Abstract

Co-author: Nick Gewecke (Dalton State College)

We discuss a model for the evolution of a mushy zone which forms during the solidification of a binary alloy cooled from below in a finite domain. Our focus is on behavior of the system that does not appear when either a semi-infinite domain or negligible solute diffusion are assumed. The problem is simplified through an assumption of negligible latent heat, and we present a numerical scheme that will permit insights that are critical for developing a more general procedure. We demonstrate that a mushy zone will initially grow rapidly, then slows down and eventually retreats slowly. The mushy zone vanishes after a long time, due to being overtaken by a slowly-growing solid region at the base of the tank. Further results for mushy zones growing from boundaries cooled well below the eutectic temperature and for systems with partial solute rejection will also be discussed.