Free boundary problems with radiation boundary conditions

Abstract

The paper is concerned with the free boundary problem of a semi-infinite body of arbitrarily prescribed initial temperature, subject to a mixed or radiation boundary condition at its face. The analytically exact solutions of temperature of both phases and the interfacial position are established in series of time and functions of the error integral family. Convergence of these series solutions is studied and proved. A few remarks on the solutions and their simplifications are then offered. A discussion on the analyticity of the solutions is also given. The paper concludes with an illustrative example, the so-called one-phase problem.