A similarity solution for phase change of binary alloy with shrinkage or expansion

A similarity solution for solidification of an undercooled binary alloy is developed including the effect of shrinkage or expansion due to change in the density. The proposed similarity solution takes into account the change in density of the alloy while undergoing a phase change. Thermo-physical properties are assumed to be constant. An analytical solution (which is an outcome of the similarity solution) for temperature and concentration distribution has been established. The effect of the density ratio and Lewis number on both interface motion and conjugate heat and mass transfer is studied. It is found that the interface moves faster with the decrease in density ratio and initial temperature during solidification.