Analytical Solution of Mushy Zone under Directional Solidification

Based on the general mathematical formulation under unidirectional solidification with mushy layer developed in Ref.[13], leading approximation of solution in mushy layer is obtained for the case that the inverse Lewis number is small parameter. For the steady state of solidification, concentration field in the mushy region is given as function of a solid volume fraction. Mushy layer width and solid volume fraction at the solid-mush interface are obtained. Effects of temperature gradient on mushy layer width and solid volume fraction at solid-mush interface are presented.