Group properties and similarity solutions for the heat equation with semi-empirical temperature

The similarity solution which is invariant under the corresponding symmetry group is obtained for fairly general coefficients in the heat equation with semi-empirical temperature. The heat equation is reduced to a nonlinear ordinary differential equation and the stability of the equilibrium manifold is considered. Numerical solutions for some kinds of coefficients are obtained. Further, on the basis of the present numerical solutions an analysis of initial boundary value problem has been considered.