1998 Volume 38 Issue 7 Pages 730-738
To estimate micro-segregation with dendritic solidification, a common method using an integral profile method has been developed. We considered three cases; (1) no diffusion in the solid and finite diffusion in the liquid, (2) finite diffusion in the solid and complete diffusion in the liquid, and (3) finite diffusion in both the solid and liquid. Expressing the solute distribution in the liquid and/or in the solid as quadratic polynomials, and assuming the linear growth case or the parabolic growth case, ordinary differential equations have been obtained. We introduced Ivantsov's solution as the initial condition of the diffusion problem to expand the model to rapid solidification conditions. Using the Runge–Kutta method, the solute distribution profile in both the liquid and solid over time was estimated. After calculation, good agreement with rigorous solutions for each case was gained. For easy way of programming and short computating time, this method has practical merits.