Review of effective thermal conductivity models for foods

The literature associated with modelling and predicting the thermal conductivities of food products has been reviewed. The uncertainty involved in thermal conductivity prediction increases as the differences between the food components' thermal conductivities increase, which means that there is greater uncertainty involved with predicting the thermal conductivity of foods which are porous and/or frozen, than with unfrozen, non-porous foods. For unfrozen, non-porous foods, a number of simple effective thermal conductivity models that are functions only of the components' thermal conductivities and volume fractions may be used to provide predictions to within ±10%. For frozen and/or porous foods, the prediction procedure is more complicated, and usually requires the prediction of porosity and/or ice fraction, which introduces another source of error. The effective thermal conductivity model for these foods may require an extra parameter (in addition to the components' thermal conductivities and volume fractions) whose value must often be determined empirically. Recommendations for selecting models for different classes of foods are provided. There is scope for more research to be done in this area.     

Determination of the thermal conductivity of xenon-helium mixtures at high temperatures by the shock-tube method

The thermal conductivity of gases at high temperatures has been measured by the shock-tube method, which is uniquely suited to measure thermal conductivities of gases at high temperatures above 2000 K. A consistent set of thermal-conductivity data over a wide range of temperatures has been obtained from optimum combinations of shock-tube experiments at high temperatures, previously published data at lower temperatures, and a theoretical correlation of the temperature dependence. In the present study, the thermal conductivity of xenon-helium mixtures has been determined at compositions of 10 and 30 mol% xenon over the temperature range from 300 to 4800 K. Even though there is a large difference between the thermal conductivity of pure xenon and that of helium, it is interesting that the dependences of the thermal conductivity of the mixture on temperature and composition are linear. The experimental results are in good agreement with the predicted values based on the corresponding-states principle and the mixing rule. From these experimental results, interpolating the corresponding-states correlation data, we represent the equation of xenon-helium gas mixtures for thermal conductivity in terms of temperature and composition.     

Effective thermal conductivity of a high porosity model food at above and sub-freezing temperatures

The modelling of heat transfer within materials with high porosity is complicated by evaporation-condensation phenomena. The aim of this work is to develop a model for apparent thermal conductivity in these products. The effective thermal conductivity of a porous food model (sponge) having 0–60% moisture contents and 0.59–0.94 porosity was measured by a line-source heat probe system in the range −35 to 25 °C. Two predictive models of the effective thermal conductivity of porous food were developed (Krischer and Maxwell models). The effective thermal conductivity predicted by Krischer model were in good agreement with the experimental data. Also, it was shown that the model including the effect of evaporation-condensation phenomena in addition to heat conduction was useful to predict the effective thermal conductivity of sponges.     

Extension of soil thermal conductivity models to frozen meats with low and high fat content

Thermal conductivity models of frozen soils were analyzed and compared with similar models developed for frozen foods. In total, eight thermal conductivity models and 54 model versions were tested against experimental data of 13 meat products in the temperature range from 0 to −40 °C. The model by deVries, with water+ice (wi) as the continuous phase, showed overall the best predictions. The use of wi leads generally to improved predictions in comparison to ice; water as the continuous phase is beneficial only to deVries model, mostly from −1 to −20 °C; fat is advantageous only to meats with high fat content. The results of this work suggest that the more sophisticated way of estimating the thermal conductivity for a disperse phase in the deVries model might be more appropriate than the use of basic multi-phase models (geometric mean, parallel, and series). Overall, relatively small differences in predictions were observed between the best model versions by deVries, Levy, Mascheroni, Maxwell or Gori as applied to frozen meats with low content of fat. These differences could also be generated by uncertainty in meat composition, temperature dependence of thermal conductivity of ice, measurement errors, and limitation of predictive models.     

Experimental determination of the thermal conductivity of three-phase syntactic foams

Syntactic foams are attractive for applications that require materials with high impact strength and low thermal conductivities. Because syntactic foams are manufactured by dispersing hollow microspheres in a resinous matrix, their characteristics are functions of the type and relative amounts of these materials. In this work, a discussion of an experimental approach to measure the thermal conductivity of three-phase syntactic foams (hollow carbon microspheres in a porous APO-BMI binder, analysis of the data and the comparison to predictive models are presented. The thermal conductivity of three-phase syntactic foams is measured using a Holometrix^© steady-state heat flow meter. The experimental data are found to be accurate to within a reasonable range of experimental error and are compared to three of the more reliable predictive models that have been used successfully to estimate the thermal conductivity of similar foams. It is observed that the model predictions at lower temperatures are more accurate as compared to those at higher temperatures. Also, that a model based on the concept of self-consistent field theory better predicts the thermal conductivity of syntactic foams than one based on resistance-in-series. Sensitivity studies indicate a strong dependency of the thermal conductivity of the three-phase foams on the thermal conductivity of the carbon used in the microspheres.     

The thermal conductivity surface for mixtures of methane and ethane

A correlation is presented for the extensive series of thermal conductivity measurements of binary methane-ethane mixtures. The composition dependences of the thermal conductivity in the dilute-gas region, dense-gas and liquid region, and critical region are discussed. The average absolute percentage deviation of the thermal conductivity surface as a function of temperature, density, and composition, from the experimental data, is 1.60%.     

