Hyperbolic heat conduction with convection boundary conditions and pulse heating effects

Abstract

This paper describes the numerical simulation of hyperbolic heat conduction with convection boundary conditions. The effect of a step heat loading, a sudden pulse heat loading, and a pulse internal heat source are considered in conjunction with convection boundary conditions. Two methods of solution are presented for predicting the transient behavior of the propagating thermal disturbances. In the first method, MacCormack's predictor-corrector method is employed for integrating the hyperbolic system of equations. Next the transfinite element method, which employs specially tailored elements, is used for accurately representing the transient response of the propagating thermal wavefronts. The agreement between the results of various numerical test cases not only validates the representative behavior of the thermal wave fronts but also provides an understanding of the representative behavior due to convection boundary conditions and varied heating effects.