Lack of oscillations in Dual-Phase-Lagging heat conduction for a porous slab subject to imposed heat flux and temperature

This study shows that the physical conditions necessary for thermal waves to materialize in Dual-Phase-Lagging porous media conduction are not attainable in a porous slab subject to a combination of constant heat flux and temperature (Neumann and Dirichlet) boundary conditions. It is demonstrated that the approximate equivalence between Dual-Phase-Lagging (DuPhlag) heat conduction model and the Fourier heat conduction in porous media subject to Lack of Local Thermal Equilibrium (La Lotheq) that suggested the possibility of thermal oscillations and resonance reveals a condition that cannot be fulfilled because of physical constraints.     

Exclusion of oscillations in heterogeneous and bi-composite media thermal conduction

Analysis of Fourier heat conduction in heterogeneous and bi-composite media (e.g. porous media, fluid suspensions, etc.) subject to Lack of Local Thermal Equilibrium (LaLotheq) reveals a condition for thermal oscillations and resonance to be possible. This paper shows that this condition cannot be fulfilled because of physical constraints leading to the exclusion of thermal waves and resonance.     

SPECIALLY TAILORED TRANS FINITE-ELEMENT FORMULATIONS FOR HYPERBOLIC HEAT CONDUCTION INVOLVING NON-FOURIER EFFECTS

The phenomenon of hyperbolic heat conduction in contrast to the classical (parabolic) form of Fourier heat conduction involves thermal energy transport that propagates only at finite speeds as opposed to an infinite speed of thermal energy transport. To accommodate the finite speed of thermal wave propagation, a more precise form of heat flux law is involved, thereby modifying the heat flux originally postulated in the classical theory of heat conduction. As a consequence, for hyperbolic heat conduction problems, the thermal energy propagates with very sharp discontinuities at the wave front. The primary purpose of the present paper is to provide accurate solutions to a class of one-dimensional hyperbolic heat conduction problems involving non-Fourier effects that can precisely help understand the true response and furthermore can be used effectively for representative benchmark tests and for validating alternate schemes. As a consequence, the present paper purposely describes modeling/analysis formulations via specially tailored hybrid computations for accurately modeling the sharp discontinuities of the propagating thermal wave front. Comparative numerical test models are presented for various hyperbolic heat conduction models involving non-Fourier effects to demonstrate the present formulations.     

Generalized Heat Transition Matrix for Arbitrarily Shaped Thermal Media and Its Applications to Steady-State Heat Conduction Problems in Large-Scale Systems

This article presents a concept of a generalized heat transition matrix (GHTM) used for expressing the steady-state heat conduction characteristics of a thermal block with almost arbitrary shapes and internal structures. A reference surface is defined to separate the thermal block completely from its environment. A generalized heat transition matrix is defined on the reference surface, which associates the equivalence surface heat sources on the reference surface to the temperatures and heat fluxes generated by heat sources outside the concerned thermal block. The generalized heat transition matrix of a thermal block can fully describe its steady-state heat conduction characteristics, and can be reused in a larger system that contains many blocks with identical structures. This property is useful in the analysis of the steady-state heat conduction problem in a multiscale large system using the domain decomposition method.     

Theoretical prediction of longitudinal heat conduction effect in cross-corrugated heat exchanger

In the elementary heat exchanger design theory, the longitudinal heat conduction through the heat transfer plate separating hot and cold fluid streams is neglected, and only the transverse heat conduction is taken into account for the conjugate heat transfer problem. In the cross-corrugated heat exchanger, the corrugated primary surface naturally leads to the highly non-uniform convective heat transfer coefficient distribution on opposite sides of the plate. In such a case, the longitudinal heat conduction may play a significant role in the thermal coupling between high heat transfer regions located on opposite sides of the plate. In the present study CFD is used to perform a quantitative assessment of the thermal performance of a cross-corrugated heat exchanger including the longitudinal heat conduction effect for various design options such as different plate thickness and corrugation geometry for a typical operating condition. The longitudinal heat conduction effect is then predicted by the theoretical method using the ‘network-of-resistance’ in the wide range of the heat exchanger design space.     

