Simultaneous Estimation of the Thermophysical Properties of Selected Liquid Dairy Products by a Transient Heat Flow Probe Method

The thermophysical properties of reconstituted whole milk, skim milk, and whey were measured at various temperatures and concentrations. A new method for the simultaneous determination of thermophysical properties using a modified version of current probe theory method was proposed. Two new correction coefficients were introduced, and using the values of these coefficients and an approximate solution of the heat conduction equation, the thermal conductivity and thermal diffusivity of each sample were determined. The specific heat of each sample was estimated from the definition of thermal diffusivity. These properties were expressed as a function of concentration and temperature.     

Simultaneous estimation of the thermophysical properties of three kinds of fruit juices based on the measured result by a transient heat flow probe method

The thermophysical properties of three kinds of fruit juices (grape juice, orange juice, and pineapple juice) were measured at various temperatures (10–50 °C) and concentrations (10–50%). A new method for the simultaneous determination of thermophysical properties using a modified version of current probe theory method was proposed. The temperature changes of the probe upon insertion in the sample were fitted to an approximate solution of the heat conduction equation, and the values of two parameters in that solution were determined. Using the values of these parameters, the thermal conductivity and thermal diffusivity of each sample were determined. The specific heat of each sample was estimated from the definition of thermal diffusivity. These thermophysical properties were expressed as a function of concentration and temperature.     

Simultaneous Estimation and Modeling of Thermophysical Properties of Big-Eyed Tuna and Pacific Cod

The thermophysical properties (thermal conductivity, thermal diffusivity, and specific heat) of big-eyed tuna and pacific cod were measured at various temperatures (5–50°C) by the modified version of current probe method. The optimal prediction models for these thermophysical properties were determined. The random model was applied to predict the thermal conductivity of seafood in a wide range of temperature and it provided the accurate predictions for the samples. The thermal diffusivities of the samples could be predicted by Martens’s equation. An additive relationship exists between the specific heat of the sample, the composition, and the specific heat of each component.     

Thermal conductivity of tomato paste

Experimental measurements of the thermal conductivity and thermal diffusivity of tomato paste at concentrations of 27–44° Brix are reported. The thermal conductivity was measured in a guarded hot-plate apparatus while the diffusivity was estimated by a simplified transient method. The thermal conductivity (λ) values fell in the region of 0·460–0·660 W m^?1 K^?1, decreasing with increasing solids concentration and increasing as the temperature was raised from 30 to 50°C. The temperature effect was less pronounced at higher solids concentration. The thermal diffusivity of tomato paste at 35° Brix and 20°C was estimated as 1·42 × 10^?7 m² s^?1, which is in good agreement with data from the steady-state method.     

Modeling and estimation of thermal conductivity of ultrafine glass wool mats by artificial neural network and correlation

Abstract

In this article, the thermal conductivity of ultrafine glass wool mats in terms of density and temperature has been modeled by artificial neural network (ANN). The thermal conductivity of ultrafine glass wool mats with different densities ranging from 5 to 35?kg/m³ and at different temperatures ranging from –10 to 70?°C was employed as training data for ANN. The optimal number of neurons in the hidden layer was proved to be 4. The maximum error between estimated results by ANN and experimental data is 1.5184, and the mean square error and correlation coefficient are 0.6216 and 0.9922, respectively. The ANN model shows excellent agreement with the experimental data and has a good ability for estimating the thermal conductivity of ultrafine glass wool mats. A correlation equation was also proposed to calculate the thermal conductivity as the function of density and temperature, which has a high fitting degree compared with the measured data but not as accurate as the ANN model.     

NEW COMPUTATIONAL PROCEDURE FOR DETERMINING THE APPARENT THERMAL DIFFUSIVITY OF A SOLID BODY APPROXIMATED WITH AN INFINITE SLAB

A computational procedure was developed for determining the thermal diffusivity of food. For this development, a theoretical formula for estimating heat conduction in an infinite slab was used. This formula was derived by assuming that temperatures on the surface of a slab change arbitrarily with time and also that its thermal diffusivity is temperature independent. A thermal diffusivity value of a solid sample is determined through estimation of the following specific diffusivity value: The specific value, which gives the least sum of squares of differences between temperatures calculated by the derived formula and those determined through heat transfer experimentation. A set of FORTRAN IV computer programs- was prepared to determine diffusivity values of solids. The diffusivity values of ice, frozen grapefruit juice, frozen 50% sucrose solution and frozen ground beef were determined by using these computer programs. Experimental temperature data, which were used for this determination, were obtained by utilizing specially fabricated rectangular cells     

