MATHEMATICAL SIMULATION OF THE THERMAL BEHAVIOR OF FROZEN MEAT DURING ITS STORAGE AND DISTRIBUTION

During the various stages of marketing, frozen food products are frequently subjected to changes in temperature which affect their quality. In the present work, a mathematical model is developed to analyze the thermal behaviour of frozen meat subjected, under different insulation conditions, to thermal step functions and periodic fluctuations in temperature varying in amplitude and frequency. The heat transfer equation has been numerically solved, since it is a system with physical properties that vary with the temperature, and fluctuating boundary conditions. At the same time, laboratory experiments were performed to verify that the mathematical model is applicable to one-dimensional and three-dimensional heat transfer problems. The obtained results were compared with analytical solutions for the heat transfer equation, with constant coefficients, determining the temperature range for which it is possible to use average values in the physical properties.     

Impact of Overall and Particle Surface Heat Transfer Coefficients on Thermal Process Optimization in Rotary Retorts

ABSTRACT: This study attempts to examine the significance of recent research that has focused on efforts to estimate values for global and surface heat transfer coefficients under forced convection heating induced by end‐over‐end rotation in retorting of canned peas in brine. The study confirms the accuracy of regression analysis used to predict values for heat transfer coefficients as a function of rotating speed and headspace, and uses them to predict values over a range of process conditions, which make up the search domain for process optimization. These coefficients were used in a convective heat transfer model to establish a range of lethality‐equivalent retort temperature–time processes for various conditions of retort temperature, rotating speed, and headspace. Then, they were coupled with quality factor kinetics to predict the final volume average and surface quality retention resulting from each process and to find the optimal thermal process conditions for canned fresh green peas. Results showed that maximum quality retention (surface and volume average retention) was achieved with the shortest possible process time (made possible with highest retort temperature), and reached the similar level in all cases with small difference between surface and volume average quality retention. The highest heat transfer coefficients (associated with maximum rotating speed and headspace) showed a 10% reduction in process time over that required with minimum rotating speed and headspace. The study concludes with a discussion of the significance of these findings and degree to which they were expected.     

Effective Thermal Conductivity of Rice Flour and Whole and Skim Milk Powder

ABSTRACT: The effective thermal conductivity for 3 kinds of powdered food (rice flour, whole milk powder, and skim milk powder) was measured at selected moisture contents, temperatures, and bulk densities. The transient heat probe method using twin probes was used for the determination of the effective thermal conductivity. The effects of moisture content, temperature, and bulk density on the effective thermal conductivity of samples were investigated. The observed values were compared with the values calculated from the thermal conductivity of air and powder, using the 3 kinds of structural model for thermal conductivity, that is, the series, parallel, and random heat transfer models. An improved random heat transfer model, in which a correction term was incorporated in the random heat transfer model, with the term written as a function of moisture content and temperature, was developed.     

Artificial neural network for the prediction of temperature, moisture and fat contents in meatballs during deep-fat frying

An artificial neural network (ANN) was developed to predict heat and mass transfer during deep-fat frying of meatballs. Frying time, radius of meatball, fat diffusivity, moisture diffusivity, heat transfer coefficient, fat conductivity, initial moisture content, thermal diffusivity, initial meatball temperature and oil temperature were all input variables. Temperature at meatball geometrical centre ( T ₀), average temperature of meatball ( T _ave), average fat content of meatball ( m _f,ave), and average moisture content of meatball ( m _ave) were outputs. The data used to train and verify the ANN were obtained from validated mathematical models. Trained ANN predicted T ₀, T _ave, m _f,ave and m _ave with 0.54, 0.14, 0.03 and 0.10% mean relative errors, respectively.     

An instrumented oven for the monitoring of thermal reactions during the baking of sponge cake