Thermal conductivity,heat capacity,and thermal diffusivity of selected commercial AlN substrates

The thermal transport properties of four commercially available AlN substrates have been investigated using a combination of steady-state and transient techniques. Measurements of thermal conductivity using a guarded longitudinal heat flow apparatus are in good agreement with published room temperature data (in the range 130–170 W · m^–1 · K^–1). Laser flash diffusivity measurements combined with heat capacity data yielded anomalously low results. This was determined to be an experimental effect for which a method of correction is presented. Low-temperature measurements of thermal conductivity and heat capacity are used to probe the mechanisms that limit the thermal conductivity in AlN.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

Absolute measurement of the thermal conductivity of alcohol + n-hexane mixtures

New absolute measurements, by the transient hot-wire technique, of the thermal conductivity of binary mixtures of n-hexane with methanol, ethanol, and hexanol are presented. The temperature range examined was 295–345 K and the pressure atmospheric. The concentrations studied were 75% by weight of methanol and 25, 50, and 75% by weight of ethanol and hexanol. The overall uncertainty in the reported thermal conductivity data is estimated to be ±0.5%, an estimate confirmed by the measurement of the thermal conductivity of water. A recently extended semiempirical scheme for the prediction of the thermal conductivity of mixtures from the pure components is used to correlate and predict the thermal conductivity of these mixtures, as a function of both composition and temperature.     

Experimental determination and modeling of thermal conductivity tensor of carbon/epoxy composite

The modeling of thermal behavior of composite parts during their forming requires an accurate knowledge of their thermo-physical properties. Because of the heterogeneous nature of composites, the thermal conductivity tensor appears to be the most tricky to determine experimentally but also to model. A wide range of experimental methods can be found in the literature in order to measure either in-plane or transverse conductivity of composite parts, but very few succeed in performing it on dry preform or uncured laminates. In this study, the effective thermal conductivity tensor of carbon/epoxy laminates is investigated experimentally in the three states of a typical LCM-process: dry-reinforcement, raw and cured composite. Samples are made of twill-weave carbon fabric impregnated with epoxy resin. The transverse thermal conductivity is determined using a classical estimation algorithm, whereas a special testing apparatus is designed to estimate in-plane conductivity for different temperatures and different states of the composite. Experimental results are then compared to modified Charles & Wilson and Maxwell models. The fiber crimping of a ply is also taken into account in modeling. The comparison shows clearly that these models can be used to predict the effective thermal conductivities of woven-reinforced composites provided that the material properties are well known.     

预测复合材料导热系数的热阻网络法

借助计算机模拟复合材料的空间结构,直接迭代求解热阻网络,得到复合材料的导热系数。分析了在随机分布条件下取样尺度对导热系数的影响,以及二维和三维条件下导热的差别。与文献中实验数据的比较表明,所述方法能够较好地预示颗粒弥散型复合材料的导热系数。     

Evaluation of thermal conductivity from temperature profiles

A new dynamic technique for the measurement of thermal conductivity is being developed at IMGC. The experiment consists in bringing the specimen to high temperatures with a current pulse and in measuring the temperature profiles during the free cooling period. Different techniques can be used to extract the information on thermal conductivity from the profiles. The numerical computation of thermal conductivity from the experimental temperature profiles in absolute space is possible, but it is difficult and cumbersome because one must know and take into the account the exact position of the infinitesimal elements of the specimen in different profiles. Computations in tube-space (a fictitious space where no thermal expansion occurs) are simpler and lead to less complex numerical computations. Complementary techniques to evaluate thermal conductivity as a function of temperature or at constant temperature are presented with a discussion of advantages and disadvantages of each method. Computer simulations have tested the precision of the complex software. Numerically generated temperature profiles from known thermophysical properties have been obtained and thermal conductivity has been recomputed from the profiles. The relative difference using different computational approaches and different fitting functions is always less than 0.1%.Paper presented at the Third Workshop on Subsecond Thermophysics, September 17–18, 1992, Graz, Austria.     

The thermal conductivity and viscosity of acetic acid-water mixtures

The viscosity and thermal conductivity of acetic acid water mixtures were measured over the entire composition range and at temperatures ranging from 293 to 453 K. Viscosity measurements were performed with a high-pressure viscometer and thermal conductivity was measured using a modified transient hot-wire technique. A mercury filled. glass capillary was used as the insulated hot wire in the measurements. The l iscosity data showed unusual trends with respect to composition. At it given temperature. the viscosity was seen to increase with increasing acid concentration, attain a maximum. and then decrease. The thermal conductivity, on the other hand, decreased monotonically with acid concentration. A generalized corresponding-states principle using water and acetic acid as the reference fluids was used to predict both viscosity and thermal conductivity with considerable sucres.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–34, 1994, Boulder. Colorado, U.S.A.     