A NEW METHOD FOR DETERMINING THE APPARENT THERMAL DIFFUSIVITY OF THERMALLY CONDUCTIVE FOOD

Two empirical parameters, j and f, have been used to determine the thermal diffusivity values of food by several researchers. Since there are considerable variations in j values, a new procedure was developed for the experimental determination of thermal diffusivity of foods without using this parametric value. A sample was filled into a cylindrical cell whose diameter and length were approximately 10 and 130 mm, respectively. The temperatures of the sample were monitored at the mid-point of the central axis and on the inside surface of the cell. These temperatures were used to estimate thermal diffusivity values together with an analytical formula for heat conduction in an infinite cylinder. The method was utilized to determine the thermal diffusivity, Biot number, and surface heat conductance values of water, 60% sucrose solution, glycerine, cherry tomato pulp, and apple pulp. There was close agreement between thermal diffusivity values determined experimentally and such values available in published literature. Mathematical procedures are presented for estimating errors in the thermophysical property values determined experimentally, where there are errors in locating temperature sensors in a sample, errors in the shape of the diffusivity cell, and errors in the temperature sensing device.     

固液混装罐头食品固体中心冷点温度预测

本文探索了固液混装罐头食品的传热特性。应用CS—2型温度信息处理机测定了固液混装罐头食品的固体和汤汁中心冷点温度值。编了计算机程序,计算传热过程的参数j,f值。建立一系列的固体和汤汁冷点处的传热方程和确立罐头食品的固液传热比方程,可预测固体中心温度值,百分误差在允许范围内。本文提出的方法是一种较理想的预测固体中心温度方法,可供制订合理杀菌工艺条件之用。     

Original article: Apparent thermal diffusivity estimation for the heat transfer modelling of pork loin under air/steam cooking treatments

Apparent thermal diffusivity linear functions vs. product temperature were estimated for pork cooked under two different treatments (forced convection, FC and forced convection/steam combined, FC/S) at 100, 110, 120 and 140 °C by means of experimental time–temperature data and a developed finite‐difference algorithm. Slope and intercept of each function were employed to calculate apparent thermal diffusivity at 40, 55 and 70 °C. Generally, FC/S treatments gave significantly higher apparent thermal diffusivities in comparison with FC conditions. Apparent thermal diffusivities were used to develop a model for cooking time and final core temperature prediction on the basis of oven setting. The model was validated by means of additional cooking tests performed at different temperatures of those employed for model development. Root mean square error values lower than 3.8 °C were obtained comparing predicted and experimental temperature profiles. Percentage errors lower than 3.1% and 3.5% were, respectively, obtained for cooking times and final core temperatures.     

Estimation of confidence interval of pasteurizing values of conduction-heated Sous Vide food in a combination oven

The thermal diffusivity of potato and the apparent heat transfer coefficients (h) in a conduction chiller and in a combination oven at 85, 90 and 95°C and vario-steaming mode were determined experimentally. Based on K-S tests and assumption, the variabilities of all six parameters (thermal diffusivity, h values for heating and cooling, initial food temperature, process medium temperatures and z value) were represented by normal distribution only (model A) or by both normal and gamma distributions (model B). The mean P₇₀ values and their 95% confidence intervals for three oven temperatures, estimated from experimental temperature histories, were 1510 ± 101, 1590 ± 131 and 1590 ± 170 min (for each oven temperature, n = 100) respectively. Good agreement was obtained between these estimations and those predicted using the Monte Carlo procedure and models A and B.     

THERMAL DIFFUSIVITY MEASUREMENTS of WHEAT FLOUR and WHEAT FLOUR DOUGH

A simple technique was used to measure thermal diffusivity of whole wheat flour and whole wheat flour dough at various levels of moisture and temperatures. the experimental values showed good agreement with the calculated values. It was found that thermal diffusivity of dough increases with moisture and temperature below 60C, but above 60C its value decreases. This is attributed to physico-chemical changes, e.g., starch gelerinization and protein coagulation. Due to these changes swelling and softening of dough occur, which reduce the ability of dough to diffuse thermal energy, thus lowering the value of the thermal diffusivity. Based on the experimental value of wheat dough at various moisture levels and temperatures, the following equation is proposed: α= (7.957 − 0.6346 M + 0.217 T + 0.008 M²− 0.00176 T²− 0.00051 M × T) × 10-7     

