A Simplified Analytical Model for Thawing Time Calculation in Foods

A simplified analytical model for the thawing 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 throughout the thawing operation. The latent heat effects were incorporated into effective diffusivity terms defined for the various phases of the thawing operation. The predictions of the model were compared to experimental and numerical data obtained on thawing of infinite slabs, infinite cylinders, and spheres. The level of agreement between the predictions of the present model, and the experimental and numerical data was quite satisfactory.     

Freezing Time Predictions for Brick and Cylindrical-Shaped Foods

A simplified model previously developed for freezing time calculations in plate freezers is extended to systems with two or three dimensional heat flow. The model combines Plank's equation with the unsteady heat transfer solutions for bodies with constant properties, through the addition of pre-cooling, change of phase and tempering times. Average thermal properties, different for each period are used in order to take into account their change with the ice content along the freezing process. Freezing time predictions show a maximum difference of 10% with respect to freezing experiments performed with meat blocks shaped as cylinders or rectangular bricks. Processing times from 0.7–5 hr were compared with satisfactory agreement.     

A Method to Determine Initial Freezing Point of Foods

An accurate initial freezing point T_sh is required for reliable analysis of a food freezing or thawing process. Two previous formulae for accurately estimating enthalpies, one for temperatures above T_sh and another below T_sh, were used for this development. The estimation of T_sh was based on the mathematical formulation of continuity in food enthalpies estimated by both formulae at T_sh. The method was validated by estimating T_sh values of aqueous solutions of sucrose and NaCl at different solutions. There was fair agreement in the T_sh values of fresh fruit and vegetables, lean beef meat and lean fish meat estimated by the proposed and a previous method. One potential advantage of our new method was the direct estimation of T_sh through analysis of food enthalpies collected at different temperatures.     

食品冷冻技术的研究进展

冷冻技术的发展异常迅速,在食品工业中的应用也越来越广泛,将其更好地应用于食品中成为当前研究者较为关注的课题。重点对冷冻过程中的理论研究及其在食品工业中的应用进行综述,并简述了近年来国内外食品冷冻技术的现状与发展趋势。     

Extracellular Ice Nucleators from Pantoea Ananas: Effects on Freezing of Model Foods

Parameters of freezing of sucrose solutions and emulsions were evaluated using differential scanning calorimetry (DSC) at cooling rates of 1 to 20°C/min. The differential and cumulative nucleation spectra of extracellular ice nucleators (ECINs) were established using a w/o emulsion technique. Freezing curves were obtained in a cabinet at ?7 and ?12°C. The ECINs increased the ice nucleation temperature and reduced the time of the supercooling stage. Although the time of phase transition increased in the presence of ECINs, the total time of freezing decreased. The ECINs caused lower onset temperatures of freezing as compared to the original cells.     

3种速冻甘薯食品的加工工艺

主要介绍了出口速冻甘薯、冷冻甘薯片和速冻甘薯茎尖的生产工艺和操作要点，以期为生产厂家起到一定的参考作用。     

Bacterial Extracellular Ice Nucleator Effects on Freezing of Foods

Extracellular ice nucleators (ECINs) were incorporated into foods and subjected to subzero freezing. Time-temperature profiles, ice-formation patterns and textures were examined by thermocouple, microscopy and texture analyzer. Onset temperatures (initial freezing), enthalpies and freezing rates were measured by DSC. Addition of ECINs to liquid foods elevated ice nucleation temperatures and promoted freezing. Solid or semisolid products frozen with ECINs resulted in a fiber-like texture. These effects were more apparent at –10°C or higher. Differential scanning calorimetry revealed onset temperatures were increased 11°C by addition of ECINs, but length of time to complete the phase transition was extended at constant cooling rates. Results indicated that ECINs can be used instead of whole bacterial cells for efficient freezing and textural modification.     

Freezing Time Predictions for Different Final Product Temperatures

A modification to an empirical food freezing time prediction formula is proposed that allows the formula to be used for a range of final product temperatures. Over a large data set (275 runs) the percentage difference between experimentally measured times and predictions has a mean of 0.2% and a standard deviation of 6.8% for the improved formula compared to -2.4% and 8.5%, respectively, prior to modification. Ninety percent of the predicted freezing times by the new method were within ± 11% of the experimentally measured times and ± 9% of predictions by an accurate finite difference scheme. This performance compares favorably with other published freezing time prediction methods. The same type of modification for varying final product temperature may be suitable for other empirical formulae.     

平板状食品冻结时间的数值预测

采用有限差分法获得平板状食品冻结时间的数值解。对凝固区（两相区）的参数进行处理,使食品在整个冻结过程可以选用统一的差分格式;通过凝固区释放热量的累积效果,判断凝固区界面的移动;对常见的平板状食品的冻结过程进行计算机模拟来预测冻结时间,并通过实验来验证可靠度。结果表明,这种计算方法可以应用在实际生产中。     

A zTurbulent Conjugate Heat-transfer Model for Freezing of Food Products

ABSTRACT: A 3-dimensional conjugate heat-transfer model for the analysis of freezing food products has been developed. The food-freezing process is a multi-medium, multi-phase, and transient heat-exchange phenomenon in connection with the cooling flow around the food items. The developed numerical model couples the energy equation with the Navier-Stokes equations outside the food items to simulate the velocity distribution around the food items and the heat flux across the food surfaces. The conjugate heat-transfer methodology and enthalpy method was used to solve the energy equation across the fluid-solid interface into the food item. The heat convection in the fluid and conduction in the foods are implicitly coupled to predict the heat-transfer rate and the enthalpy change during its freezing process. The conjugate heat-transfer model presented here is applicable to perform various heat-transfer calculations involved in the design of storage and refrigeration equipment and to estimate the process time required for freezing of foods. The article presents the mathematical model used, the outline of the numerical scheme, and the results of computations. The model-predicted results are compared with the experimental data available in the literature. Overall good agreement was obtained.     

