Yp. Lee et St. Ro, APPROXIMATE DETERMINATION OF THE SHAPE OF SOLIDIFIED MATERIALS WITH EITHER SHRINKAGE OR EXPANSION, KSME journal, 9(4), 1995, pp. 502-505
The differences in densities between liquid and solid phases results i
n a concave surface during solidification. The final shape after compl
ete solidification is obtained by considering the conservation of the
nass without any reference to the detailed transport processes. An eas
y and quick procedure is described to predict the final shape of the s
olid phase for planar and cylindrical configurations. The results are
validated by comparison with an existing data.