Modeling of multidimensional solidification of an alloy

The solidification of an alloy and pure metal is distinct because of the morphological differences between the respective interfaces. For certain conditions of imposed heat extraction, this distinction can lead to large differences in the times required for complete solidification of the alloy over the pure metal. These conditions are examined in this paper. To do this, a numerical technique to model alloy solidification is introduced which allows for the precise integration of the Scheil equation. The model takes into account the nonlinearity of the fraction liquid with temperature as well as the interface nonlinearity in the heat flow. As a test for the model, accurate temperature profiles from a previously published experiment are numerically simulated. The numerical results closely match experimental values, and as a consequence, contact heat transfer values are tabulated. One- and two-dimensional solidification of aluminum-copper alloys are simulated for different cooling conditions (i.e., varying Biot numbers). The results indicate the essential differences for alloy solidification at low and high Biot numbers and highlight the importance of properly accounting for the mushy zone.