Heat Transfer in Plane with Temperature Dependent Thermal Variables

Abstract

In this paper we consider heat transfer in a wall with temperature dependent heat conductivity and internal heat generation. It turns out the model considered is non-linear. We employ the classical Lie point symmetry analysis to determine the exact solutions. A number of cases for thermal conductivity and internal heat generation are considered. In some cases the exact solutions are not possible to construct. However, we first use the obtained exact solution as a bench mark for the quasilinear method. Since confidence is established, we then use the quasilinear method to solve some other applicable problem.