Convergence of the solution of the one-phase Stefan problem when the heat transfer coefficient goes to zero

A. C. BRIOZZO - D. A. TARZIA

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

ACADEMIC PRESS INC ELSEVIER SCIENCE

Lugar: Amsterdam; Año: 2012 vol. 389 p. 138 - 146

0022-247X

We consider the one-phase unidimensional Stefan problem with a convective boundary condition at the fixed face, with a heat transfer coefficient (proportional to the Biot number) $h>0.$ We study the limit of the temperature $\theta _{h}$ and the free boundary $s_{h}$ when $h$ goes to zero, and we also obtain an order of convergence. The goal of this paper is to do the mathematical analysis of the physical behavior given in C. Naakgeboren, Int. J. Heat Mass Transfer, 50(2007), 4614-4622