Certain Anomalies in the Analysis of Hyperbolic Heat Conduction

Abstract

The hyperbolic diffusion equation is often used to analyze laser heating of dielectric materials and in thermal processing of nonhomogeneous materials. In this paper, anomalies in existing solutions of the hyperbolic heat equation are identified. In particular, the singularities associated with the interaction of a wave front and a boundary may cause a violation of the imposed boundary condition. This violation may give rise to physically unacceptable results such as a temperature drop due to heating or a temperature rise due to cooling. The development of appropriate remedies for these happenings is a major focus of this paper. In addition, the unique mathematical features of the hyperbolic heat equation are studied and set forth. Green’s function solutions for semi-infinite and infinite bodies are presented. For finite bodies, it is demonstrated that the relevant series solutions need special attention to accelerate their convergence and to deal with certain anomalies.