A Converging-Front Model for the Asymmetric Freezing of Slab-Shaped Food

In food freezing situations where heat flows at different rates from the two surfaces of a slab, a Plank-type converging-front model enabled the position of the thermal center and hence the freezing time, to be calculated. The thermal center was defined as the point where the freezing fronts meet, i.e. the last point to cross the “mean freezing temperature”. Finite-difference calculations showed that this model successfully accounted for the effect of asymmetry in heat transfer coefficient or coolant temperature and enabled previously developed simplified prediction methods to be applied to asymmetric situations.     

A New Model for Describing the Water Sorption Isotherm of Foods

This work investigated the applicability in the food area of a new sorption equation recently developed by Ferro Fontán et al. (1982). The equation may be written, 1n (γ/a_w) =α (m)^-r, where, γ, α and r are parameters to be determined, m is the moisture content, and a_w is water activity. It was found that the three parameter equation is able to describe the water sorption isotherm of 18 different foods in an extensive range of a_w (up to about 0.95) with only 2–4% error (average) in the predicted moisture contents. Foods examined comprised, among other, oilseeds, starchy foods, and proteins.     

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.     

软冷冻条件对动物性食物营养成分的影响

为评价软冷冻条件对动物性食物储存的影响，选择动物性食品为研究样品，观察在软冷冻（-7℃）和传统冷冻（-18℃）条件下，食物的外在表观变化和营养成分的变化。结果表明，在适宜的短期储存条件下，软冷冻可以达到人们对食物储存的保鲜要求，而且保持食物的营养素水平。该研究为软冷冻冰箱的开发和研究提供了科学依据。     

Structural Studies on Unpackaged Foods during Their Freezing and Storage

ABSTRACT:  During the freezing and frozen storage of unpackaged foods, their surface is exposed to mass transfer with the environment. Basically, ice sublimes and forms a dry, porous layer. This fact alters the sensory characteristics of the products and originates an important quality loss. In this work, a mathematical model was used to predict the thickness of the dehydrated layer, taking into account the influence of operating conditions and food characteristics. Based on the predictions of the numerical model, 2 regression equations were proposed to calculate the size of the dehydrated layer after freezing and storage, having the operating conditions and food properties as parameters. Besides, the frozen storage of the products was studied over different time periods (1, 2, and 3 mo) using beef cylinders and slices, as well as minced beef balls and hamburgers. The dimension of the dehydrated layer and the induced changes in the food surface structure were determined by image analysis and environmental scanning electron microscopy (ESEM). The experiments determined an increase in the depth of the dehydrated layer when storage times are longer, which could be adequately related to storage conditions through the predictions from the numerical model and the regression equations.     

Assessment of Freezing Time Prediction Methods

A systematic procedure for testing the accuracy of freezing time prediction methods is discussed. It involves carrying out freezing time predictions by an accurate numerical method as well as the method under test, and careful cross-checking of prediction errors for correlation with a number of physical parameters. Criteria are given for selection of an appropriate numerical method. The need for systematic cross-checking is illustrated by comparisons between four recent prediction methods. The comparisons show the strengths and weaknesses of the four methods. They also indicate general shortcomings in available methods and data, and so highlight those areas in which future research might be most profitable.     

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.     

Use of Average Molecular Weights for Product Categories to Predict Freezing Characteristics of Foods

ABSTRACT:  In the design of food freezing process, food property parameters, initial freezing temperature ( T_Fi ), and frozen water fraction ( X_I ) are required. The predictive approaches of these 2 parameters have been developed based on mass fractions and molecular weights of specific food components such as proteins, carbohydrates, minerals, and acids/bases. In this study, the molecular weights of the key mineral and acid/base components were successfully represented using average molecular weights (     ) and 4  T_Fi  and  X_I  calculation approaches were proposed. Based on an analysis of 212 food products, the absolute differences (AD) between the experimental and predicted  T_Fi  values for the 4 approaches were small. The prediction for the food model category was excellent with average AD (     ) values as low as ± 0.03 °C. For the other food categories, the prediction efficiency was impressive with     values between ± 0.22 and ± 0.38 °C. The predicted relationship between temperature and  X_I  for all analyzed food products provided close agreements with experimental data.     

响应面法优化食品浸渍速冻冻结液配方

为优化食品浸渍快速冻结的冻结液配方,以甜菜碱、丙二醇、氯化钠为主要组分,添加少量甘氨酸、低聚木糖、甘露醇,组成低温冻结液,在单因素试验基础上,运用Box-Behnken试验设计原理进行试验设计,探讨浸渍快速冻结的冻结液配方的最佳配比。结果表明：以占冻结液总质量分数计,由21%甜菜碱、15%丙二醇、10%氯化钠、1%甘氨酸、1%低聚木糖、1%甘露醇和水组成的多元冻结液,冻结点可达－38.10℃,可用作食品浸渍快速冻结的冻结液,用于水产品及冷冻方便食品的冷冻加工。     

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.