An existence result for a two-phase Stefan problem arising in metal casting

✍ Scribed by A. Bermúdez; M. V. Otero

• Publisher: John Wiley and Sons
• Year: 2005
• Tongue: English
• Weight: 259 KB
• Volume: 29
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/mma.683

✦ Synopsis

Abstract

We present a model arising from the thermal modelling of two metal casting processes. We consider an enthalpy formulation for this two‐phase Stefan problem in a time varying three‐dimensional domain and consider convective heat transfer in the liquid phase. Then, we introduce a weak formulation in a fixed domain, by means of a suitable transformation. Existence of solution is obtained by applying an abstract theorem. The proof of this theorem is done by taking an implicit discretization in time together with a regularization. By passing to the limit in the regularization parameter and in the time step, we obtain the existence of solution of the continuous problem. Copyright © 2005 John Wiley & Sons, Ltd.