The Stefan problem in nonlinear heat conduction (Q579054)

An exact parametric solution for the planar solidification of a liquid metal occupying the infinite half-space is presented. The metal is assumed to exhibit nonlinear thermal characteristics of the Storm type. Both the idealized one phase and the full two phase problems are considered. For both problems an approximate analysis of the underlying coupled transcendental equations is presented which provides initial estimates for use in a numerical scheme. Typical numerical results are given which illustrate the monotonic nature of the solution.