Thermal Properties of Sweet Potato with its Moisture Content and Temperature

Thermal properties of sweet potato were experimentally determined and modeled as a function of temperature and moisture content. The purpose is to develop empirical correlations that could predict thermal properties during sweet potato processing. Thermal conductivity from the study was 0.49 ± 0.038 Wm^?1K^?1 (mean ± s.d.), thermal diffusivity was 1.2?×?10^?7 ± 9.05?×?10^?9 m²s^?1, specific heat was 3660 ± 477.4 Jkg^?1K^?1, and density was 1212 ± 73.5 kgm^?3. All properties were determined within temperature range of 20 to 60°C and moisture content range of 0.45 to 0.75 w.b. Prediction models for the thermal properties of sweet potato were developed as a function of product temperature and moisture content with experimental data from this study. Mechanistic models were also developed for thermophysical properties of sweet potato using major food components of the product. Developed models were all presented and compared.     

Thermophysical Properties of Papaya Puree

The effects of soluble solids content and temperature on thermal properties of papaya puree were studied. Density and specific heat were measured using a pycnometer and differential scanning calorimeter, respectively, while thermal conductivity was measured using a line heat source probe. Thermal diffusivity was then calculated from the experimental results of the specific heat, thermal conductivity, and density. Thermal properties of papaya puree were experimentally determined within a soluble solids content range of 10 to 25 °Brix and temperature between 40 and 80°C. The density, specific heat, thermal conductivity, and thermal diffusivity of papaya puree were found to be in the ranges of 1014.6 to 1098.9 kg/m³, 3.652 to 4.092 kJ/kg °C, 0.452 to 0.685 W/m °C, and 1.127?×?10^?7 to 1.650?×?10^?7 m²/s, respectively. Moreover, the empirical models for each property as a function of soluble solids content and temperature were obtained.     

Influence of temperature and concentration on thermophysical properties of yellow mombin (Spondias mombin, L.)

Thermal conductivity, thermal diffusivity, and density of yellow mombin juice were determined at 8.8–49.4 °Brix and at temperature from 0.4 to 77.1 °C. Apparent viscosity was also measured between 7.8 and 30 °Brix and at temperature from 0 to 60 °C. Yellow mombin juice was produced from fruits of two different batches and the concentration process was performed using a roto evaporator or a rising film evaporator, single effect, with recirculation, under vacuum, to obtain concentrated juice. In order to obtain different concentrations, concentrated juice was diluted with distilled water. Multiple regression analysis was performed to fit thermal conductivity, thermal diffusivity and density experimental data obtaining a good fit. Arrhenius and power law relationships were proposed to fit apparent viscosity as a function of temperature and juice concentration at typical shear rates found during processing. The rheological parameters together with experimental values of pressure loss in tube flow were used to calculate friction factors, which were compared to those resulting from theoretical equation.     

Thermal diffusivity of foods measured by simple equipment

This paper describes how measurements of thermal diffusivity can be made by cheap, simple equipment available in most laboratories. The food sample is filled into a cylinder and a thermogram is plotted after placing the cylinder in a thermostatically controlled water bath. The diffusivity is calculated from the graph. Diffusivities thus obtained are in good agreement with data from literature.     

Heat Transfer During Brining of Cuartirolo Argentino Cheese

The heat transfer which occurs during the brining of Cuartirolo Argentino cheese is mathematically modelled as a conduction process. The thermal diffusivity of the cheese was determined experimentally and shown to agree with the value calculated from thermal conductivity, density and heat capacity measurements. The theoretical and experimental temperature profiles in the time and spatial domains showed good agreement, thus demonstrating the applicability of the proposed model.     

Influence of Moisture Content and Temperature on Thermal Conductivity and Thermal Diffusivity of Rice Flours

The thermal conductivity and thermal diffusivity for four types of rice flours and one type of rice protein were determined at temperatures ranging from 4.8 to 36.8?°C, bulk densities 535 to 875.8 kg m^?3, and moisture contents 2.6 to 16.7% (w.b.), using a KD2 Thermal Properties Analyzer. The thermal conductivity of rice flours and rice protein increased with the increase in temperature, moisture content as well as with increase in bulk density. Thermal diffusivity decreased with increase in moisture content, increase in temperature and bulk density. The thermal conductivities values obtained were within the range of 0.045 to 0.124 W m^?1 K^?1 whereas the thermal diffusivity values were in the range of 0.094 to 0.138 mm² s^?1.     

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.     

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.     

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。