NUMERICAL SOLUTION OF THE UNSTEADY SOLIDIFICATION PROBLEM WITH A SOLUTE ELEMENT BY USING THE BOUNDARY-FITTED COORDINATE SYSTEM

Abstract

A numerical method suitable for solving the unsteady solidification problem with a solute element is proposed. The schemes are based on a finite-difference solution of the equations of the transient heat and mass transfer on a boundary-fitted coordinate system, which is always adjusted to the current solid-liquid interface. The temperature and concentration on the moving solid-liquid interface are obtained from the conditions of the heat and solute balance on it. Several examples are displayed. The numerical results of the solid-liquid interface instability are in good agreement with the prediction of Mullins and Sekerka's theory.