The Dual-Phase-Lag Heat Conduction Model in Thin Slabs Under a Fluctuating Volumetric Thermal Disturbance

In the present work, the thermal behavior of a thin slab, under the effect of a fluctuating volumetric thermal disturbance described by the dual-phase-lag heat conduction model is investigated. It is found that the use of the dual-phase-lag heat conduction model is essential at large frequencies of the volumetric disturbance. It is found that the hyperbolic wave model deviates from the diffusion model when and the dual-phase-lag model deviates from the diffusion model when . where is the angular velocity of the fluctuating wall temperature, is the phase-lag in the heat flux vector and is the phase-lag in the temperature gradient vector.     

Analytical Prediction of Quench Energies of Cooled Superconductors Based on the Hyperbolic Heat Conduction Model

The critical energy characteristics of cooled composite superconductors is analytically predicted based on the one-dimensional hyperbolic heat conduction model. The temperature dependence of the Ohmic heat generation, the finite speed of heat transfer, and the finite duration and finite length of the thermal disturbances are taken into account in the present model. The critical energies are calculated using a model based on the analytical solution of the hyperbolic heat conduction equation by the Laplace transformation method. The computational model results show that the critical energy depends on the relaxation time and disturbance duration. It is found that the hyperbolic conduction model predicts a lower-critical energy as compared to the predictions of the parabolic heat conduction model.     

Thermal Behavior of a Stagnant Gas Confined in a Horizontal Microchannel as Described by the Dual-Phase-Lag Heat Conduction Model

The transient thermal behavior of a stagnant gas confined in a horizontal microchannel is investigated analytically under the effect of the dual-phase-lag heat conduction model. The microchannel is formed from two infinite horizontal parallel plates where the upper plate is heated isothermally and the lower one is kept adiabatic. The model that combines both the continuum approach and the possibility of slip at the boundary is adopted in this study. The effects of the Knudsen number Kn, the thermal relaxation time _q, and the thermal retardation time _T on the microchannel thermal behavior are investigated using three heat conduction models. It is found that the deviations between the predictions of the parabolic and the hyperbolic models are insignificant. On the other hand, the deviations between the parabolic and dual-phase-lag models are significant under the same operating conditions.     

Superconductor Thermal Stability under the Effect of the Dual-Phase-Lag Conduction Model

The superconductor thermal stability is investigated under the effect of the dual-phase-lag heat conduction model. Two types of superconductors are considered, Types I and II. It is found that the dual-phase-lag model predicts a wider stable region as compared to the predictions of the parabolic and the hyperbolic heat conduction models. Also, the superconductor thermal stability under the effect of different design, geometrical and operating conditions is studied.     

Thermal Behavior of a Multi-layered Thin Slab Carrying Periodic Signals Under the Effect of the Dual-Phase-Lag Heat Conduction Model

The thermal behavior of a two–layered thin slab carrying periodic signals under the effect of the dual-phase-lag heat conduction model is investigated. Two types of periodic signals are considered, a periodic heating source and a periodic imposed temperature at the boundary. The deviations among the predictions of the classical diffusion model, the wave mode, and the dual-phase-lag model are investigated. Analytical closed-form solutions are obtained for the temperature distribution within the slab. The effect of the angular frequency, thickness of the plate, dimensionless thermal relaxation time, dimensionless phase-lag in temperature gradient, thermal conductivity, and thermal diffusivity on the temperature distribution of the slab was studied. It is found that the deviations among the three models increase as the frequency of the signals increases and as the thickness of the plate decreases. It is found that the use of the dual-phase-lag heat conduction model is necessary when the metal film thickness is of order 10^–6 m and the angular frequency of the signals is of order 10¹²rad · s^–1.     

