Effect of computational domain size on the mathematical modeling of transport processes and segregation during directional solidification

Using a finite-element simulator, a directionally solidified hypoeutectic P b-Sn alloy was modeled in two dimensions to determine the effect of the hei ght of the overlying liquid on convective transport and macrosegregation. I t was determined that, while the strength of the convection in the overlyin g liquid depends on the square root of its height, one need not model the e ntire domain to predict freckling. Furthermore, the assumption of a constan t thermal gradient in the liquid causes the predicted convection to be some what weaker than the convection in the temperature field used in directiona l solidification processing.