A model of the interfacial heat-transfer coefficient during unidirectional solidification of an aluminum alloy

A model is presented for the prediction of the interfacial heat-transfer coefficient during the unidirectional solidification vertically upward of an Al-7 wt pet Si alloy cast onto a water cooled copper chill. It has been experimentally determined that the casting surfaces were convex toward the chill, probably due to the deformation of the initial solidified skin of the casting. The model was, therefore, based upon a determination of the (macroscopic) nominal contact area between the respective rough surfaces and, within this region, the actual (microscopic) contact between the casting and the chill surfaces. The model produced approximate agreement with both experimentally determined values of the heat-transfer coefficient and the measured curvature of the casting surface and showed a reasonable agreement with measured temperatures in the casting and the chill also. A common experimental technique for the experimental determination of the heat-transfer coefficient involves the assumption of one-dimensional heat transfer only. An implication of the approach adopted in this model is that the heat transfer in the region of the casting-chill interface may be two-dimensional, and the subsequent error in the experimentally determined values is discussed.