Domingo A. Tarzia

Explicit solutions to the one-phase Stefan problem with temperature-dependent thermal conductivity and a convective term

A one-phase Stefan problem for a semi-infinite material with temperature-dependent thermal conduc- tivity and convective term with a constant temperature or a heat flux condition of the typeq0= ffiffi p ðq0 > 0Þ at the fixed face x ¼ 0 is studied. For both cases a parametric representation of the solution of the similarity type is also obtained. 2003 Elsevier Science Ltd. All rights reserved.

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.

Explicit solution for freezing of humid porous half-space with a heat flux condition

Abstract Explicit solutions for temperature and moisture distribution in a porous half-space with a heat flux condition at x=0 of the type q 0 / t are obtained. An inequality for the coefficient q0 is necessary and sufficient in order to obtain that exact solution. An equivalence between this problem and the analogous corresponding to a phase change problem with a temperature condition is also obtained.

Asymptotic behaviour of a non-classical heat conduction problem for a semi-infinite material

The asymptotic behaviour of a heat conduction problem involving a non-linear heat source depending on the heat-flux occurring in the extremum of a semi-infinite slab is discussed. Conditions are given on the non-linearity so as to accelerate the convergence of the solution to zero.

The determination of unknown thermal coefficients through phase change process with temperature-dependent thermal conductivity

Abstract We study the determination of unknown thermal coefficient of a semi-infinite material through a phase-change process with an overspecified condition on the fixed face with temperature-dependent thermal conductivity. We determine necessary and sufficient conditions on data in order to obtain the existence of the solution. We also give formulae for the unknown coefficients.

Similarity Solutions for Thawing Processes with a Heat Flux Condition at the Fixed Boundary

AbstractSimilarity solutions for a mathematical model for thawing in a saturated semi-infinite porous medium is considered when change of phase induces a density jump and a heat flux condition of the type

A one-phase Stefan problem for a non-classical heat equation with a heat flux condition on the fixed face

- q_0 t^{ - (1/2)}

An initial-boundary value problem for the one-dimensional non-classical heat equation in a slab

is imposed on the fixed face x = 0. Different cases depending on physical parameters are analysed and the explicit solution is obtained if and only if an inequality for the thermal coefficient q0 is verified. An improvement for the existence of a similarity solution for the same free boundary problem with a constant temperature on the fixed face x = 0 is also obtained. Sommario. Vengono considerate soluzioni di similarità per un modello matematico di disgelo di un mezzo poroso saturo semi-infinito allorquando il cambiamento di fase induce un salto di densità ed una condizione di flusso di calore del tipo