Thermal anisotropy in binary alloy solidification: An equivalent isotropic model

A continuum mixture model is proposed for phase change of binary alloy including the effect of thermal anisotropy. Thermal anisotropy is incorporated by an additional departure source in the conventional isotropic heat transfer-based energy equation. The governing equations for heat, mass, momentum, and species transport are solved using implicit finite volume method. The pressure and velocity in the momentum equation are coupled using SIMPLER algorithm. The solute mixture concentration is updated using two commonly used methods, the lever rule model and the Scheil rule model. A comprehensive study is made to investigate the effect of thermal anisotropy on solidification physics and final macrosegregation pattern after complete solidification for two cases: one with three sides of the enclosure insulated where planar front generates and the other with two opposite sides insulated where irregular front evolves. The directional effect of thermal anisotropy ratio (AR) on binary alloy phase change behavior has been investigated in detail.