Unsteady Temperature Distribution in a Sphere Subjected to Time-Dependent Surface Heat Flux and Internal Heat Source

Abstract

General expressions are derived for the three-dimensional unsteady heating of a solid sphere under the influence of a variable internal heat source and an arbitrary initial temperature distribution when the entire surface is subjected to a variable heat flux. Both the volume heat source and the surface heat flux are prescribed in terms of arbitrary functions of space and time. Various forms of solutions are noted. These expressions, not available hitherto, contain the solutions of many special problems of technological importance. The results presented in two recent studies on the arbitrary heating of spheres are shown to be special cases of the general sphere problem treated here and the errors appearing in these studies are corrected. Other special cases are also discussed.