On a two‐phase Stefan problem with convective boundary condition including a density jump at the free boundary. (10th January 2020)

• Record Type: Journal Article
• Authors: Briozzo, Adriana C.; Natale, María F.
• Is Part Of: Mathematical methods in the applied sciences. Volume 43:Number 6(2020)
• Page Start: 3744
• Page End: 3753
• Publication Date: 2020-01-10
• Subjects: two‐phase Stefan problem -- density jump -- asymptotic behavior -- phase‐change process; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.6152
• Languages: English
• ISSNs: 0170-4214

Abstract

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.