Analysis of three-dimensional solidification interface shape

The determination of the shape of the solidification interface in a cooling melt by the thermal boundary conditions is investigated analytically, extending the analysis of Siegel (1982) and Siegel and Sosoka (1982) to the three-dimensional case. The solutions are generated by continuation into the solid region from conditions at the cooled wall, and some numerical results are presented in tables and graphs. These findings and the analytical approach employed are applicable to crystallization and metal-forming processes.