Thermal Behavior of Perfect and Imperfect Contact Composite Slabs Under the Effect of the Hyperbolic Heat Conduction Model

This work studies the heat transfer mechanisms during rapid heating of two-layer composite thin slabs from a macroscopic point of view using the hyperbolic heat conduction model. The composite slabs consist of two thin metal layers which may be in perfect or imperfect thermal contact. The effects of parameters such as the two films' thickness ratio, thermal conductivity ratio, heat capacity ratio, thermal relaxation time, and interfacial heat transfer coefficient on the thermal behavior of the composite slabs are investigated.     

分形理论在耐火纤维材料的导热特性研究中的应用

运用分形理论对多孔介质的几何结构进行描述，建立了耐火纤维材料的导热分形模型，并据此模型推导出其有效导热系数计算式；公式表明，耐火纤维材料的导热过程除了与气、固两相的物性和温度有关外，还与其体积分率以及孔隙分形维数有关。通过应用此计算式进行计算，得出了耐火纤维材料的有效导热系数计算值，而且计算结果与实验数据吻合得比较好，表明该导执模型计算式具有较高的表达精度。     

An Analytical Study on a Model Describing Heat Conduction in Rectangular Radial Fin with Temperature-Dependent Thermal Conductivity

The coupling of the homotopy perturbation method (HPM) and the variational iteration method (VIM) is a strong technique for solving higher dimensional initial boundary value problems. In this article, after a brief explanation of the mentioned method, the coupled techniques are applied to one-dimensional heat transfer in a rectangular radial fin with a temperature-dependent thermal conductivity to show the effectiveness and accuracy of the method in comparison with other methods. The graphical results show the best agreement of the three methods; however, the amount of calculations of each iteration for the combination of HPM and VIM was reduced markedly for multiple iterations. It was found that the variation of the dimensionless temperature strongly depends on the dimensionless small parameter ${\varepsilon_1}$ . Moreover, as the dimensionless length increases, the thermal conductivity of the fin decreases along the fin.     

填充颗粒导热性对复合材料导热性能的影响

基于ANSYS Workbench稳态热分析模块,利用均匀化方法,研究了填充颗粒导热性对填充型复合材料导热性能的影响。结果表明,依靠增大填充颗粒导热系数来提高复合材料整体的导热性能有一定局限性,填料导热系数与基体材料导热系数之比存在一个临界值。在相同体积分数下,随着比值的增大复合材料导热系数增加,当达到临界值后继续增大比值复合材料的导热系数基本不变。不同形状的填充颗粒有不同的临界值,圆柱形颗粒的临界值略大于正方体形和球形,而且对于同一种形状的填充颗粒,随着填充分数的增大临界值略有增加。     

Application of Radial Effective Thermal Conductivity for Heat Transfer Model of Steel Coils in HPH Furnace

The hot/cold rolled steel coil can be considered as a periodically laminated material composed of layers of steel strips and gas gaps in the radial direction. The conduction of steel, of gas, of contact points due to the surface roughness, as well as radiation have been included in a determination of the radial effective thermal conductivity. Based on the analysis of heat transfer mechanisms in radial coils, a new formula for the radial effective thermal conductivity has been derived, which depends not only on the temperature but also on the type of atmosphere gas, the surface characteristic of coils, strip thickness, and compressive stress. Using this effective conductivity, a detailed mathematical model has been developed to predict the temperature distribution of coils in a high performance hydrogen (HPH) furnace. The calculated annealing curves are in good agreement with experimental data.     

热处理对热障涂层孔隙率及热导率的影响

热障涂层高温使用过程中不可避免发生烧结,引起涂层失效。为探索烧结过程对涂层可靠性的影响,采用等离子喷涂制备氧化钇稳定氧化锆(YSZ)涂层,并对其进行1 000,1 100,1 200,1 300℃高温烧结试验,研究其高温烧结过程中的微观结构及热导率演变规律。结果表明:高温热处理引起热障涂层组织结构和热导率均发生变化,稳定状态的孔隙率为12%~14%,在热障涂层服役温度范围内热导率增加到1.25~1.45 W/(m·K)。     

The Thermal Conductivity, Thermal Diffusivity, and Heat Capacity of Gaseous Argon

