Modelling of coupled heat and mass transfer during a contact baking process

A mathematical model of coupled heat and mass transfer of a contact baking process is developed. In the current model formulation, a local evaporation of water is described with a reaction-diffusion approach, where a simultaneous diffusion and evaporation of water takes place. The resulting coupled model equations (unsteady state heat transfer, liquid water and water vapour) were solved using the Finite Element Method (COMSOL Multi-physics® version 3.5). During the baking process, local temperatures and overall moisture loss were measured continuously. The model - predicting temperature, liquid water content in the product and water in the vapour phase - was calibrated and partially validated using data obtained during baking of a representative food model (a pancake batter) under controlled conditions on a specially designed experimental rig. The unknown parameters in the model equations were estimated using the standard least squares method by comparing the measured with the predicted temperature profile. Good agreement was achieved between model predictions and the experimental values.     

Interactions of heat and mass transfer in steam reheating of starchy foods

Steaming is a common practice in both household and industrial food processing; however, the process of heat transfer during steaming has not been fully explored. In this study, mathematical models that consider coupled energy, water and vapor transport were developed, and were solved using finite element software (COMSOL Multiphysics) for their application to the steam reheating of non-porous starch gel radish cake and steamed buns with porous matrices. Our simulation results indicated that the reheating of non-porous starch gel is a heat conduction process. During the reheating of the porous starch matrix, the infusion of condensate and evaporation–condensation mechanism contribute to steep sigmoid-shaped temperature profiles that are different from those of normal heat conduction. The validity of our mathematical model is corroborated by our experimental work of the steam reheating of samples with and without PE film wraps in a rice cooker. It shows a good agreement between the simulation and experimental results in terms of temperature and increased moisture. The implications of these models can provide a basis for future elucidation of more complicated food steaming processes.     

CFD modeling of heat transfer and flow field in a bakery pilot oven

A bakery pilot oven is modeled using computational fluid dynamics software. This approach relies on integration of an instrument into modeled geometry. The instrument is a heat flux measuring device that can be used in the industrial baking process. All three heat transfer mechanisms are considered and coupled with turbulent flow. Turbulence is taken into account via the k–ε realizable model whereas the surface-to-surface model simulates the radiation. Additionally, buoyancy forces are introduced by means of a weakly compressible formulation. The model predictions show a good qualitative agreement with the experimental measurements. A quantitative agreement was obtained to some extent. Limitations came from the difficulty to measure the temperature of the radiant surfaces of the oven. Operating conditions used are typical of bakery products and, as expected, radiation was the dominant mode of heat transfer. The integration of the instrument was useful for assessing the model. Since it is designed for industrial use, it may be a valuable tool for future challenges in the field, such as simulation of an industrial scale oven.     

Effect of oven temperature profile and different baking conditions on final cake quality

This study discusses the effect of airflow on oven temperature profiles, the internal cake temperature and the final cake quality. It was found that the presence of airflow reduced the oscillation in the oven temperature profile from 12.98–30.27% to 3.17–4.02%. The bottom of the oven chamber experienced the greatest reduction in temperature oscillation in the presence of airflow. During the second stage of baking with airflow, the heating rate was increased from 5.07 to 7.52 °C min^?1 and 8.35 °C min^?1 to the increase of the baking temperature from 160 to 170 °C and 180 °C, respectively. The cake volume expansion rate was also increased 5–10% during second stage when baking with airflow condition. The cakes baked in the presence of airflow had a more porous crumb texture and lower moisture content compared to the cakes baked without airflow.     

Uncertainty and sensitivity analysis: Mathematical model of coupled heat and mass transfer for a contact baking process

Similar to other processes, the modelling of heat and mass transfer during food processing involves uncertainty in the values of input parameters (heat and mass transfer coefficients, evaporation rate parameters, thermo-physical properties, initial and boundary conditions) which leads to uncertainty in the model predictions. The aim of the current paper is to address this uncertainty challenge in the modelling of food production processes using a combination of uncertainty and sensitivity analysis, where the uncertainty analysis and global sensitivity analysis were applied to a heat and mass transfer model of a contact baking process. The Monte Carlo procedure was applied for propagating uncertainty in the input parameters to uncertainty in the model predictions. Monte Carlo simulations and the least squares method were used in the sensitivity analysis: for each model output, a linear regression model was constructed and the standardized regression coefficients (SRCs) and R² were computed. The effect of input parameters on model predictions was calculated, and the relative impact of the parameters on each of the outputs was ranked. Results of the uncertainty and sensitivity analysis can be used to prioritize future experimental efforts, as discussed for the contact baking process.     