Thermo-Elastic Analysis of a Cracked Half-Plane Under a Thermal Shock Impact Using the Hyperbolic Heat Conduction Theory

The transient thermal stresses around a crack in a thermo-elastic half-plane are obtained under a thermal shock using the hyperbolic heat conduction theory. Fourier, Laplace transforms and singular integral equations are applied to solve the temperature and thermal stress fields consecutively. The integral equations are solved numerically and the asymptotic fields around the crack tip are obtained. Numerical results show that the hyperbolic heat conduction have significant influence on the dynamic temperature and stress field. It is suggested that to design materials and structures against fracture under thermal loading, the hyperbolic model is more appropriate than the Fourier heat conduction model.     

An analytic approach to the unsteady heat conduction processes in one-dimensional composite media

The transient heat conduction problems in one-dimensional multi-layer solids are usually solved applying conventional techniques based on Vodicka's approach. However, if the thermal diffusivity of each layer is retained on the side of the heat conduction equation modified from the application of the separation-of-variables method where the time-dependent function is collected, then the modified heat conduction equation by itself represents a transparent statement of the physical phenomena involved. This `natural' choice so simplifies unsteady heat conduction analysis of composite media that thermal response computation reduces to a matter of relatively simple mathematics when compared with traditional techniques heretofore employed.     

多层打孔隔热材料热分析计算模型研究

基于能量守恒定律,构建可应用于空间机构热防护的多层打孔隔热材料热性能分析计算模型,该模型考虑相邻两层反射屏间辐射换热、反射屏与间隔物接触导热、间隔物本身导热以及残余气体导热,能够准确预测多层打孔隔热材料内部传热特性。并在此基础上,进行了隔热材料热真空实验研究,以验证所建热分析计算模型的准确度。     

Heat flow choking in carbon nanotubes

Based on Einstein’s mass–energy relation, the equivalent mass of thermal energy or heat is identified and referred to as thermomass. Hence, heat conduction in carbon nanotubes (CNTs) can be regarded as the motion of the weighty phonon gas governed by its mass and momentum conservation equations. The momentum conservation equation of phonon gas is a damped wave equation, which is essentially the general heat conduction law since it reduces to Fourier’s heat conduction law as the heat flux is not very high and the consequent inertial force of phonon gas is negligible. The ratio of the phonon gas velocity to the thermal sound speed (the propagation speed of thermal wave) can be defined as the thermal Mach number. For a CNT electrically heated by high-bias current flows, the phonon gas velocity increases along the heat flow direction, just like the gas flow in a converging nozzle. The heat flow in the CNT is governed by the electrode temperature until the thermal Mach numbers of phonon gas at the tube ends reach unity, and the further reduction of the electrode temperature has no effect on the heat flow in the CNT. Under this condition, the heat flow is said to be choked and temperature jumps will be observed at the tube ends. In this case the predicted temperature profile of the CNT based on Fourier’s law is much lower than that based on the general heat conduction law. The thermal conductivity which is determined by the measured heat flux over the temperature gradient of the CNT will be underestimated, and this thermal conductivity is actually the apparent thermal conductivity. In addition, the heat flow choking should be avoided in engineering situations to prevent the thermal failure of materials.     

Fractional heat conduction in a thin hollow circular disk and associated thermal deflection

The time nonlocal generalization of the classical Fourier law with the “Long-tail” power kernel can be interpreted in terms of fractional calculus and leads to the time fractional heat conduction equation. The solution to the fractional heat conduction equation under a Dirichlet boundary condition with zero temperature and the physical Neumann boundary condition with zero heat flux are obtained by integral transform. Thermal deflection has been investigated in the context of fractional-order heat conduction by quasi-static approach for a thin hollow circular disk. The numerical results for temperature distribution and thermal deflection using thermal moment are computed and represented graphically for copper material.     

