Analytical Solutions of Heat Conduction Problems for Anisotropic Solid Body

Abstract

Exact analytical solutions of heat conduction problems in anisotropic twodimensional solid bodies are presented in this study. Timedependent and steadystate problems are considered. A linear coordinate transformation is introduced which reduces the anisotropic heat conduction problem to an equivalent isotropic one. The solution of the anisotropic heat conduction problem is expressed in terms of solutions of the corresponding isotropic heat conduction problem. The connection of data of the applied linear coordinate transformation and the thermal material properties of anisotropic solid body is analysed. All result of the paper is based on the Fourier’s theory of heat conduction in solid bodies. Examples illustrate the applications of the developed method