A mathematical model for solidification of binary eutectic system including relaxation time

Abstract

In this paper we have developed the time relaxation model for solidification of a binary eutectic system. In this model, we have considered the melt of a binary eutectic composite filled in a container; the flat probe is kept inside the container. The surface temperature of the flat probe decreases linearly with time. The solidification process occurs in three stages and, whole region is divided into solid, mushy, and liquid regions. The heat released in the mushy region is considered as discontinuous heat generation. The solid fraction present in the mushy region is characterized in two different ways: (i) when the solid fraction depends on distance and (ii) when the solid fraction depends on temperature. To solve this model we have developed the Legendre wavelets spectral Galerkin method. The whole analysis is presented in a dimensionless form and the results thus obtained are discussed in detail. © 2016 by Begell House, Inc.