TRANSIENT CONDUCTION AND RADIATION HEAT TRANSFER WITH VARIABLE THERMAL CONDUCTIVITY

The effect of variable thermal conductivity on transient conduction and radiation heat transfer in a planar medium is investigated. Thermal conductivity of the medium is assumed to vary linearly with temperature, while the other thermophysical properties and the optical properties are assumed constant. The radiative transfer equation is solved using the discrete transfer method, (DTM) and the nonlinear energy equation is solved using an implicit scheme. Transient as well as steady state results are found for an absorbing, emitting, and anisotropically scattering gray medium. Thermal conductivity has been found to have significant effects on both transient as well as steady state temperature and heat flux distributions. Some steady state results are compared with the results reported in the literature.     

NUMERICAL ALGORITHM FOR ESTIMATING TEMPERATURE-DEPENDENT THERMAL CONDUCTIVITY

Abstract

The hybrid scheme of the Laplace transform technique and the central difference approximation is applied to estimate the temperature-dependent thermal conductivity by utilizing temperature measurements inside the material at an arbitrary specified time. In the present study the functional form of the thermal conductivity is not known a priori. Thus, this problem can be regarded as the functional estimation in inverse calculation. The accuracy of the predicted results is examined from various illustrated cases using simulated exact and inexact temperature measurements obtained within the medium. Results show that a good estimation on the thermal conductivity can be obtained with any arbitrary initial guesses of the thermal conductivity. The advantage of the present method in the inverse analysis is that, for most types of boundary conditions, the relation between the thermal conductivity and temperature at any specified time can be determined without measuring the early temperature data.     

THERMAL STRESSES IN ANNULAR FINS WITH TEMPERATURE-DEPENDENT CONDUCTIVITY UNDER PERIODIC BOUNDARY CONDITION

A stress-field in an annular fin of temperature-dependent conductivity under a periodic heat transfer boundary condition is analyzed by the Adomian's decomposition method. The distribution of the transient thermal stress is obtained by direct integration of the temperature distribution. The heat transfer process is governed by the parameters of the convectional fin parameter N, the thermal conductivity parameter k , the frequency parameter B, and the amplitude parameter s. For k < 0 , the mean temperature is decreased, which in turn increases the thermal stress and enhances the oscillation of the timewise thermal stresses. The opposite effect occurs for k > 0 . The maximum radial stress appears at R = 1.3 , and the maximum tangential stress occurs at the inner base of the fins. Detailed results showing the effects of various parameters on temperature and thermal stresses are presented and discussed.     

INVERSE HEAT CONDUCTION PROBLEM OF SIMULTANEOUSLY ESTIMATING SPATIALLY VARYING THERMAL CONDUCTIVITY AND HEAT CAPACITY PER UNIT VOLUME

An inverse heat conduction method for simultaneously estimating spatially varying thermal conductivity and heat capacity per unit volume under the conditions of a flash method type of experiment is developed. The unknown thermal properties are assumed to vary only in the space dimension normal to the slab sample and are modeled with piecewise linear representations. Lacking in the literature are specific requirements that must be satisfied by the number of measurements in the spatial domain in order to ensure uniqueness of the inverse solution. We prepared a series of numerical experiments to provide a better understanding of this issue. Multiple temperature sensors are shown to be necessary to determine spatially varying properties. The effectiveness of the method is illustrated through simulated experimental applications of the method.     

THERMAL STRESS PROBLEM FOR MIXED HEAT CONDUCTION BOUNDARY AROUND AN ARBITRARILY SHAPED HOLE WITH CRACK UNDER UNIFORM HEAT FLUX

This article deals with a thermal stress problem for thermal conduction around an arbitrarily shaped hole with a crack under uniform heat flux. Two cases for the hole edge and the crack faces are assumed: adiabatic and isothermal conditions or vice versa (isothermal and adiabatic). A closed-form solution is obtained using conformal mapping, dislocation functions, and the complex variable method. Results of temperature, heat flux, stress, and stress intensity factor are illustrated.     

THERMAL STRESSES IN ELASTIC-PLASTIC TUBES WITH TEMPERATURE-DEPENDENT MECHANICAL AND THERMAL PROPERTIES

The thermoelastic-plastic deformations of internal heat-generating tubes are investigated by considering the temperature dependence of the thermal conductivity coefficient, Young's modulus, the coefficient of thermal expansion, and the yield limit of the material. A model describing the elastic-plastic behavior of the tube is developed. The model consists of a system of two second-order ordinary differential equations and a first-order ordinary differential equation involving nonlinear temperature-dependent coefficients. The computer solution of the model is obtained, and the results are compared with the analytical solution that assumes constant thermomechanical properties. It is found that the difference between the two solutions becomes significant in the regions of high temperatures.     

