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February  2005, 13(2): 429-450. doi: 10.3934/dcds.2005.13.429

A tridimensional phase-field model with convection for phase change of an alloy

José Luiz Boldrini 1, and  Gabriela Planas 2,

1. 

IMECC-UNICAMP, CP 6065, Campinas-SP, 13081-970, Brazil
2. 

Departamento de Matemática, ICMC-USP, CP 668, São Carlos-SP, 13560-970, Brazil

Received  June 2004 Revised  February 2005 Published  April 2005

We consider a tridimensional phase-field model for a solidification/melting non-stationary process, which incorporates the physics of binary alloys, thermal properties and fluid motion of non-solidified material. The model is a free-boundary value problem consisting of a highly non-linear parabolic system including a phase-field equation, a heat equation, a concentration equation and a variant of the Navier-Stokes equations modified by a penalization term of Carman-Kozeny type to model the flow in mushy regions and a Boussinesq type term to take into account the effects of the differences in temperature and concentration in the flow. A proof of existence of generalized solutions for the system is given. For this, the problem is firstly approximated and a sequence of approximate solutions is obtained by Leray-Schauder's fixed point theorem. A solution of the original problem is then found by using compactness arguments.
Keywords: phase change, Phase-field models, convection, solidification..
Mathematics Subject Classification: 80A22, 76D05, 35K55, 82B2.
Citation: José Luiz Boldrini, Gabriela Planas. A tridimensional phase-field model with convection for phase change of an alloy. Discrete and Continuous Dynamical Systems, 2005, 13 (2) : 429-450. doi: 10.3934/dcds.2005.13.429
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