Exact solution for a two-phase Stefan problem with variable latent heat and a convective boundary condition at the fixed face

BOLLATI, J. ; TARZIA, D.A.

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK

BIRKHAUSER VERLAG AG

Año: 2018 vol. 69

0044-2275

Recently, in Tarzia (Thermal Sci 21A:1?11, 2017) for the classical two-phase Lamé?Clapeyron?Stefan probleman equivalence between the temperature and convective boundary conditions at the fixed face under a certain restrictionwas obtained. Motivated by this article we study the two-phase Stefan problem for a semi-infinite material with a latentheat defined as a power function of the position and a convective boundary condition at the fixed face. An exact solution isconstructed using Kummer functions in case that an inequality for the convective transfer coefficient is satisfied generalizingrecent works for the corresponding one-phase free boundary problem. We also consider the limit to our problem when thatcoefficient goes to infinity obtaining a new free boundary problem, which has been recently studied in Zhou et al. (J EngMath 2017. https://doi.org/10.1007/s10665-017-9921-y).