Low temperature thermal conductivity of aluminum alloy 5056

The thermal conductivity of 5056 aluminum alloy was determined from 4.2 K to 120 K using a differential steady-state method. This method has been implemented in a low temperature cryostat using a Gifford–McMahon cryocooler as heat sink. The thermal conductivity of the 5056 H39 aluminum alloy was determined since it was under consideration as a part of a thermal link for the Planck research satellite. As expected, below 10 K the thermal conductivity is exclusively given by the electron-defect scattering term. At higher temperature, the other terms from the electronic and the lattice contributions come into play but the electronic thermal conductivity term is still dominant. A workable fit, based on theory, is presented and can be used up to 300 K. Our measurements are compared with data at lower temperature and available fits from the literature.     

Influence of thermal conductivity on the breakdown field of niobium cavities

To experimentally check the predictions of the thermal model for the influence of thermal conductivity on breakdown field levels in Nb cavities, eight elliptical cavities at 8600 MHz have been built from material with RRRs of 25, 50 and 100 (RRR α thermal conductivity). After several rf tests on each cavity, the RRRs were increased by outgassing at -2000 C in a vacuum ofsim10^{-9}torr using resistive and induction heating furnaces with high pumping speeds. From a total of 40 tests on these cavities with RRRs ranging from 25 to 1400 the breakdown field is found to be roughly proportional to the square root of the RRR. Fabrication methods were kept the same for all the cavities and identical chemical surface preparation procedures were applied to the cavities before and after changing RRRs.     

The thermal conductivity of binary mixtures of polar gases

A method is proposed for the calculation of the thermal conductivity of binary mixtures of polar gases and of mixtures containing a polar component. It is demonstrated that the thermal conductivity of the mixtures of the polar gases is an almost linear function of the composition     

The thermal conductivity of n-hexadecane+ ethanol and n-decane+butanol mixtures

New absolute measurements, by the transient hot-wire technique, of the thermal conductivity of n-hexadecane and binary mixtures of n-hexadecane with ethanol and n-decane with butanol are presented. The temperature range examined was 295–345 K and the pressure atmospheric. The concentrations of the mixtures studied were 92% (by weight) of n-hexadecane and 30 and 70% (by weight) of n-decane. The overall uncertainty in the reported thermal conductivity data is estimated to be ±0.5%, an estimate confirmed by the measurement of the thermal conductivity of water. A recently extended semiempirical scheme for the prediction of the thermal conductivity of mixtures from the pure components is used to correlate and predict the thermal conductivity of these mixtures, as a function of both composition and temperature.     

A two-scale homogenization framework for nonlinear effective thermal conductivity of laminated composites

In this study, we formulate the effective temperature-dependent thermal conductivity of laminated composites. The studied laminated composites consist of laminas (plies) made of unidirectional fiber-reinforced matrix with various fiber orientations. The effective thermal conductivity is obtained through a two-scale homogenization scheme. A simplified micromechanical model of a unidirectional fiber-reinforced lamina is formulated at the lower scale. Thermal conductivities of fiber and matrix constituents are allowed to change with temperature. The upper scale uses a sublaminate model to homogenize temperature-dependent thermal conductivities of only a representative lamina stacking sequence in laminated composites. The effective thermal conductivity of each lamina, in the sublaminate model, is obtained using the simplified micromechanical model. The thermal conductivities from the micromechanical and sublaminate models represent average nonlinear properties of fictitiously homogeneous composite media. Interface conditions between fiber and matrix constituents and within laminas are assumed to be perfect. Experimental data available in the literature are used to verify the proposed multi-scale framework. We then analyze transient heat conduction in the homogenized composites. Temperature profiles, during transient heat conduction, in the homogenized composites are compared to the ones in heterogeneous composites. The heterogeneous composites, having different fiber arrangements and sizes, are modeled using finite element (FE) method.     

复合材料热传导系数均匀化计算的实现方法

均匀化理论可以有效预测周期性结构复合材料的等效热传导系数,然而其控制方程的载荷项形式特殊,通用有限元软件中没有对应的载荷形式,难以直接求解.提出一种本构关系及场变量的类比方法,证明了在此类比下等效热传导系数均匀化方程与等效弹性模量均匀化方程是等价的.根据求解等效弹性模量均匀化方程的热应变法,提出一种新的等效热传导系数均匀化方程数值求解方法.以ABAQUS为平台,预测单向纤维复合材料以及金属蜂窝夹芯板的等效热传导系数,计算结果与参考值吻合良好.该方法为基于通用有限元软件的复合材料等效热传导系数的均匀化计算提供了简便途径.     

Model for thermal conductivity of CNT-nanofluids

This work presents a simple model for predicting the thermal conductivity of carbon nanotube (CNT) nanofluids. Effects due to the high thermal conductivity of CNTs and the percolation of heat through it are considered to be the most important reasons for their anomalously high thermal conductivity enhancement. A new approach is taken for the modeling, the novelty of which lies in the prediction of the thermal behaviour of oil based as well as water based CNT nanofluids, which are quite different from each other in thermal characteristics. The model is found to correctly predict the trends observed in experimental data for different combinations of CNT nanofluids with varying concentrations.