An electric convective oven was conceived and equipped to allow monitoring thermal reactions during the baking of sponge cake. High total heat fluxes of between 6000 and 9000 W m⁻² were recorded under baking temperatures of 140-200 °C. The mapping of thermal conditions indicated satisfactory thermal homogeneity, with average temperature variations of 5 °C and maximum relative variations of the convective heat transfer coefficient of 15% on the thermal domain investigated. Internal heat and mass transfers, the extent of thermal reactions within the sponge cake and repeatability of the baking operation were all characterized by experimental measurements. Some of the main operating variables were monitored in the cake (core and surface temperatures, moisture content, levels of chemical reactants and products) and others in the baking atmosphere (temperature, humidity and concentrations of volatile compounds). Specific non-disruptive sampling devices were designed to extract data from cakes and the oven atmosphere in order to follow the kinetics of thermal reactions during the baking operation. Three phases could be identified during baking, corresponding to the relative importance of conductive and evaporative internal heat transfer regimes and to macroscopic changes in the cake structure with formation of a crust. The progress of thermal reactions was monitored with satisfactory precision in both the cake and the baking vapors: relative standard deviations of 2% and 8.7% were obtained respectively for the water content and hydroxymethylfurfural (HMF) content of three replicates during a baking operation.     

OPTIMIZATION OF QUALITY RETENTION IN CONDUCTION‐HEATING FOODS OF CONICAL SHAPE1

A cone frustum is an alternative shape for packaging thermally processed foods that can be useful in modeling the increasing number of microwaveable, ready‐to‐eat conical‐shaped food containers seen on supermarket shelves. Thermal processing in a cone frustum can be optimized by using numerical models for heat transfer to predict temperature distribution profiles, together with thermal destruction kinetics of target organisms and nutrient/quality factors. Iso‐lethality curves, showing combinations of process time and retort temperature that deliver equal lethality, were developed for each of three different cone frustum geometries (different dimensional proportions of major and minor diameters and height). Total volume average quality retention was determined for equivalent process time‐temperature combinations for quality factors with assumed thermal degradation kinetic parameters (D and Z‐values). Response of quality retention to the equivalent process combinations (designated by their retort temperature) revealed optimum process conditions that delivered maximum quality retention. The effect of kinetic parameters, thermal properties, and surface heat transfer coefficient on quality retention response to equivalent process conditions was also studied and compared with findings reported in the literature for the case of more traditional finite cylinder shapes.     

滚筒干燥过程中叶丝状态变化对其热物性的影响

为了分析烟草热湿加工处理中的传热过程,通过自行搭建的滚筒干燥过程中烟丝热物性在线测试平台,利用瞬态平面热源法测定了滚筒干燥过程中烟丝的热物性,考察分析了该过程中烟丝温度、含水率对烟丝导热系数、热扩散系数、体积热容的影响。结果表明:①当含水率相同时,烟丝导热系数、体积热容随着烟丝温度的升高而增大,热扩散系数随温度的升高而降低;②当烟丝温度相同时,烟丝导热系数、体积热容随含水率的降低而减小,热扩散系数随着含水率的降低而增大;③干燥过程中,烟丝含水率逐渐减小,烟丝温度逐渐升高,烟丝导热系数在温度与含水率的共同作用下整体有减小的趋势,表明烟丝含水率对导热系数的影响较温度显著。     

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.     

石蜡基复合相变材料的制备及性能研究

采用熔融共混法,将不同相变温度的2种石蜡及石墨进行复合,得到新的相变材料,并将它们应用于服装面料。通过差示扫描量热法(DSC)及导热性测试获得相变材料的相变温度、相变焓及导热速率等;采用红外热成像仪测试面料的控温效果。结果表明,复合的含石墨的相变材料保留着高相变潜热的优点,同时传热效率有所增高,应用于服装面料可实现控温效果。     

Effect of Packaging Materials on Temperature Fluctuations in Frozen Foods: Mathematical Model and Experimental Studies

An analytical solution of the conduction heat transfer equation was developed for prediction of temperature in frozen foods exposed to periodic environmental temperature fluctuations. The prediction model includes the effect of surface heat transfer resistances. Theoretical predictions were compared with experimental values recorded from frozen ice cream at different storage regimes. Slab-shaped metal containers were used in the experiment. Surface heat transfer resistances were simulated with single layers of commercial packaging cardboard sheets and restricted air movement over the containers. A satisfactory agreement was obtained between predicted values and experimental data. Packaging materials coupled with a layer of stagnant air are effective barriers against thermal fluctuations.     

Temperature prediction in air drying of food materials: a simple model

The problem of one-dimensional heat and mass transfer in infinite slabs during drying of porous solids is considered. Assuming a known distribution of moisture and temperature, it is possible to estimate effective thermal and mass diffusion coefficients in solids. In this paper it is demonstrated that from these coefficients the equations describing heat and mass transfer processes in the system are easily integrated to obtain average sample temperature and moisture during drying. These theoretical results may be used to evaluate the effects of the degradation reactions during food drying, which depend on the foodstuff moisture content and temperature.     