多孔介质导热的分形模型

多孔介质中热量传递与多孔介质内部的几何结构有密切的关系，讨论了多孔介质的分形结构和相关的分形维数，利用能量方程，导出了分形维数为D的有限尺度多孔介质中的广义热传导方程，在此基础上，假定热量在多孔介质中的传导路线也是一种分形结构，提出了一个筒化的多孔介质并联通道分形导热模型，求出了基于分形理论的多孔介质有效导热系数表达式。     

3-Omega Method for Thin Films with the Non-Fourier Boundary Condition

The effect of non-Fourier boundary condition on the 3-omega method for measuring the thermal conductivity of microscale thin films using the hyperbolic heat conduction equation and the Fourier equation is examined. Non-Fourier boundary condition with the Fourier equation leads to 80% error in the temperature oscillations and increases the error to 85% in the case of non-Fourier boundary condition with the hyperbolic heat conduction equation. The solution of the non-Fourier boundary condition with the hyperbolic heat conduction equation gives the most accurate thermal conductivity expression. The analysis also provides a method for determining the relaxation time of thin films.     

BEHAVIOR OF THERMAL STRESSES IN A RAPIDLY HEATED THIN PLATE

Using the hyperbolic heat conduction model, thermal stresses generated within a rapidly heated thin metal plate are investigated numerically. The effects of different parameters such as the form, duration, amplitude, and penetration depth of the heating source on the temperature, thermal moment, deflection, and thermal stresses are studied. It is found that under ultra-fast heating of very thin plates, the hyperbolic heat conduction model must be adopted to model the thermal behavior.     

Examination of the Thermal Equilibrium Assumption in the Microscopic Parabolic Heat Conduction Model Under the Effect of Two Types of Heating Sources

Abstract

The validity of using the microscopic parabolic heat conduction model under the effect of two types of volumetric heating sources is investigated analytically. The considered volumetric heating sources are a fluctuating periodic source and a unit step source of short duration. Also, the role of the electron gas thermal capacity term is investigated. Criteria are derived to show the necessity of using the microscopic parabolic heat conduction model. Other criteria are derived to show a justification for neglecting the electron gas thermal capacity term from the microscopic parabolic heat conduction model.     

Comparative numerical analysis of magnetized rectangular and trapezoidal fins

Fins are extended surfaces that are designed to dissipate heat from hot sources to their surroundings. The different profiles of fins are used on the equipment surface to improve heat transfer. Fins are extensively used in refrigeration, solar panels, superheaters, electric equipment, automobile parts, combustion engines, and electrical equipment. On the basis of these applications, we study the thermal performances of magnetized convective–radiative-rectangular fins with magnetized trapezoidal fins with internal heat generation. The shooting technique is used to numerically study the suggested model. It is revealed that magnetized trapezoidal fins transfer more heat than magnetized rectangular fins. It is also revealed that magnetized trapezoidal fins have higher thermal transfer competence than magnetized rectangular fins. When thermal conductivity, radiation–conduction number, and convection–conduction number increase, the fin's efficiency increases. In addition, a Hartmann number indicating the magnetic effect is found to improve heat transfer from the fins. Increasing the magnetism parameter from 0.1 to 0.3 reduced temperature by approximately 4.5%, changing internal heat generation from 0.1 to 0.5 increased temperature distribution by approximately 16%, and changing the Peclet number from 0.1 to 0.3 increased temperature distribution by approximately 15%. The effect of heat transfer coefficient, thermal radiation–conduction and convection–conduction, and dimensionless radiation are also investigated on the performance of the fins.     

Heat transfer through woven textiles

A mathematical model based on the principles of heat transfer to predict the thermal resistance of fabrics has been presented in this paper. The woven fabric is considered as a system of porous yarns, interlacements between warp and weft yarns and air pores and all the basic weaves can be depicted by this system. The conduction and radiation heat transfer together, was calculated based on the construction parameters of the fabric. The thermal insulation, which is equivalent to the thermal resistance, was predicted with the help of these parameters. The total heat transfer by conduction through each part was calculated using Fourier’s equation. Radiation heat transfer through the air pore was calculated with the help of net radiation method. Linear anisotropic scattering was used to model the radiation heat transfer through fibrous media. The total thermal resistance obtained was validated with actual values obtained from a standard thermal resistance measuring instrument.     

