stationary potato sphere impinged by a single round liquid jet in a hydrofluidization system

The hydrofluidization (HF) is a method of chilling and freezing of foods which consists in a circulating system that pumps a refrigerating liquid upwards through orifices or nozzles, creating agitating jets. The objectives of this work were to develop a mathematical model to represent the combined heat and mass transfer between a food and a refrigerant liquid medium in a HF system and to validate the model using a single stationary sphere of food impinged by a single round jet of liquid. The food domain consisted of a rigid solid matrix, a liquid phase and the ice phase. Transport equations were applied to each phase and solved by a control-volume approach. The transport phenomena in the fluid domain were studied by computational fluid dynamics. The surface heat transfer coefficients obtained from fluid flow simulations were used to model the heat and mass transfer inside the food. Experimental central temperature and average solute uptake profiles were obtained when potato spheres were placed in a HF system using a NaCl-water as refrigerant and considering different temperatures (−10 and −15 °C), flow rates (1 and 3 L min⁻¹), and orifice-sphere distances (1 and 5 cm). The predicted values agreed well with the experimental ones, the maximum root mean square errors being 3.3 g NaCl kg⁻¹ potato and 2.9 K for the average solute concentration and temperature profiles studied, respectively. The simulations improved the understanding of the HF process and it may help to study and control different operation scenarios.