Numerical Solution for Rubinstein's Phase Change Problem

Bruno dos Reis Jaccoud¹; Helcio Rangel Barreto Orlande¹; Olivier Fudym²; Abdelhalim Benberrah³; Aldélio Bueno Caldeira⁴

¹ Federal University of Rio de Janeiro; ² CNRS Brasil - Bureau CNRS Brésil; ³ RAPSODEE - Ecole des Mines d'Albi; ⁴ Military Institute of Engineering

doi:10.20906/CPS/COB-2015-1915

Resumo

A model is described for the solidification of an undercooled binary alloy in a one-dimensional semi-infinite medium. The model implemented in this work can be used for cases where the alloy is constituted of nanoparticles dissolved in a base phase change material. The equations of heat and mass transfer are coupled through the conditions at the moving phase change boundary. The equations are rewritten in conservative form to implement a numerical technique based on the enthalpy method, which does not require the explicit tracking of the phase change boundary. The obtained results compare well with known analytical solutions and explicit numerical solutions, for a test case available in the literature. The proposed numerical technique can accurately predict the temperature and the solute concentration for several conditions of practical interest. The effects of the Lewis number on the solidification behavior are examined in the paper as well.

Palavras-chave: Binary Alloy; Enthalpy Method; Nanoparticles; Phase Change Materials