Does nanoparticles dispersed in a phase change material improve melting characteristics?

Nanoparticles dispersed in a phase change material alter the thermo-physical properties of the base material, such as thermal conductivity, viscosity, and specific heat capacity. These properties combined with the configuration of the cavity, and the location of the heat source, influence the melting characteristics of the phase change material. In this paper, an assessment of the influence of the nanoparticles in the base material subjected to a heat generating source located in the center of an insulated square cavity, which is a common configuration in thermal capacitors for temporal heat storage is investigated. The interplay between heat conduction enhanced due to an increase in thermal conduction and buoyancy driven heat convection damped by the increase in viscosity of nanoparticles dispersed in the phase change materials is studied with the calculated streamlines and isotherms. We observed three regimes during the melting process, first at an early time duration dominated by heat conduction, later by buoyancy driven convection till the melting front levels with the center of the cavity, and lastly once again heat conduction in the bottom portion of the cavity. During the first two regimes, addition of nanoparticles have no significant performance gain on the heat storage cavity, quantified by maximum temperature of the heat source and average Nusselt number at the faces of the heat source. In the late regime, nanoparticles provide a slight performance gain and this is attributed to the increase in the specific heat of the melt due to the nanoparticles.     

NON-FOURIER HEAT CONDUCTION PHENOMENA IN POROUS MATERIAL HEATED BY MICROSECOND LASER PULSE

Experiments on porous material heated by a microsecond laser pulse and the corresponding theoretical analysis are carried out. Some non-Fourier heat conduction phenomena are observed in the experimental sample. The experimental results indicate that only if the thermal disturbance is strong enough (i.e., the pulse duration is short enough and the pulse heat flux is great enough) is it possible to observe apparent non-Fourier heat conduction phenomenon in the sample, and evident non-Fourier heat conduction phenomenon can only exist in a very limited region around the thermal disturbance position. The hyperbolic heat conduction (HHC) equation and the dual-phase lag (DPL) model are employed, respectively, to describe the non-Fourier heat condution process happening in the experimental sample, and the finite-difference method (FDM) is used to solve them numerically. The numerical solutions show that both the HHC equation and the DPL model can predict the non-Fourier heat conduction phenomenon emerging in the experimental sample qualitatively. Moreover, if τ_q and τ_T are assumed to have suitable values, the theoretical result of the DPL model is more agreeable to the experimental result.     

Analytical solution for transient temperature and thermal stresses within convective multilayer disks with time-dependent internal heat generation,Part I: Methodology

This work deals with the exact solution for asymmetric transient problem of heat conduction and accordingly thermal stresses within multilayer hollow or solid disks which lose heat by convection to the surrounding ambient. The combination of the separation of variables method (SVM) and Duhamel's theorem is applied to the heat conduction problem which provides a versatile technique. The temperature distribution is obtained by the SVM which concerns the heat conduction problem with time-independent internal heat generation. Applying Duhamel's theorem on the previous solution, temperature distribution with time-dependent internal heat generation can be achieved. Accordingly, assuming plane stress condition, radial and tangential stresses are obtained which are incorporated into the equivalent tensile stress formulation to calculate von Mises stress. The comprehensive methodology described here can be useful addition for many new emerging fields in which both transient and steady-state temperature distributions and thermal stresses for composite disks are important.     

A simple direct estimation of temperature-dependent thermal conductivity with kirchhoff transformation

A direct method is proposed to estimate the temperature-dependent thermal conductivity without internal measurements. In the proposed method, the steady-state nonlinear heat conduction equation is transformed into the Laplace equation via the Kirchhoff transformation. The thermal conductivity is modeled as a linear combination of known functions with unknown coefficients, which are directly determined from the imposed heat flux and measured temperatures at the boundary. Several inverse heat conduction problems are successfully introduced to confirm the validity of the proposed method.