A new solution approach for simultaneous heat and mass transfer during convective drying of mango

The present investigation is contemplated to fill a gap in analytical modelling of coupled heat and mass transfer during convective drying process. A transport model to describe the temperature and moisture evolutions of mango slab is established. The main innovation introduced in this study is represented with the procedure of temperature and moisture predictions. Mango fruit dehydration can be easily simulated with implementation of the present advanced analytical technique at different operating conditions. Moreover, the temperature and moisture history of mango slice are presented for varying values of the drying air factors counting temperature, velocity, relative humidity and initial food temperature. This work confirms that notable time can be saved without sacrificing accuracy by applying proposed model. This method is expected to be useful for fast and accurate drying simulation. The agreement between published experimental results and model predictions is remarkable and an accurate simulation of experimental drying curves is obtained.     

Two-dimensional CFD modeling and simulation of crustless bread baking process

A special type of baking oven was developed where crustless bread was made by gently baking the dough at controlled temperature by spraying water at prefixed intervals on the surface of the dough. In this study, a two-dimensional (2D) CFD model for crustless bread during baking has been developed to facilitate a better understanding of the baking process. Simultaneous heat and mass transfer from the bread during baking was successfully simulated. It was found that core temperature of the bread reached at 95 °C at the end of baking where as moisture of the bread satisfies the normal bread quality. The model can be successively applied to study the unsteady heat and mass transfer from the crustless bread during baking.     

Heat and mass transfer in combined convective and far-infrared drying of fruit leather

Combined convective and far-infrared drying is a challenging assignment due to complex relationship between heat and mass transfer. In this paper, heat and mass transfer of fruit leather drying with combination of hot air and far-infrared has been carried out. The heat and the mass transfer coefficients were analyzed by heat–mass analogy. It could be found that the ratio between heat and mass transfer coefficients for the combination technique could not be obtained from the heat–mass analogy classical model and a modification is needed. The modified correlations for predicting ratio of heat and mass transfer coefficients and the heat transfer coefficient in term of heat transfer Nusselt number are developed. The model could fit the experimental data quite well within ±10% deviation.     

Determining convective heat transfer coefficient during sterilisation of canned evaporated whole milk

The effect of retort temperature, rotation speed, headspace and radius of rotation on mean convective heat transfer coefficient during sterilisation of canned evaporated whole milk was studied. The mean total solids content of evaporated milk obtained in a pilot plant installation was 25.25 g/100 g. Processing variables used ranged as follows: retort temperature: 117-123 °C; speed of rotation: 10-20 rpm; headspace: 4-12 mm; radius of rotation: 3.5-16.5 cm. The model developed for heat transfer coefficient was adequate, showing no significant lack of fit and satisfactory coefficient of determination. Retort temperature, speed of rotation, headspace and radius of rotation have a significant effect. Dimensional correlations were developed for convective heat transfer coefficient, in terms of Nusselt number as a function of Reynolds number, Prandtl number and relative headspace; the best agreement was obtained using the diameter of rotation as the characteristic dimension.     

Natural convective cooling of cheese: Predictive model and validation of heat exchange simulation

The proposed FEM model describes natural convective air cooling of cheese curd and cheeses with different sizes, chemical composition and initial temperature, including temperature-dependent functions accounting for the variation of specific heat capacity and thermal conductivity of cheeses. Both the calculated convective heat transfer coefficients (from 3.58 to 15.15 W/m² K) and the ratio between Grashof and square Reynolds numbers confirmed that heat exchange was natural convective. The model permitted to accurately predict the transient temperature change into the cheese, as shown by the mean RMSEs values (from 0.34 to 2.29 °C). Higher RMSEs values (up to 3.29 °C) were obtained for cheese curds, because some deviations from the assumptions of the model occurred. These higher RMSEs values for cheese curds quantify the importance of compliance with the model’s assumptions to ensure a best fit between the simulated and experimental data.     

Experimental and numerical investigation of heat and mass transfer during drying of Hayward kiwi fruits (Actinidia Deliciosa Planch)

In this paper we undertake an experimental and numerical study on heat and mass transfer analysis during drying of kiwi fruits. In the experimental part, the effects of various drying conditions in terms of air velocity, temperature and relative humidity on drying characteristics of kiwi fruits are investigated. In the numerical part, the external flow and temperature fields are studied using a commercial CFD package. From these fields, the local distributions of the surface convective heat transfer coefficients for the fruits are determined to predict the local convective mass transfer coefficients through the analogy between the thermal and concentration boundary layers (known as the Chilton–Colburn analogy). In addition, the time-dependent temperature and moisture distributions for different cases are obtained using the code developed to investigate heat and mass transfer aspects inside the fruits. Numerical results are then compared with experimental data and a considerably high agreement is obtained.     

计算流体力学在食品传热传质过程中的应用

对计算流体力学(CFD)技术进行了简单介绍，并对采用CFD技术模拟食品加工过程中的传热传质过程的研究现状进行了综述，探讨了采用CFD对这些传热传质过程进行数值模拟的优势。CFD模拟的结果详细、直观，模拟得到的流体流动和各种热力学参数的分布信息，可以为装置的设计、传热过程的优化提供参考。     

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.     

