Efficient estimation of diffusion during dendritic solidification

A very efficient finite difference method has been developed to estimate the solute redistribution during solidification with diffusion in the solid. This method is validated by comparing our computed results to the results of an analytical solution derived by Kobayashi^[4] for the as-sumptions of a constant diffusion coefficient, a constant equilibrium partition ratio, and a par-abolic rate of the advancement of the solid/liquid interface. The flexibility of our method is demonstrated by applying it to the dendritic solidification of a Pb-15 wt pct Sn alloy, for which the equilibrium partition ratio and diffusion coefficient vary substantially during solidification. The fraction eutectic at the end of solidification is also obtained by estimating the fraction solid, in greater resolution, where the concentration of solute in the interdendritic liquid reaches the eutectic composition of the alloy.