Effects of simplified enthalpy relations on the prediction of heat transfer during solidification of a lead-tin alloy

Abstract

An investigation into the effects of enthalpy functions that vary with both concentration and temperature on the prediction of heat transfer during solidification using a volume-averaged mixture energy equation is presented. Results are presented for the solidification of a Pb-20 wt.% Sn alloy in a semi-infinite domain using both the Lever Rule and Scheil models to relate temperature and volume fraction. The effects of simplifying the enthalpy relations so that the derivatives of the phase enthalpies with respect to temperature and concentration are constant or zero are examined. The resulting predictions all underestimate the movement of the eutectic and liquidus isotherms in comparison with fully variable enthalpy terms. The additional simplifications of linearizing the phase diagram and using the same properties for the α-phase and eutectic solids introduce a small improvement in the predictions. In addition, the consequences of neglecting the effects of microscopic concentration profiles in the solid on the solid enthalpy are investigated, and the resulting predictions overestimate the movement of the eutectic and liquidus isotherms. The results should serve as an estimation of the magnitude of the differences in the modelling of heat transfer during solidification introduced by simplifying the enthalpy relations or ignoring microscopic concentration variations within the solid.