Transfer of heat and moisture during oven baking of potatoes

Potatoes were baked for up to 60 min in a conventional fan‐assisted oven. Temperature profiles within the potato tubers were determined both by direct measurement and by following the inward progress of starch gelatinisation, which occurs at 65 °C. Temperature profiles with time were S‐shaped and about 30 min was needed for the centre to reach 100 °C. From the nature of the temperature profiles, long potato tubers will cook faster than round tubers of the same weight, and a varietal ‘shape factor’ was defined to quantify this effect. The slow temperature rise, compared to other forms of cooking, was due to evaporative cooling. Moisture loss was linear with time after an initial lag and reached 15–20% of the mass of the potato after 1 h of cooking. Approximately half of the moisture was lost from the outermost layer of the potato under the periderm, leaving behind a dried layer of flesh that appeared to restrict water transport and, unlike any other part of the potato, could exceed 100 °C. This has consequences for the thermal development of flavour compounds as well as for perceived texture. © 2002 Society of Chemical Industry     

微波冷冻干燥传热传质模型的研究进展

微波冷冻干燥技术是一种快速干燥脱水技术,可应用在一些特定食品上,尤其是海产品、水果和蔬菜等。与传统冷冻干燥技术相比,微波冷冻干燥可节约干燥时间和能量,提高产品质量。文章主要介绍微波冷冻干燥的原理、国内外对其传热传质数学模拟的研究进展及在线检测技术,同时在干燥模拟过程考虑物料的介电特性,分析问题所在,并展望微波冷冻干燥数学模拟的发展方向。     

Mathematical modeling of the heat transfer process and protein denaturation during the thermal treatment of Patagonian marine crabs

Southern Ocean swimming crab Ovalipes trimaculatus and the Patagonian stone crab Platyxanthus patagonicus are fishing resources with commercial value. Thermal treatment of crabs is necessary to denature muscle proteins, facilitating meat detachment from the crab shell (picking procedure). The proximal composition, protein patterns of crab muscle, thermophysical properties and heat transfer coefficients were determined. Heat transfer during thermal processing of body (i.e., cephalothorax) and claws of both crab species was simulated using a finite element computational code; the simulations were experimentally validated. Color changes in crab muscle during the heating process were measured. Thermal denaturation kinetics of myofibrillar proteins was determined using Differential Scanning Calorimetry (DSC) in small samples previously heated in water under controlled conditions. DSC thermograms of raw crab muscle showed two peaks at 49.0 ± 0.4 and 77.5 ± 0.6 °C corresponding to myosin and actin respectively. Activation energies for the denaturation of myosin (145.70 kJ/mol) and actin (156.42 kJ/mol) were calculated from Arrhenius equation. The degree of denaturation achieved by the myofibrillar proteins at the coldest point of the muscle in body and claws during the heating process was established by considering the protein denaturation kinetics determined by DSC, the activation energies and the heat penetration curves. Adequate conditions for the detachment of meat from the crab exoskeleton were established. The obtained results may help in determining the optimal heating times during the industrialization of these crustaceans.     

Investigation of dielectric properties of different cake formulations during microwave and infrared-microwave combination baking

ABSTRACT:  Dielectric properties can be used to understand the behavior of food materials during microwave processing. Dielectric properties influence the level of interaction between food and high frequency electromagnetic energy. Dielectric properties are, therefore, important in the design of foods intended for microwave preparation. In this study, it was aimed to determine the variation of dielectric properties of different cake formulations during baking in microwave and infrared–microwave combination oven. In addition, the effects of formulation and temperature on dielectric properties of cake batter were examined. Dielectric constant and loss factor of cake samples were shown to be dependent on formulation, baking time, and temperature. The increase in baking time and temperature decreased dielectric constant and loss factor of all formulations. Fat content was shown to increase dielectric constant and loss factor of cakes.     

仓储粮堆内部自然对流和热湿传递的数学分析及验证

本文基于仓储粮堆内部自然对流、热湿耦合传递的数学模型,采用数学分析的方法对模型中各个方程中的各项的物理意义和数量级大小进行了分析,探讨了仓储粮堆内部自然对流、热量传递和水分迁移过程的相互关系。提出了判断粮堆内部自然对流强弱的瑞利数及其影响因素,分析了仓型结构、粮种及仓外大气温度对粮堆内部自然对流、热量传递和水分迁移的影响,并通过数值模拟对数学分析结果进行了验证。结果表明,数学分析方法是分析仓储粮堆内部自然对流、热量传递和水分迁移过程的一种有效途径,数学分析的结果可以为仓型设计、储粮生态系统的模拟、仓储技术管理提供借鉴。