On a two‐phase Stefan problem with convective boundary condition including a density jump at the free boundary

Abstract

We consider a two-phase Stefan problem for a semi-infinite body x > 0, with a convective boundary condition including a density jump at the free boundary with a time-dependent heat transfer coefficient of the type h∕ √t, h > 0 whose solution was given in D. A. Tarzia, PAMM. Proc. Appl. Math. Mech. 7, 1040307–1040308 (2007). We demonstrate that the solution to this problem converges to the solution to the analogous one with a temperature boundary condition when the heat transfer coefficient h → +∞. Moreover, we analyze the dependence of the free boundary respecting to the jump density.