The classical one-phase Stefan problema with temperature-dependent thermal conductivity and a convective term

M.F. NATALE – D.A. TARZIA

MAT - Serie A

Asociacion Civil de Estudios Superiores (Univ. Austral)

Lugar: Rosario; Año: 2008 vol. 15 p. 1 - 16

1515-4904

We study a one-phase Stefan problem for a semi-infinite material with temperature-dependent thermal conductivity and a convective term with a constant temperature boundary condition or a heat flux boundary condition of the type }$-q_{0}/sqrt{t}$ $left( q_{0}>0 ight) $ { m at the fixed face } $x=0$. 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. We improve the results given in Rogers-Broadbridge, ZAMP, 39 (1988), 122-129 and Natale-Tarzia, Int. J. Eng. Sci., 41 (2003), 1685-1698 obtaining explicit solutions through the unique solution of a Cauchy problem with the time as a parameter and we also give an algorithm in order to compute the explicit solutions.