Propagation of thermal waves with lateral heat transfer

Abstract

The wave nature of heat propagation in a one-dimensional semi-infinite medium with lateral convective heat transfer is investigated by solving the hyperbolic heat conduction equation in the longitudinal direction. The situation involves a large relaxation time which is relevant at low temperatures or for materials with a non-homogeneous inner structure, and the heat conduction in the lateral direction is assumed to be parabolic due to the number of lateral heat wave reflections compared to those in the longitudinal direction. The results for a unit heat flux condition at the boundary are compared with those obtained from parabolic heat conduction. This reveals that the classical heat diffusion theory predicted by parabolic heat conduction significantly underestimates the magnitude of the temperature and heat flux in thermal wave propagation. The results also reveal that when the dimensionless lateral heat transfer, known as the wave shape factor, is equal to unity, the thermal wavefront which travels through the medium at a finite speed decays exponentially along its path of travel while retaining the shape of the input wave. This theoretical prediction can be implemented experimentally for estimation of thermal relaxation times.