Analytical Method of the Unsteady Heat Conduction in Anisotropic Materials by a Congruence Matrix Transformation.

Abstract

In this paper, a new analytical method for unsteady-state problems of heat conduction in anisotropic materials is presented. Under the assumption that the form of the heat conduction equation in anisotropic materials is invariant under a congruence matrix transformation, the equation of heat conduction can be transformed to an equation of the same form as that for the isotropic case. For this matrix transformation, the temperature gradient and heat flux must satisfy the continuity coditions at a boundary between two different media. This method is applicable to the treatment of thermal resistance of composite slabs, the determination of the Green function for the three-dimensional equation of heat conduction in an anisotropic conductor, and the analysis of temperature distribution in the composite regions of infinite anisotropic heat-conducting solids.