Analytical solutions of transient heat conduction in semi-infinite solid with time varying boundary conditions by means of similarity transformation

An anlytical solution to the transient one dimensional linear heat conduction with time varying boundary conditions is obtained by means of similarity transformation via one-parameter groups. Two types of time varying boundary conditions are considered. These are; time varying surface temperature and time varying surface heat flux boundary conditions. In the analysis, thermal conductivity and thermal diffusivity, are assumed to be constant. The solution is generalized for a general polynomial type of time varying boundary conditions.