A refined similarity solution for the multicomponent alloy solidification

This paper deals with a refined similarity solution for the solidification of ternary or higher-order multicomponent alloys. The present approach not only retains the existing features of binary systems such as temperature–solute coupling, shrinkage-induced flow, solid–liquid property differences and finite back diffusion, but also is capable of handling a multicomponent alloy without restrictions on the partition coefficient and microsegregation parameter. A new exact solution to the energy equation including the convection term in the pure liquid region is successfully derived, which allows the present analysis to cover a high initial superheating. For an alloy of K-solute species, governing equations in the mushy region reduce to (K+2) simultaneous ordinary differential equations via similarity transform, which are to be solved along with the closed-form temperature profiles in the solid and liquid regions. A linearized correction scheme adopted in the solution procedure facilitates to determine the solidus and liquidus position stably. Good agreements are found in comparison with the numerical predictions and available simplified similarity solutions for binary and ternary alloys.