Taking account of the simultaneous heat and mass transfer in liquid and solid region, mathematical formulations are developed to describe the solute redistribution in dendritic solidification of alloys.
Namely, an analytical solution is presented under the conditions of the negligible undercooling in liquid and solid region and the complete mixing in liquid phase. Moreover, both the relation between the solid fraction and the concentration and that between Péclet number (Rl/E) and the physical properties of metal are mathematically presented. In addition, four kinds of effective distribution coefficients which are indispensable for the explanation of dendritic solidification are defined and given by the analytical expression.