Freezing Time Prediction: An Enthalpy-Based Approach

Equations were developed for prediction of freezing times of foods of slab geometry, for three different boundary conditions, using a method of solving for enthalpy per unit volume instead of temperature. Experimental verification was performed for the operation with a convective heat transfer boundary condition, using ice cream and green peas in a granular packed bed as test materials. Results indicate good prediction of freezing times over a range of conditions. Results of thawing tests are less satisfactory if the ambient temperature lies in the zone of rapidly changing food properties. A comparison with literature predictions is presented.     

虾仁热物性的计算及冻结时间的数值模拟

在虾仁热物性参数计算和等效比热容处理潜热的基础上,采用有限差元法对不规则虾仁建模,分别预测虾仁对称截面距冰箱冷冻层底部15,50,100mm处的冻结时间,在该基础上,对冰箱冻结虾仁进行实验验证。通过数值模拟与实验验证结果的对比发现,模拟冻结时间与实验冻结时间曲线相关系数为0.996,虾仁切面中心测点的最大误差值为1.85K,说明该数值模拟方法可以有效预测食品冻结过程中温度分布,对虾仁的冷冻加工、品质控制以及设备的优化具有重要意义。     

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.     

Sterilization of Conduction-Heated Foods in Oval-Shaped Containers

A finite difference approximation of the differential equation for transient heat conduction in three dimensions was used to evaluate thermal processes for foods in oval-shaped containers. A sensitivity analysis on the basis of thiamin retention was used to select the time increment and the size of the volume elements required by the numerical method. Estimations of the temperature for the center of the oval container were in close agreement with an analytical solution valid for sufficiently long times, constant boundary conditions, and uniform initial temperature. To validate the model, published experimental data for the retention of thiamin, chlorophyll and betanin were compared with values predicted by the numerical method.     

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.     

数值模拟在食品冻结过程中的应用

文章主要通过综述冻结过程的数值模型、求解微分方程、预测冻结时间及分析送风速度、温度和送风方式等,讨论数值模拟技术在食品冻结过程中的应用现状;总结了国内外研究者针对不同冻结对象所采用的数值模拟方法,为今后数值模拟方法在食品传热过程中进一步发挥作用提供理论参考。     

CALCULATION of INITIAL FREEZING POINT,EFFECTIVE MOLECULAR WEIGHT and UNFREEZABLE WATER of FOOD MATERIALS FROM COMPOSITION and THERMAL CONDUCTIVITY DATA1

A procedure was developed for simultaneous determination of the effective molecular weight, unfreezable water, and initial freezing point of foods based on composition and thermal conductivity data. Freezing properties were determined by trial and error and optimized by minimizing the difference between calculated and reported values of thermal conductivity. the procedure involved determination of the ice fraction at several temperature levels. Corresponding thermal conductivity values at each temperature level were then calculated. Results showed that calculated values of effective molecular weight, unfreezable water, and initial freezing point for various types of meat and fish are comparable to those published. the parallel-perpendicular model was found an excellent predictor of thermal conductivity of frozen meat and fish with muscle fibers oriented toward the direction of the heat flow.     

Parametric Analysis for Thawing Frozen Spheroidal (Prolate and Oblate) or Finitely Cylindrical Food

A screening analysis was performed to determine the influence of independent parameters (18) on thawing times of frozen spherical (prolate and oblate) and finitely cylindrical foods using a computerized simulation procedure assuming food volume shrinkage from density changes and temperature dependent physical properties. Of 18 independent parameters, 6 were significant for both foods: thawing medium temperature, initial freezing point, Biot number, radiative heat exchange, a parameter for effective specific heat and shape factor (nonsignificant influence of volumetric changes). Predictive regression equations were developed for estimating thawing time as function of significant parameters. Predictive equations were validated experimentally. A sensitivity analysis showed errors in thawing time were influenced most strongly by food dimensions, followed by operational temperatures, thermophysical properties and convective surface heat-transfer coefficient.     

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.     

青豆速冻过程冻结时间的数值计算

青豆近似为球状，采用完全隐式差分法，建立描述近似青豆的球状食品冻结过程传热特性的偏微分方程：通过数值计算获得青豆冻结时间的数值解，并与实验值比较。结果表明：数值法计算结果与实测值吻合较好，具有较高的精度。     

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.     

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.     

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.     

Analysis of Propagation of Freezing and Thawing Fronts

The modified isotherm migration method (MIMM) is used to calculate the temperature profiles and freezing (thawing) times for symmetrically cooled (heated) slabs with meat-like thermal properties. MIMM, which is reviewed briefly is not restricted to the usual idealizations such as zero surface resistance, uniform critical temperature distribution, and infinitely large sample. Dimensional analysis is used to identify the dimensionless groups controlling freezing and thawing front propogation in slabs, cylinders, and spheres having uniform thermal properties and constant freezing temperature. The MIMM results provide a basis for evaluating the qualitative origins and the quantitative extent of the success of Plank's (1913) old model. The freezing times predicted by the moving front model used here agree with those predicted by the empirical correlation found by Cleland and Earle for the Karlsruhe test substance.     

