Similarity Solution for Phase Change of Dilute Binary Isomorphous Alloy with Density Variation during Phase Change

Abstract

A similarity solution for conduction dominated solidification of a dilute binary isomorphous alloy has been developed. The effect solidification due to density change during phase transformation has been highlighted and investigated in detail. The governing equations for solid, liquid and mushy phase has been proposed, taking into account the effect of shrinkage or expansion due to density change during phase change. The thermo-physical properties (thermal conductivity and specific heat), equilibrium temperature and phase fraction are evaluated within the mushy zone using averaging technique. The effect of equilibrium and non-equilibrium solidification is investigated using Lever and Scheil’s rule models respectively. In addition, the effect of boundary and initial temperature on solidification behavior of the alloy is also addressed. It has been observed that the interface (liquidus and solidus) moves faster with increase in density ratio and decrease in boundary and initial temperature. No major changes in temperature distribution and interface position has been observed with variation partition coefficient and microscale behavior model (Lever rule and Scheil’s rule).

Keywords

• binary alloy
• variable density
• similarity variable
• conduction dominated
• mushy zone