Numerical simulation for non-linear thermal wave

The present work applies the hybrid method of the Laplace transform technique and a modified discretization scheme to analyze the non-linear hyperbolic heat conduction problems in a semi-infinite domain with either linearly or exponentially temperature-dependent thermal conductivity. The Laplace transform method is used to remove the time-dependent terms in the governing differential equation and the boundary conditions, and then the transformed equations are discretized by a modified discretization scheme. To show the rationality and reliability of the present results, a comparison between the present numerical results and those in the literature is made. Results show the behavior of hyperbolic heat conduction is sensitive to the function form of thermal conductivity. The speed of heat propagation changes for the variation of thermal conductivity.