Macroscopic global modeling of binary alloy solidification processes

Abstract

A macroscopic mathematical model is constructed describing the evolution of the phases of a binary alloy or mixture undergoing solidification under the action of simultaneous conduction of heat and diffusion of solute. The formulation is global, in the form of a pair of conservation laws valid over the whole region occupied by the alloy in a weak (distributional) sense. Thus it is especially convenient for numerical solution since it does not require tracking of the interface, which, in fact, may develop into a “mushy zone".