Temperature Distribution in Graded SiGe Thin Films: A Preliminary Study

In this article we develop a model of a square-shaped heat conductor, with thermal conductivity taking different values along two orthogonal directions in the domain. In order to achieve a complete study of heat conduction in such a domain, preliminarily, we approximate the square-shaped domain with two non-graded SiGe thin films with different constitutive equations for thermal conductivity. For both systems, by using Mathematica, we find the solution of a suitable boundary value problem arising in the problem under study and compare the corresponding temperature profiles. Such profiles can be concave or convex depending on the thermal properties of the conductor. The heat flux values and privileged direction of heat conduction in different physical situations are calculated as well. The obtained results can be regarded as a first step toward the solution of the complete problem.