Heat-Flow Refraction across Dissimilar Media

Abstract

Refraction of heat flow across near surface boundaries between dissimilar media results in local variations in heat flow. The magnitude of the perturbation from the regional value is a function of position, conductivity ratio, and the configuration of media. New analytical solutions are given for a semi-ellipsoid and a pair of parallel semi-cylinders immersed in an otherwise homogeneous semi-infinite medium. An analytical solution is also derived for the case of a buried cylinder. For two-dimensional but arbitrary geometric configurations, a numerical scheme based on the finite element method is formulated to include the effects of conductivity contrast as well as relief, non-uniform surface temperature, and internal heat generation. The applicability of this scheme is demonstrated by comparing the numerical results with analytical solutions and results obtained from a finite difference method.