María F. Natale

Determination of unknown thermal coefficients for Storm's-type materials through a phase-change process

Abstract Unknown thermal coefficients of a semi-infinite material of Storm’s type through a phase-change process with an overspecified condition on the fixed face are determined. We follow the ideas developed in C. Rogers (Int. J. Non-Linear Mech. 21 (1986) 249–256) and in Tarzia (Adv. Appl. Math. 3 (1982) 74–82; Int. J. Heat Mass Transfer 26 (1983) 1151–1157). We also find formulae for the unknown coefficients and, the necessary and sufficient conditions for the existence of a similarity solution.

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

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.

One-phase Stefan problem with temperature-dependent thermal conductivity and a boundary condition of Robin type

Abstract We study a one-phase Stefan problem for a semi-infinite material with temperature-dependent thermal conductivity with a boundary condition of Robin type at the fixed face x = 0. We obtain sufficient conditions for data in order to have a parametric representation of the solution of similarity type for t ≥ t0 > 0 with t0 an arbitrary positive time. This explicit solution is obtained through the unique solution of an integral equation with the time as a parameter.