Diffusion of Heat From a Sphere to a Surrounding Medium

Abstract

In a recent paper, Philip (1964) discussed a heat flow problem in which, as an idealization, spherical symmetry is assumed and the medium is regarded as composite, with a spherical core of one material embedded in a larger mass of a second material. One application in mind was to laccoliths, where an intrusion of igneous rock in sedimentary material can produce dome-shaped bulging at the surface. The idea of treating this as a problem involving spherical symmetry was put forward by Lovering (1935), who gave a solution for the case where the core and its surroundings are taken as uniform. In a subsequent paper, Lovering (1936) considered in more detail what variations in the thermal conductivity and diffusivity are to be expected. From the figures he quotes, a composite model should give a better approximation, though remaining a considerable simplification of the physical problem.