Recent developments in novel freezing and thawing technologies applied to foods

This article reviews the recent developments in novel freezing and thawing technologies applied to foods. These novel technologies improve the quality of frozen and thawed foods and are energy efficient. The novel technologies applied to freezing include pulsed electric field pre-treatment, ultra-low temperature, ultra-rapid freezing, ultra-high pressure and ultrasound. The novel technologies applied to thawing include ultra-high pressure, ultrasound, high voltage electrostatic field (HVEF), and radio frequency. Ultra-low temperature and ultra-rapid freezing promote the formation and uniform distribution of small ice crystals throughout frozen foods. Ultra-high pressure and ultrasound assisted freezing are non-thermal methods and shorten the freezing time and improve product quality. Ultra-high pressure and HVEF thawing generate high heat transfer rates and accelerate the thawing process. Ultrasound and radio frequency thawing can facilitate thawing process by volumetrically generating heat within frozen foods. It is anticipated that these novel technologies will be increasingly used in food industries in the future.     

Heat Transfer During the Freezing of Liver in a Plate Freezer

The overall heat transfer coefficient was determined for a vertical plate freezer by the transient temperature method and used in a modification of Plank's equation by Cleland and Earle to predict the freezing time of blocks of pig liver. A comparison of predicted and previously published experimental freezing times showed an average absolute error of 6.5%. Overall heat transfer coefficients for the main types of fibreboard packaging were also determined together with their effect on predicted freezing time. This work has highlighted many of the advantages of plate freezing which has yet to gain wide acceptance in the U.K. meat industry.     

Mathematical modeling of the heat transfer and flow field of liquid refrigerants in a hydrofluidization system with a stationary sphere

Hydrofluidization is a method of chilling and freezing of foods that uses a circulating system that pumps the refrigerating liquid upwards through orifices and/or nozzles into a refrigerating vessel, thereby creating submerged agitating jets and increasing heat transfer to foods during freezing. The objective of this work was to develop a model to estimate the fluid flow and heat and mass transfer in a hydrofluidization system. A study case of modeling and validating the heat transfer to a single stationary copper sphere of 20-mm diameter impinged by a single round jet of liquid was carried out using computational fluid dynamics. The simulations were performed using parameters such as: velocity of the liquid at the orifice exit (2.36–7.07 m s⁻¹), temperature of the liquid refrigerant (−5 to −15 °C) and distance between the orifice and the stagnation point of the sphere (1 and 5 cm). In general, the errors of the model were in the order of magnitude of the uncertainty of the experimental data of Nusselt number averaged over the sphere surface. Also, the simulated heat transfer and flow field parameters were comparable with those obtained in literature for similar systems.     

A Novel Method for Simultaneous and Continuous Determination of Thermal Properties during Phase Transition Applied to Calanus finmarchicus

Abstract: The thermal properties of a product are the most important parameters for practical engineering purposes and models in food science. Calanus finmarchicus is currently being examined as a marine resource for uncommon aquatic lipids and proteins. Thermal conductivity, specific heat, enthalpy and density were measured over the temperature range from −40 to +20 °C. The initial freezing point was determined to be −2.3 °C. The thermal properties were recorded continuously on 4 samples using a new method, and the results were compared with predictive models. The accuracy of the new method is demonstrated by different calibration runs. Significant differences in the thermal conductivity of the frozen material were found between the parallel-series model and the data, whereas the model of Pham and Willix (1989) or the Maxwell–Euken adaption showed better agreement. The measured data for specific heat, enthalpy, and density agreed well with the model. Practical Application: The thermal data obtained can be used directly in food engineering and technology applications, for example, in a thin layer model for freezing food for which precise thermal data for each layer are now available, enabling the more accurate prediction of freezing times and temperature profiles. Dimensionless numbers (such as the Biot number) can also be based on measured data with minor deviations compared to more general modeled thermal properties. Future activities will include the generation of a comprehensive database for different products.     

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.     

PREDICTION of MASS-AVERAGE and SURFACE TEMPERATURES, and the TEMPERATURE PROFILES AT the COMPLETION of FREEZING FOR SHAPES INVOLVING ONE-DIMENSIONAL HEAT TRANSFER

A model for predicting the temperature profiles of simple-shaped foodstuffs at the end of freezing was developed. It was shown that with appropriate selection of effective thermal diffusivity and initial temperature data, the standard solution of the unidimensional unsteady state heat conduction equation can be used in predicting the average and surface temperatures of infinite slabs at the end of freezing operation. For the calculation of average and surface temperatures in infinite cylinders and spheres, unsteady state solutions were corrected by an empirical factor that was derived from temperature profiles predicted by an accurate finite difference scheme. the temperature profiles calculated from the proposed model were compared with the predicted results obtained from a numerical model. Mean absolute errors between the predictions of the proposed model and the numerical model were 0.54C and 0.46C for average and surface temperatures, respectively.