Heat Flow Model for Surface Melting and Solidification of an Alloy

The heat flow model previously developed for a pure metal is extended to the solidification of an alloy over a range of temperatures. The equations are then applied to rapid surface melting and solidification of an alloy substrate. The substrate is subjected to a pulse of stationary high intensity heat flux over a circular region on its bounding surface. The finite difference form of the heat transfer equation is written in terms of dimensionless nodal temperature and enthalpy in an oblate spheroidal coordinate system. A numerical solution technique is developed for an alloy which precipitates a eutectic at the end of solidification. Generalized solutions are presented for an Al-4.5 wt pct Cu alloy subjected to a uniform heat flux distribution over the circular region. Dimensionless temperature distributions, size and location of the “mushy” zone, and average cooling rate during solidification are calculated as a function of the product of absorbed heat flux,q, the radius of the circular region, a, and time. General trends established show that for a given product ofqa all isotherms are located at the same dimensionless distance for identical Fourier numbers. The results show that loss of superheat and shallower temperature gradients during solidification result in significantly larger “mushy” zone sizes than during melting. Furthermore, for a given set of process parameters, the average cooling rate increases with distance solidified from the bottom to the top of the melt pool.