Propagation and reflection of thermal waves in a rectangular plate

Abstract

The wave nature of heat propagation in a two-dimensional rectangular plate with an instantaneous thermal disturbance released in an arbitrary position is investigated by solving the hyperbolic heat conduction equation. The exact analytical solutions are developed for the temperature field and heat flux using the Green's function technique to deal with two limiting boundary conditions, the constant wall temperature and the adiabatic condition, around the region. The disturbance gives rise to a severe thermal wave front, which differs completely front that obtained through one-dimensional analysis, traveling through the medium at a finite speed with a sharp peak at the leading edge. The significant findings in these results are that a negative trailer is generated and follows behind the wave front. In addition, the magnitude of the front is significantly attenuated from the side adjacent to the trailer because the increasing area available to it for diffusion, and decays exponentially along its path of travel, since the thermal energy is dissipated in the wake of the moving wave front. The results also reveal that different boundary conditions strongly influence the reflection of a thermal wave front from the exterior surfaces and the reflection and interaction among thermal waves are more complicated than those found through one-dimensional analysis.