Propagation and reflection of thermal waves in a finite medium

Abstract

For situations involving extremely short times following the start of transients or for very low temperatures near absolute zero, the classical diffusion theory of heat conduction breaks down since the wave nature of thermal energy transport becomes dominant. In this work, analytical solutions are developed for the hyperbolic heat conduction equation describing the wave nature of thermal energy transport in a finite slab with insulated boundaries subjected to a volumetric energy source in the medium. The exact analytical solutions developed for the temperature field and heat flux show that the release of a concentrated pulse of energy gives rise to a severe thermal wave front which travels through the medium at a finite propagation speed, dissipating energy in its wake and reflecting from the insulated surfaces.