A mathematical model of the splat cooling process using the piston and anvil technique

A mathematical model has been developed to represent the spreading of the slug and its subsequent solidification for the piston and anvil splat cooling technique. In the statement of the problem allowance has been made for fluid flow effects regarding the spreading, convective heat flow and the actual movement of the piston after the impact. In representing heat flow allowance has been made for convection for the two dimensional transient temperature fields and the existence of a mushy zone on solidification. The computed results gave predictions regarding the effect of the piston velocity and of the substrate-splat heat transfer coefficient on both the final splat thickness and on the cooling rates. It was found that the higher the piston velocity and the higher the splat-substrate heat transfer coefficient, the faster are the attainable cooling rates, although there is a tendency to approach limiting values. A critical comparison of the present work with previous modeling efforts shows marked spatial variations in the cooling rates so that the previously used one dimensional models are not likely to be satisfactory. Furthermore, the analysis of the fluid flow phenomena given in the present paper allows a realistic assessment of the final splat thickness, which was not available up to the present.