Convergence of the solution of the one-phase Stefan problem with respect two parameters

Abstract

A one-phase unidimensional Stefan problem with a convective boundary condition at the fixed face x = 0, with a heat transfer coefficient h > 0 (proportional to the Biot number) and an initial position of the free boundary b = s(0) > 0 is considered. We study the limit of the temperature θ = θb,h and the free boundary s = sb,h when b → 0 + (for all h > 0) and we also obtain an order of convergence. Moreover, we study the limit of the temperature θb,h and the free boundary sb,h when (b, h) → (0+, 0 +).