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|Type:||Artigo de periódico|
|Title:||Weak Solutions Of A Phase-field Model With Convection For Solidification Of An Alloy|
|Abstract:||In recent years, the phase-field methodology has achieved considerable importance in modeling and numerically simulating a range of phase transitions that occur during solidification processes. In attempt to understand the mathematical aspects of such methodology, in this article we consider a simplified model of this sort for a nonstationary process of solidification/melting of a binary alloy with thermal properties. The model includes the possibility of occurrence of natural convection in non-solidified regions and, therefore, leads to a free-boundary value problem for a highly non-linear system of partial differential equations consisting of a phase-field equation, a heat equation, a concentration equation and a modified Navier-Stokes equations by a penalization term of Carman-Kozeny type, which accounts for the mushy effects, and Boussinesq terms to take in consideration the effects of variations of temperature and concentration in the flow. A proof of existence of weak solutions for the system is given. 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. © Dynamic Publishers, Inc.|
|Appears in Collections:||Unicamp - Artigos e Outros Documentos|
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