The Stefan Problem of a Polymorphous Material

Abstract

The problem of freezing or melting of a polymorphous material in a semi-infinite region with arbitrarily prescribed initial and boundary conditions is studied. Exact solutions of the problem are established. The solutions of temperature of all phases are expressed in polynomials and functions in the error integral family and time t and the position of the interfacial boundaries in power series of t1/2. Existence and uniqueness of the series solutions are considered and proved. It is also shown that these series are absolutely and uniformly convergent. The paper concludes with some remarks on density changes at the interfacial boundary and various special cases, one of which is the similarity solution.