Explicit solutions for a one-phase Stefan problem with temperature-dependent thermal conductivity

M.F. NATALE – D.A. TARZIA

Bollettino dell’Unione Matematica Italiana

Pitagora Editrice

Lugar: Bologna; Año: 2006 vol. 9B p. 79 - 99

We study a one-phase Stefan problem for a semi-infinite material with temperature-dependent thermal conductivity with a constant temperature or a heat flux condition of the type }$-q_{0}/sqrt{t}$ $left( q_{0}>0 ight) ${ m at the fixed face} $x=0$. { m We obtain in both cases sufficient conditions for data in order to have a parametric representation of the solution of the similarity type for }$tgeq t_{0}>0$ { m with} $t_{0}$ { m % an arbitrary positive time. These explicit solutions are obtained through the unique solution of an integral equation with the time as a parameter.}