Solution of Hyperbolic Heat Conduction Equation in Spherical Media with Nonlinear Boundary Condition

In this paper hyperbolic heat conduction equation in spherical media with its outer surface subjected to time dependent laser heat source and combined convective-radiative cooling is solved using Laplace transform method. In order to perform this method، the nonlinear boundary condition is linearized by Taylor’s series expansion. The Riemann-sum approximation method is used to obtain the inverse of Laplace transform. The temperature distribution is studied for different values of thermal relaxation time، pulse duration، convection-conduction and radiation-conduction parameters and the solutions of hyperbolic and Fourier equations are also compared. The results of the present method is verified by being compared with available analytical solution results under a simpler boundary condition.