A THREE-LEVEL FINITE-DIFFERENCE SCHEME FOR SOLVING MICRO HEAT TRANSPORT EQUATIONS WITH TEMPERATURE-DEPENDENT THERMAL PROPERTIES

Heat transport at the microscale is important for the processing of materials with a pulsed laser. In this study, we develop a three-level finite-difference scheme for solving micro heat transport equations with temperature-dependent thermal properties obtained based on the parabolic two-step model. It is shown by the discrete energy method that for constant thermal properties the scheme is unconditionally stable. Numerical results for thermal analysis of a gold film are obtained.     

TRANSIENT HEAT-TRANSFER PHENOMENON OF TWO-DIMENSIONAL HYPERBOLIC HEAT CONDUCTION PROBLEM

This article presents a numerical analysis of the two-dimensional hyperbolic heat conduction problem in an anisotropic medium under a point heat source with different boundary conditions. A simple model has been developed to solve the anisotropic problem. In this analysis, the second-order total variation diminishing (TVD) scheme is employed to solve this problem. The effects of boundary conditions and anisotropy on the thermal wave induced by different types of heat sources in the medium are examined in detail. The results show that the transient behavior of the propagation of the two-dimensional thermal wave is muck more complicated than that of the one-dimensional thermal wave due to a circular wave formed to propagate uniformly in alt directions, reflections by boundaries, interaction with each other, and serious discontinuity on the wavefront.     

SIMULTANEOUS ESTIMATION OF FRICTIONAL HEAT FLUX AND TWO THERMAL CONTACT PARAMETERS FOR SLIDING CONTACTS

In the dry friction between two solids in imperfect contact, the determination of temperature distribution within solids needs the knowledge of: (1) heat flux generated by friction, (2) thermal contact conductance, and (3) intrinsic heat partition coefficient. In this article, numerical study is conducted in order to estimate the values of these parameters from simulated temperatures. Numerical investigations and a sensitivity analysis are performed in order to show the feasibility and the needed conditions for an accurate estimation. In order to take into account the measurements noise, statistical investigations using a stochastic approach and Monte Carlo method are also performed.     

SOLUTION OF DISPLACEMENT BOUNDARY VALUE PROBLEM UNDER UNIFORM HEAT FLUX

The general solution of the displacement boundary value problem is obtained for an infinite plate with an arbitrary shaped hole under uniform heat flux in any direction. The complex stress functions, the dislocation method, and a rational mapping function are used and the closed solution is obtained. An infinite plate with a circular hole and a slit is analyzed under the condition of the constrained displacements. The singularity at the tip of the slit of the constrained displacement is investigated     

THERMAL STRESSES AROUND AN ELASTIC RIBBONLIKE INCLUSION WITH GOOD THERMAL CONDUCTIVITY

Plane-deformation problems of thermal stresses around an elastic ribbonlike conductor in an infinite, homogeneous, isotropic medium under uniform heat flow are analyzed by the method of continuous distribution of singular points. The line heat sources and concentrated forces are distributed continuously along the ribbonlike conductor. The boundary conditions yield a system of singular integral equations for density functions with Cauchy kernels and logarithmic singular kernel. A solution is assumed in the form of the product of a series of Chebyshev polynomials of the first kind and their weight function and is determined by transforming the singular integral equations into linear algebraic equations. One of the advantages of this method is that the strength of the thermal-stress singularity at the tips of the ribbonlike conductor can be easily evaluated. Numerical results for the strength of the thermal-stress singularity are plotted in terms of nondimensional parameters, consisting of the dimensions of the ribbonlike conductor and the material constants of the conductor and matrix.     

UPPER AND LOWER BOUNDS ON HEAT FLUX

Some bounds on heat flow and entropy production analogous to those obtained in linear elasticity theory are discussed. The analogy is observed by introducing “mechanical” counterparts to a heat conduction process     

AXIALLY SYMMETRIC THERMAL STRESS OF A PENNY-SHAPED CRACK UNDER GENERAL HEAT FLUX

This paper presents a solution of the steady-state thermal stress and displacement in an infinite isotropic elastic solid containing a penny-shaped crack whose surfaces are exposed to the general mechanical loading and nonsymmetric heat flux. That is, the heat flux applied to both surfaces of the crack is not the same. The problem is solved using Hankel transforms and the Abel operator of the second kind. Using limiting values of the stress, displacement, and temperature fields at the crack plane in terms of the stress, displacement, temperature, and heat flux discontinuities and boundary conditions of the crack, the problem is reduced to that of solving Abel integral equations that admit closed-form solutions. For a special case of heat flux conditions, stresses at a general point of the medium have been computed and presented graphically.     

