Hyperbolic heat conduction with surface radiation

Numerical solutions for hyperbolic heat transfer in a semi-infinite medium are developed. The solutions involve nonlinear, radiation boundary conditions. The numerical computations for the hyperbolic equation are performed using MacCormack's predictor-corrector method while a combined implicit/explicit method is used to solve the parabolic equation. The results of the parabolic equation are compared with those obtained by the standard parabolic heat conduction equation. The difference between them if that parabolic heat conduction involves a gradual increase in surface temperature and an infinite rate of energy diffusion, while hyperbolic heat conduction involves an instantaneous increase in surface temperature and a finite rate of energy diffusion. This difference results in the temperature variations evident for extremely short times.