Mathematical simulation of melt flow, heat transfer and non-equilibrium solidification in planar flow casting

This paper describes a two-dimensional model of fluid flow and heat transfer with phase change for the planar flow casting process. Boundary-layer theory is used to model fluid flow and heat transfer in the solidification puddle, and a semi-implicit finite difference scheme is used to solve the corresponding governing equations. In order to take into account non-equilibrium solidification with melt undercooling, a kinetics relationship between the interface velocity and the interface undercooling is incorporated in the model. The location of the interface and its temperature are calculated using an interface tracking technique based on control volume integrals with element subdivision. Besides the interface velocity and temperature, the model also predicts the shape of the downstream meniscus formed between the crucible and the moving wheel. Some results for the planar flow casting of an aluminium melt with undercooling are also presented, including predictions of the streamlines and isotherms in the puddle. The effect of the interface kinetics and melt undercooling on the solidification characteristics is quantified through comparison with an equilibrium solidification model.