The Stefan problem with temperature-dependent thermal conductivity and a
convective term with a convective condition at the fixed face
Adriana C. Briozzo - Depto. de Matemática and CONICET, FCE, Universidad Austral, Paraguay 1950, S2000FZF Rosario, Argentina (email)
Abstract: We study a one-phase Stefan problem for a semi-infinite material with temperature-dependent thermal conductivity and a convective term with a convective boundary condition at the fixed face $x=0$. We obtain sufficient conditions for data in order to have a parametric representation of the solution of the similarity type for $t \geq t_0 > 0$ with $t_0 $ an arbitrary positive time. We obtain 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 solution.
Keywords: Stefan problem, free boundary problem, moving boundary problem,
phase-change process, nonlinear thermal conductivity, fusion, solidification, similarity solution.
Received: August 2009; Revised: September 2009; Published: May 2010.
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