Reduced complexity solidification models

The solidification of a binary alloy, flowing between two cooled parallel plates is considered. A two-dimensional model for this system, involving the conservation equations of heat, solute, mass, and momentum, is constructed – the hi-fidelity model. Through a depth integration, a Reduced Complexity Model (RCM), in terms of one-dimensional advection equations, expressing the transient conservation of heat and solute, is obtained– the transient- RCM. For thermo-physical data, consistent with a dilute Al-Cu binary alloy, numerical predictions from the transient- RCM are shown to be in close agreement with predictions obtained from a numerical solution of the hi-fidelity model. The RCM is reduced further, to a model formed as a single initial value problem, predicting the steady-state axial temperature and liquid fraction profiles between the plates – the steady-RCM. Analysis and numerical solutions of the transient- RCM and steady-RCM, provide a means of modeling, evaluating, and illustrating the role of solid phase motion in the timing and pattern of a binary alloy solidification.