Coupling fluid flow,heat transfer and thermal denaturation-aggregation of beta-lactoglobulin using an Eulerian/Lagrangian approach

The transformation of liquid food product under heat treatment is often represented by considering average temperature evolution along the exchanger and by assuming plug-flow. Our aim is to demonstrate that thermal denaturation-aggregation of whey proteins can be more realistically represented by taking into account the different dynamical and thermal histories associated with fluid parcels which progress more or less quickly, far or close to the heating wall, inside the processing unit. A numerical approach is proposed for evaluating the thermal denaturation-aggregation of whey proteins, combining computational fluid dynamics and the population balance equation. The approach is illustrated by the evolution of a suspension of beta-lactoglobulin. Fluid flow and heat transfer are solved through the finite element method in the Eulerian frame, while product transformation is evaluated along representative Lagrangian trajectories. Outlet bulk results show that the product reaches a higher level of transformation than in assuming plug-flow and radially-independent temperature.     

Quantifying Enhancement in Heat Transfer Due to Natural Convection During Canned Food Thermal Sterilization in a Still Retort

Thermal sterilization of canned viscous liquid foods using saturated steam is enabled by natural convective heat transfer. However, the governing equations for two-dimensional convective heat transfer may be only rigorously solved by numerical calculations. On the other hand, if conduction is assumed to be the only mode of heat transfer, the thermal sterilization problem has analytical solutions for simple boundary conditions. However, the conduction model may not be appropriate in describing thermal sterilization of even viscous liquid foods and may cause considerable error in the prediction of the important parameters such as slowest heating zone (SHZ) temperature and lethality. The longer time for sterilization recommended by the conduction model may lead to overprocessing and an unacceptable food product. The objective of this work is to quantify the faster temperature rise in the food can due to natural convection when compared to the temperature rise obtained by only conductive heating. The consequent enhancement in lethalities is also reported. In addition, this work’s objective is to investigate how quickly the natural convective heat transfer effects begin to dominate over the solely conduction heating mode. The volume-averaged temperature as well as the SHZ temperature variations with time was calculated for the convection-augmented mode using computational fluid dynamics (CFD) simulations. Lethality values were then calculated based on volume-averaged temperature as well as the SHZ temperature. Food cans of different aspect ratios and food medium thermal conductivities are considered in this analysis. For the food system investigated, the critical Fourier number at which the transition to convection-augmented mode of heat transfer occurred is identified and explained from scaling considerations. In the conduction-dominated mode, it was possible to use analytical solutions to predict the volume-averaged and SHZ temperatures of the liquid food undergoing thermal sterilization. The Nusselt number correlation developed by Kannan and Gourisankar (2008) was used in the lumped parameter transient heat transfer model to predict the volume-averaged temperatures in the convection-dominated region. The volume-averaged temperatures from this approach were found to be in good agreement with the CFD simulation results. The time predicted for the SHZ to reach the minimum sterilization temperature was significantly lower when convective heating was also considered. The volume-averaged temperature and SHZ temperature enabled an estimation of overall sterility levels attained and minimum sterility levels prevalent inside the can, respectively. Even though the volume-averaged temperature increase due to convection was only about 10 K, the resulting accumulated lethality values were higher by an order of magnitude. The increase in SHZ temperatures was much higher in the convection-augmented mode, and consequently greater integrated lethalities were attained. The simple conduction model that is amenable to analytical solution cannot be used to approximate the heat-transfer-related phenomena even for “quick estimation” purposes when convection effects are significant. This precaution is found necessary even for the reasonably high viscous carboxy methyl cellulose system, whose average viscosity values ranged between 13 and 3 Pa s during the course of the sterilization process.     

基于辐射衰减特征的隔热防护织物有效导热系数简化模型

高温下辐射传热对织物热传递过程贡献显著,为此,介绍火灾高温环境下的耐高温防护织物的内部传热特点,进而提出高温下织物有效导热系数数值传热模型.针对火灾等高温环境下耐高温防护织物内部热辐射渗透衰减问题进行分析,应用有限差分法对隔热防护织物的有效导热系数模型进行数值分析.通过数值求解传热方程,计算出织物的稳态有效导热系数,且...     

