AbstractA new solution procedure for binary-constituent solid-liquid phase-transition problems has been applied to several one- and two-dimensional problems. Three one-dimensional applications (a pure material melting problem, a unidirectional Ag-Sn solidification problem, and a Bridgman furnace simulation) illustrate different interface solute redistribution and Ste number sensitivity results. In addition, two-dimensional applications examine Pb-Sn and NH₄Cl-H₂O solidification problems within moderate- and tow-aspect-ratio enclosures. In these problems, buoyancy-driven and shear-driven recirculation cells in the liquid regions of the cavity, penetration of bulk fluid across the liquids interface, and energy and species advection are observed. The model's results agree closely with previous analytical and experimental results, and its performance indicates a cost-effective and physically based approach to solid-liquid phase-transition discrete analysis