A mathematical model for solute redistribution during dendritic solidification.

Abstract

To quantify the solute redistribution during solidification, an approxi- mate solution of the Brody-Flemings model of dendritic solidification has been derived on the assumption of parabolic solidification and a constant partition ratio, and compared with an exact solution of the model. It has been shown that the approximate solution has good accuracy. Further, on the basis of the derived equation, an extended mathematical model is proposed, incorporating a thermal model of solidification into the analysis without assumption on the solidification rate. The extended model includes the treatment of multi-component alloy and of 1 transformation, the temperature dependence of diffusion coefficients and the estimation of the diffusion path. The extended model provides the results consistent with the available data. Key