Explicit Finite Difference Methods for Heat Transfer Simulation and Thermal Process Design

A considerable difference between two explicit finite difference heat transfer simulation approaches was described. Time step restrictions, which are often the basis for criticism of explicit methods, were shown to be less severe when the surface was not considered to have thermal mass. Thermal process design combines heat transfer and reaction kinetics considerations. Accuracy of lethality estimates depends on time step size. Guidelines were developed for applying discrete time-temperature data to thermal process calculations. For time steps small enough to permit a linear temperature change approximation, it was shown that for increasing (decreasing) temperatures, a value within 50 to 60% (40 to 50%) of total temperature change should be used.     

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 ℃。     

电子烟多口抽吸过程的传热传质数值模拟

为探究电子烟烟液在多孔雾化芯内雾化过程中的传热传质行为, 建立了适用于模拟电子烟多口抽吸使用场景的多口抽吸模型, 并应用MATLAB软件对模型进行求解, 经验证模型具有一定的准确性。利用多口抽吸模型模拟逐口抽吸条件下电子烟烟液相变过程的传热传质特性、烟液成分变化并计算热效率。结果表明:①雾化芯孔隙中的烟液在抽吸间隙发生降温, 在30 s的抽吸间隙内, 烟液温度无法降至环境温度, 随着抽吸口数的增加, 逐口抽吸开始时刻和结束时刻的烟液温度较上一口相比平均提高4.4%;②在模拟的5口抽吸中, 烟液的平均气化速率呈现先增大后减小的趋势, 第2口抽吸时烟液的平均气化速率达到最大值2.80 mg/s;③随着抽吸口序的增大, 逐口的系统升温耗能呈现先减小后增大的趋势, 逐口的烟液气化耗能呈现先增大后减小的趋势, 逐口的导热、对流、辐射3项热损失不断增大, 每一口抽吸的热损失较上一口分别平均提高8.4%、6.8%、11.6%。每口抽吸的热效率随抽吸口数的增加而减小, 当抽吸口数从1口增加至5口, 每口抽吸的热效率从93.3%降至90.9%。      

Heat Transfer and Moisture Loss of Spherical Fresh Produce

A computerized procedure was developed for simulating the post harvest cooling and moisture loss of produce by using a reliable mathematical model. This model was derived by assuming temperature and time variable respiration heat generation and temperature variable thermophysical property values. The developed procedure was employed to examine influence of five key dimensionless parameters on the cooling rate and moisture loss. These parameters are related to the rates of changes in density and thermal conductivity with changes in produce temperature, surface heat transfer conductance, transpiration rate, and environmental relative humidity. Theoretical results obtained from our examination were verified through heat transfer and moisture loss experiments by using fresh potatoes and tomatoes.     

Prediction of thermal skin burn based on the combined mathematical model of the skin and clothing

As the result of exposed to thermal radiation and fire exposure, skin burn or even worse injuries are very common for building occupants and fire fighters. To accurately predict their skin temperature and burn situation, an assessment method of the mathematical model is developed for various thermal radiation conditions. The combined mathematical model includes the heat and moisture transfer within the skin and clothing systems. It is validated with a good agreement with the previous experimental study. The effects of thermal radiation, air gap and moisture transfer on burn prediction were also studied. The results showed that the time to the second degree burn is affected by the heat flux level, gap size and moisture location. It is expected that the developed method can be used to evaluate the thermal protective performance of protective clothing during exposure to thermal hazards and provide appropriate information to clinical observation and decision-making for skin thermal injuries.     

Heat transfer properties of the numerical human body simulated from the thermal manikin

This paper seeks to predict the heat transfer properties of the numerical manikin. It also aims to establish a simplified clothing model based on computational fluid dynamics (CFD) to predict the temperature in air layers between thermal manikin and clothing under different environments. The field experiments of naked or clothed thermal manikin were conducted in a climatic chamber. The CFD method was employed to build a naked or clothed numerical manikin to simulate the field experiment. The distribution of temperature and the velocity field around the naked human body and heat transfer coefficients was simulated in the optimized numerical climate chamber with a temperature of 20°C and velocity of 0.05?m/s. The temperature in air layers entrapped in clothing on the torso of manikin was also predicted under the same environmental condition. The CFD results showed good agreement with that of the naked or the dressed thermal manikin experiment. It demonstrated that CFD could properly predict the heat transfer properties of indoor human and temperature distribution in the air layer between human body and clothing.