Explicit solutions to the two-phase Stefan problem for Storm-type materials

Abstract

A reciprocal transformation is employed to reduce a two-phase Stefan problem in nonlinear heat conduction into a form which admits a class of exact solutions analogous to the classical Neumann solution. The problem is considered for materials of Storm type (Rogers 1985 J. Phys. A: Math. Gen. 18 105-9). Two related cases are considered, one of them has a flux condition of the type -q 0 /(t )1/2 (q 0 >0) and the existence and uniqueness of the solution is proved when q 0 satisfies a certain inequality which generalizes the work of Tarzia (1981 Q. Appl. Math. 39 491-7), obtained for constant thermal coefficients, the other one has a temperature condition on the fixed face and the existence and uniqueness is proved for all data.