Planar solidification in a finite slab: Effects of density change

Abstract

Planar solidification in a slab of finite thickness, cooled from below, is addressed. The solid density is supposed to be greater than the liquid density. The fluid flows toward the moving phase-change front, accompanied by heat transfer in the emerging solid, in the liquid and cavity, resulting due to the contraction of the volume of the material, are analyzed. The Rubinstein transformation, which immobilizes the interface, is modified in order to take the density change into account. It enables one to reduce the problem to that without the density change. Several approximate analytic solutions for transient solidification, some of which are new even for equal solid and liquid densities, are presented.