Premium
On a two‐phase Stefan problem with convective boundary condition including a density jump at the free boundary
Author(s) -
Briozzo Adriana C.,
Natale María F.
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6152
Subject(s) - mathematics , free boundary problem , jump , boundary (topology) , boundary value problem , mathematical analysis , temperature jump , stefan problem , phase boundary , convection , thermodynamics , phase (matter) , physics , quantum mechanics
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.