A NOTE ON THE CONSTANT THERMAL CONDUCTIVITY HYPOTHESIS AND ITS CONSEQUENCE FOR CONDUCTION HEAT TRANSFER PROBLEMS

Abstract

This work discuss the usual constant conductivity assumption and its consequences when a given material presents a strong dependence between the temperature and the thermal conductivity. The discussion is carried out considering a sphere of silicon with a given heat generation concentrated in a vicinity of its centre, giving rise to high temperature gradients. This particular case is enough to show that the constant thermal conductivity hypothesis may give rise to very large errors and must be avoided. In order to surpass the mathematical complexity, the Kirchhoff transformation is used for constructing the solution of the problem. In addition, an equation correlating thermal conductivity and the temperature is proposed.