Analytical Solution for Heat Conduction in a Two-Material-Layer Slab With Linearly Temperature Dependent Conductivity

Abstract

In many electronic components or some composite materials, the structure is made of different material layers, which have different thermal conductivities. Investigations of heat conduction, incorporated with abrupt changes of thermal conductivity, are of interest to heat transfer problems because of their importance in many engineering applications. Furthermore, when temperature variations are great or the transport properties vary rapidly with temperature, variations of the transport properties must be considered in the formulation of the problem. The governing equation of heat conduction associated with temperature-dependent thermal conductivity is nonlinear and the powerful superposition principles of the linear theory of mathematics cannot be applied to obtain analytical solutions. Previous analytical investigations were mainly concerned with the heat conduction problems in a homogeneous slab. Solutions to the corresponding problems in a composite slab are very often difficult to obtain in analytical form because of the presence of nondifferentiability at in the interface and nonlinearity of the governing equations. This study attempts to obtain an exact solution of heat conduction in a two-material layer slab in which the temperature dependency on thermal conductivity is taken into account.