ASSESSMENT OF MATHEMATICAL-MODELS FOR THE FLOW IN DIRECTIONAL SOLIDIFICATION

In a binary solution unidirectionally solidified from below, the bulk melt and the eutectic solid is separated by a dendritic mushy zone. Th e mathematical formulation governing the fluid motion shall thus consi st of the equations in the bulk melt and the mushy zone and the associ ated boundary conditions. In the bulk melt, assuming that the melt is a Newtonian fluid, the governing equations are the continuity equation , the Navier-Stokes equations, the heat conservation equation, and the solute conservation equation. In the mushy layer, however, the formul ation of the momentum equation and the associated boundary conditions are diversified in previous investigations. In this paper, we discuss three mathematical models, which had been previously applied to study the flow induced by the solidification of binary solutions cooling fro m below. The assessment is given on the bases of the stability charact eristics of the convective flow and the comparison between the numeric al and experimental results.