TRANSIENT THERMAL CHANGE ON A SOLID SURFACE: COUPLED DIFFUSION OF HEAT AND MOISTURE

Abstract

The sudden change of moisture and/or temperature on a solid can significantly disturb the resulting stresses and strains and cause material damage. This investigation is concerned with the sudden rise (or drop) of temperature over a finite segment of a half-space that is free of tractions. The mutual dependence of moisture and temperature is examined by coupled equations such that the hygrothermal stresses and strains are transient in character. The moisture, temperature, and stress are computed by a time-dependent finite-element method and are found to peak and oscillate as a function of time in the vicinity where the surface temperature is altered. These effects are displayed for the 5208 epoxy resin material commonly used in fiber-reinforced composities.

The locations of possible failure sites are also determined by application of the strain-energy density criterion. This assumes that the peaks and valleys of the strain-energy density function dW/dV within the solid are associated with material damage. Depending on the characteristic value of dW/dV, the failure sites may alter in location, a result which was not known previously.     

储能材料(介质)导热性能研究Ⅰ.高分子材料导热系数研究(平板法)

为了能对固体蓄能材料和液态蓄冷介质的导热系数进行测量，搭建了一座平板导热实验台，对普通有机玻璃和蒸馏水进行了测试以校核精度，对几种新型有机高分子材料的导热系数进行了测试并进行了讨论。     

DEFORMATION OF AN INFINITELY LONG,DC CABLE WITH TEMPERATURE-DEPENDENT ELECTRIC CONDUCTIVITY OF THE INSULATION

We investigate the deformation of an infinitely long, circular cylindrical electric conductor carrying a uniform axial current, for the case when the electric conductivity of the coating is temperature dependent. This model conforms with the real situation for many of the existing modern dc cables with polyethylene coating. The distributions of temperature, magnetic field, stresses, and displacements in the cable are obtained and discussed under a thermal radiation condition at the boundary of the cable. In particular, it appears that there is a critical temperature for the ambient medium to the cable, above which no solution for the steady heat problem can exist and the thermal equilibrium of the cable is no longer fulfilled. A formula for the calculation of this critical value is given, which may turn out to be of practical importance for a reliable design of the cable. The obtained results also show that the electric conductivity of the coating strictly decreases as one moves from the core to the boundary of the cable in conformity with the behavior of temperature. Some numerical results are presented.     

A SERIAL SOLUTION FOR THE 2-D INVERSE HEAT CONDUCTION PROBLEM FOR ESTIMATING MULTIPLE HEAT FLUX COMPONENTS

A serial algorithm for the inverse heat conduction problem (IHCP) has been developed to estimate the individual flux components, one by one, at the unknown boundary, based on the function specification method. The sensitivity coefficient defined in this algorithm brings out the influence of the heat flux components independent of each other. The objective function minimizes the difference in the measured temperature and the contribution of the individual flux component to the thermal field at the sensor location. The serial algorithm developed here could be used with data from both overspecified and underspecified sensors with respect to the number of flux components. The method was tested for delineating independent heat fluxes at the boundary of a two-dimensional solid for both space- and time-varying heat fluxes. Simulated thermal histories obtained from direct solution were used as inputs for the inverse problem for characterizing the new algorithm.

Three types of analyses were done on the results of the IHCP, focused on (1) the convergence of error in estimated temperatures at the different sensor locations, (2) overall error in estimated temperatures for the whole domain, and (3) the total heat energy transferred across the boundary. It is shown that the optimum configuration of independent unknown fluxes is given by the one with minimum energy estimates across the boundary, for both cases.     

REVERSE TIME TLM MODELING OF THERMAL PROBLEMS DESCRIBED BY THE HYPERBOLIC HEAT CONDUCTION EQUATION

A method for reverse-time transmission line matrix (TLM) modeling of thermal diffusion problems described by the hyperbolic heat conduction equation is presented. The method involves pulse scattering governed by the inverse of the usual scattering matrix. Consideration is given to the accuracy of the reverse time method by comparison with the forward scatter. The numerical behavior of the reverse-time algorithm is investigated, and related to the amplification factor of the inverse scattering matrix.     

板式相变贮能换热器传热模型和热性能分析

建立了板式相变贮能换热器的无量纲传热模型。它对流体入口流量、入口温度随时间变化情况和需考虑入口效应及添加肋片的情况均适用。模型解和文献准稳态解吻合。作为算例,藉此模型从各时刻的流体温度、相变界面随空间的分布情况和相变蓄热比、相变传热效率、传热系数、完全相变截面位置随时间的变化情况六个角度分析了一板式相变贮能换热器的相变传热性能。该模型可为板式相变贮能换热器的结构优化设计和热性能分析提供帮助。