This paper presents new absolute measurements for the thermal conductivity and thermal diffusivity of gaseous argon obtained with a transient hot-wire instrument. Six isotherms were measured in the supercritical dense gas at temperatures between 296 and 423 K and pressures up to 61 MPa. A new analysis for the influence of temperature-dependent properties and residual bridge unbalance is used to obtain the thermal conductivity with an uncertainty of less than 1% and the thermal diffusivity with an uncertainty of less than 4%. Isobaric heat capacity results were derived from measured values of thermal conductivity and thermal diffusivity using a density calculated from an equation of state. The heat capacities presented here have a nominal uncertainty of 4% and demonstrate that this property can be obtained successfully with the transient hot wire technique over a wide range of fluid states. The technique will be useful when applied to fluids which lack specific heat data.     

周期热流法测定金属导热系数

根据周期热流法的测试原理,采用理论分析、实验测定和数值仿真相结合的研究方法,设计了一套导热系数测试系统.利用先进的数据采集系统,通过自编程实现了数据的自动采集与处理.通过数值实验发现所需测试试样的最小长度远小于相关文献中的穿透深度.对几种试样进行了测试,发现导热系数最大误差不超过5%,经仿真修正后误差在3%以内.该测试系统具有简单、可行、数据可靠的特点.     

Specific Heat Measurements by a Thermal Relaxation Method: Influence of Convection and Conduction

This paper involves the well-known thermal relaxation method for measurement of the specific heat (c) of thin solid samples. Although this method was applied successfully in recent years for the characterization of different materials, in this work some aspects that must be taken into account in order to avoid problems based on satisfying the required experimental conditions of heat flux imposed by the physical model used for data analysis and processing will be discussed. For this purpose, for a given experimental geometry, the heat diffusion equation will be solved in order to obtain the sample’s requirements for reliable measurements of c, regarding its thickness and thermal conductivity. An experimental device is described that can be used for the study of the influence of heat dissipation by convection on the method. A computer simulation was performed for comparing the simple model with one that takes to in account the gradient of temperature inside the sample. The results of measurements are presented.Paper presented at the Seventeenth European Conference on Thermophysical Properties, September 5–8, 2005, Bratislava, Slovak Republic.Part of this work was performed when the author was at Universidad de La Habana, Facultad de Física, San Lázaro y L, Vedado 10400, La Habana, Cuba.     

The Thermal Conductivity, Thermal Diffusivity and Isobaric Heat Capacity of Toluene and Argon

This paper presents absolute measurements for the thermal conductivity and thermal diffusivity of toluene obtained with a transient hot-wire instrument employing coated wires over the density interval of 735 to 870 kgm^–3. A new expression for the influence of the wire coating is presented, and an examination of the importance of a nonuniform wire radius is verified with measurements on argon from 296 to 323 K at pressures to 61 MPa. Four isotherms were measured in toluene between 296 and 423 K at pressures to 35 MPa. The measurements have an uncertainty of less than ±0.5% for thermal conductivity and ±2% for thermal diffusivity. Isobaric heat capacity results, derived from the measured values of thermal conductivity and thermal diffusivity, using a density determined from an equation of state, have an uncertainty of ±3% after taking into account the uncertainty of the applied equation of state. The measurements demonstrate that isobaric specific heat determinations can be obtained successfully with the transient hot wire technique over a wide range of fluid states provided density values are available.     

