A computational study of binary eutectic system with convection under volumetric freezing: A Moving Boundary Problem

Abstract

A reduction in the operating time during the solidification of an eutectic alloy is one of the prime demands in front of the investigators. The classical theory of solidification was not able to offer rapid solidification of an alloy due to not account the structural property of the material. To account convection and external heat sink effect, an external volumetric heat sink is considered and it depends on the distance and time. The thermal conductivity, density, and specific heat of the mushy zone are assumed to be the linear combination of solid and liquid regions properties with a solid fraction distribution. The mathematical model accounts for the solid fraction distribution, which has a linear relationship with the temperature of the mushy zone. The analytical solution of the problem has been determined via similarity transformation. To explore the current study, numerical data of the Copper-Aluminum alloy with 5% Copper is presented. It has been found that with a volumetric heat sink, the rate of solidification becomes faster than usual. Further, the rate of heat removal from the surface accelerates. Convection enhances the rate of freezing of the eutectic alloy. The temperature of the mushy region is going up for the increasing value of the solid fraction in mushy zone, which is lying in [0,1] and when we increase the strength of volumetric heat, then the temperature profile decreases and, the first-interface and second-interface increase gradually in the whole medium. We compared the current result with Tien and Geiger’s result, and it is found in good compliance. It is expected that the current study will improve the fundamental understanding of the solidification of an eutectic alloy and reduce the time for freezing, which is useful to design industrial freezing devices for alloys.