Model of Fractional Heat Conduction in a Thermoelastic Thin Slim Strip under Thermal Shock and Temperature-Dependent Thermal Conductivity

The present paper paper, we estimate the theory of thermoelasticity a thin slim strip under the variable thermal conductivity in the fractional-order form is solved. Thermal stress theory considering the equation of heat conduction based on the time-fractional derivative of Caputo of order α is applied to obtain a solution. We assumed that the strip surface is to be free from traction and impacted by a thermal shock. The transform of Laplace (LT) and numerical inversion techniques of Laplace were considered for solving the governing basic equations. The inverse of the LT was applied in a numerical manner considering the Fourier expansion technique. The numerical results for the physical variables were calculated numerically and displayed via graphs. The parameter of fractional order effect and variation of thermal conductivity on the displacement, stress, and temperature were investigated and compared with the results of previous studies. The results indicated the strong effect of the external parameters, especially the time-fractional derivative parameter on a thermoelastic thin slim strip phenomenon.     

The Variational Form of the Mathematical Model of a Thermal Explosion in a Solid Body with Temperature-Dependent Thermal Conductivity

The variational form of a mathematical model of a thermal explosion has been developed based on a variational formulation of a nonlinear problem of stationary thermal conductivity in a homogeneous solid body. The model takes the temperature dependence of the thermal conductivity of a solid body into account. The presented example of quantitative analysis of the model demonstrates a method for finding the combination of parameters for determining a thermal explosion in a plate with an exponential temperature dependence of the thermal conductivity. At the same time, the analysis allows one to identify the number of steadystate temperature distributions inside a body whose energy release intensifies with a temperature increase.     

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.     

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。     

Measurement of the In-plane Thermal Diffusivity and Temperature-Dependent Convection Coefficient Using a Transient Fin Model and Infrared Thermography

The transient fin model introduced recently for determination of the in-plane thermal diffusivity of planar samples with the help of infrared thermography was modified so as to be applicable to poor heat conductors. The new model now includes a temperature-dependent heat loss by convective heat transfer, suitable for an experimental setup in which the sample is aligned parallel to a weak, forced air flow stabilizing otherwise the convective heat transfer. The temperature field in the sample was measured with an infrared camera while the sample was heated at one edge. The symmetric temperature field created was averaged over the central fifth of the sample to obtain one-dimensional temperature profiles, both transient and stationary, which were fitted by a numerical solution of the fin model. One of the fitting parameters was the thermal diffusivity, and with a known density and specific heat capacity, the thermal conductivity was thus determined. The test measurements with tantalum samples gave the result (57.5 ± 0.2) W · m⁻¹ · K⁻¹ in excellent agreement with the known value. The other fitting parameter was a temperature-dependent heat loss coefficient from which the lower limit for the temperature-dependent convection coefficient was determined. For the stationary state the result was (1.0 ± 0.2) W · m⁻² · K⁻¹ at the temperature of the flowing air, and its temperature dependence was found to be (0.22 ± 0.01) W ·m⁻² · K⁻².     

泡沫混凝土导热系数模型研究

研制了系列不同容重的泡沫混凝土,对泡沫混凝土的气孔率和导热系数进行了测试.在此基础上利用二相体系材料导热系数模型对实验结果进行了分析,运用Matlab软件进行了拟合;改进了Maxwell方程,提出并验证了适用于泡沫混凝土的新方程.经测算,理论预测值与实验结果显示了良好的一致性,研究结果表明,所提出的导热系数新方程适合于指导设计特定配比的泡沫混凝土.     

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.     

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.     

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.     

An Inverse Analysis to Estimate Relaxation Parameters and Thermal Diffusivity with a Universal Heat Conduction Equation1

This paper presents an inverse analysis for simultaneous estimation of relaxation parameters and thermal diffusivity with a universal heat conduction model by using temperature responses measured at the surface of a finite medium subjected to pulse heat fluxes. In the direct analysis, the temperature responses in a finite medium subjected to a pulse heat flux are derived by solving the universal heat conduction equation. The inverse analysis is performed by a nonlinear least-squares method for determining the two relaxation parameters and thermal diffusivity. Here, the nonlinear system of algebraic equations resulting from the sensitivity matrix is solved by the Levenberg–Marquardt iterative algorithm. The inverse analysis is utilized to estimate the relaxation parameters and the thermal diffusivity from the simulated experimental non-Fourier temperature response obtained by direct calculation.     