利用瞬态热线法测量固体导热系数

在利用瞬态热丝法测量固体与流体导热系数方法研究的基础上,对固体的导热系数进行了计算,提出了既有理论意义又包含了测量参数、既严格又简便的新表达式;分析与定量计算了模型误差、截断误差、热阻误差、热容忽视误差及测量系统的合成误差;并指出了减小误差的措施。在实验研究中,建立了试件测试台和自动化参数采集与数据处理的计算机测控系统。测量结果表明,所测得的3种固体材料的导热系数值与文献参照值相差约5％。具有一定的实用价值。     

Conventional Simultaneous Measurement of Specific Heat Capacity and Thermal Conductivity by Thermal Radiation Calorimetry

Thermal radiation calorimetry has been applied to measure the thermal conductivity and the specific heat capacity of an isolated solid specimen simultaneously. The system, in which a disk-shaped specimen and a flat heater are mounted in a vacuum chamber with the specimen heated on one face by irradiation, is presented. A theoretical formulation of the simultaneous measurement at quasi-steady state is described in detail. Noncontact temperature measurement of both specimen surfaces has been performed using pyrometers and a thermocouple set in the gap between the heater and the specimen. Pyroceram 9609 specimens, whose surfaces were blackened with colloidal graphite, were used in the measurement. The largest error involved in the noncontact temperature measurement is ±2°C in the range from 450 to 650°C. The resultant values of the specific heat capacity and the thermal conductivity deviate by about 10% from the recommended values for the Pyroceram specimen.     

Thermal Conductivity,Thermal Diffusivity,and Heat Capacity of Gaseous Argon and Nitrogen

Low-pressure thermal conductivity and thermal diffusivity measurements are reported for argon and nitrogen in the temperature range from 295 to 350 K at pressures from 0.34 to 6.9 MPa using an absolute transient hot-wire instrument. Thermal conductivity measurements were also made with the same instrument in its steady-state mode of operation. The measurements are estimated to have an uncertainty of 1% for the transient thermal conductivity, 3% for the steady-state thermal conductivity, and 4% for thermal diffusivity. The values of isobaric specific heat, derived from the measured thermal conductivity and thermal diffusivity, are considered accurate to 5% although this is dependent upon the uncertainty of the equation of state utilized.Paper presented at the Sixteenth European Conference on Thermophysical Properties, September 1–4, 2002, London, United Kingdom     

Superconductor Thermal Stability Under the Effect of a Two-Dimensional Dual-Phase-Lag Heat Conduction Model

The thermal stability of superconducting thick wire has been numerically investigated under the effect of a two-dimensional dual-phase-lag heat conduction model. Two types of superconductors are considered, Types I and II. It is found that the dual-phase-lag model predicts a wider stable region as compared to the predictions of the parabolic and the hyperbolic heat conduction models. Also, the superconductor thermal stability under the effect of different design, geometrical, and operating conditions is studied.     

Phase Transformation Contributions to Heat Capacity and Impact on Thermal Diffusivity,Thermal Conductivity,and Thermoelectric Performance

The accurate characterization of thermal conductivity κ, particularly at high temperature, is of paramount importance to many materials, thermoelectrics in particular. The ease and access of thermal diffusivity D measurements allows for the calculation of κ when the volumetric heat capacity, ρc_p, of the material is known. However, in the relation κ = ρc_pD, there is some confusion as to what value of c_p should be used in materials undergoing phase transformations. Herein, it is demonstrated that the Dulong–Petit estimate of c_p at high temperature is not appropriate for materials having phase transformations with kinetic timescales relevant to thermal transport. In these materials, there is an additional capacity to store heat in the material through the enthalpy of transformation ΔH. This can be described using a generalized model for the total heat capacity for a material $$\rho {\mathit{c}}_p={\mathit{C}}_{p?}+\mathrm{\Delta }\mathit{H}{(??\mathrm{?}/\mathrm{?}?\mathit{T})}_p$$ where φ is an order parameter that describes how much latent heat responds “instantly” to temperature changes. Here, C_pφ is the intrinsic heat capacity (e.g., approximately the Dulong–Petit heat capacity at high temperature). It is shown experimentally in Zn₄Sb₃ that the decrease in D through the phase transition at 250 K is fully accounted for by the increase in c_p, while κ changes smoothly through the phase transition. Consequently, reports of κ dropping near phase transitions in widely studied materials such as PbTe and SnSe have likely overlooked the effects of excess heat capacity and overestimated the thermoelectric efficiency, zT.