Comparative Studies on Nonlinear Hyperbolic and Parabolic Heat Conduction for Various Boundary Conditions: Analytic and Numerical Solutions

Abstract

With the advent of lasers with very short pulse durations and their use in materials processing, the effect of thermal wave propagation velocity becomes important. Also, localized heating in laser-aided materials processing causes significant variations in the material properties. To account for these two effects, hyperbolic heat conduction is studied in this paper by considering all the thermophysical properties, except the thermal diffusivity, to be temperature dependent. The resulting nonlinear hyperbolic equations are linearized by using Kirchhoff transformation. Both analytical and numerical solutions are obtained for finite domains. Results are presented and compared with parabolic conduction results.