Exact and Approximate Analytic Methods to Calculate Maximum Heat Flow in Annular Fin Arrays with a Rectangular Step Profile

Exact and approximate techniques to determine the performance of annular fins with a step rectangular profile are developed. A simple approximate method is proposed to analyze the prevalent heat transfer characteristics of the fin array. An algebraic expression based on the mean value approach is used as an approximation tool, and the temperature distribution in the fins is determined using an exponential function. A method based on a modified Bessel function formulation is employed for exact analysis. The analyses are extended to optimize fins based on the principle of maximizing heat transfer rate for a given volume. The results obtained from the exact and approximate analyses are presented in a one-to-one comparative manner to allow for a wide range of practical design variables. The error in the approximate analysis calculations is investigated, and it is found to be well within engineering accuracy requirements. It is expected that the approximate analytical tool designed here will be extremely useful for designers who want to easily determine design parameters. Because the approximate methodology is so simple, all calculations can easily be done.     

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.     

固体吸附式制冷中强化吸附剂导热性能的研究

通过添加膨胀石墨并固结成型使吸附剂及复合吸附剂的导热系数有了较大提高,并测定了几种吸附剂的导热系数,分析了膨胀石墨所具有的特性是使其成为合适的添加剂的原因。     

Nonlinear Waves in Two-Layer Systems with a Temperature-Dependent Interfacial Heat Release

Nonlinear convective flows developed under the joint action of buoyant and thermocapillary effects in a two-layer system with periodic boundary conditions on the lateral walls, have been investigated. The influence of a temperature-dependent interfacial heat release/consumption on oscillatory regimes, has been studied. It is shown that sufficiently strong temperature dependence of interfacial heat sources and heat sinks can lead to the change of the sequence of bifurcations and the development of new nonlinear regimes.     

Simultaneous Measurement of Thermal Conductivity and Specific Heat in a Single TDTR Experiment

Time-domain thermoreflectance (TDTR) technique is a powerful thermal property measurement method, especially for nano-structures and material interfaces. Thermal properties can be obtained by fitting TDTR experimental data with a proper thermal transport model. In a single TDTR experiment, thermal properties with different sensitivity trends can be extracted simultaneously. However, thermal conductivity and volumetric heat capacity usually have similar trends in sensitivity for most materials; it is difficult to measure them simultaneously. In this work, we present a two-step data fitting method to measure the thermal conductivity and volumetric heat capacity simultaneously from a set of TDTR experimental data at single modulation frequency. This method takes full advantage of the information carried by both amplitude and phase signals; it is a more convenient and effective solution compared with the frequency-domain thermoreflectance method. The relative error is lower than 5 % for most cases. A silicon wafer sample was measured by TDTR method to verify the two-step fitting method.     

Non-homogeneous Steady-State Heat Conduction Problem in a Thin Circular Plate and Its Thermal Stresses

The present paper deals with the determination of the displacement and thermal stresses in a thin circular plate defined as 0 ≤ r ≤ b, 0 ≤ z ≤ h under a steady temperature field, due to a constant rate of heat generation within it. A thin circular plate is insulated at the fixed circular boundary (r = b), and the remaining boundary surfaces (z = 0, z = h) are kept at zero temperature. The governing heat conduction equation has been solved by using an integral transform technique. The results are obtained in series form in terms of modified Bessel functions. The results for displacement and stresses have been computed numerically and are illustrated graphically.     

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.     

Analytical and Numerical Investigation on Effective Thermal Conductivity of Polymer Composites Filled with Conductive Hollow Particles

The thermal behavior of hollow conductive particles filled in epoxy resin has been investigated using 3D finite element computation. The effect of the filler concentrations associated with the particle/matrix interfacial resistance on the effective thermal conductivity of the composites was considered. The relationship between the out-of-plane effective thermal conductivity, the wall thickness of the hollow particles, and the ratio of the thermal conductivities of the filler to the matrix material were also taken into account. The numerical results show an increase of the effective thermal conductivity with increasing wall thickness of the hollow particles. However, for a large contact resistance and/or for a high effective thermal conductivity, it is shown that the contact resistance has a dominant influence on the effective thermal conductivity of the composites. The numerical results were also compared to some well-known analytical effective thermal conductivity models.