Three-Dimensional Effects of Solidification

There have been many papers concerning the computational studies of unidirectional solidification for solar cells, in which the growth system was imposed to be axisymmetric. However, the actual crystal shape is square, calculation of square-shaped crystals is necessary. When square crucibles are used, the configuration of the furnace becomes asymmetric, and heat transfer in the furnace consequently becomes three-dimensional. Three-dimensional (3D) global modeling is, therefore, necessary for the investigation of m-c interface shape with square crucibles [20], 

There have been no works using global analysis to investigate the effect of crucible shape on m-c interface shape. The author developed a steady code with 2D and 3D global models for the unidirectional solidification process used for cylindrical and square crucibles, respectively. 

Three-dimensional global analysis with square crucibles requires large computational resources because of the huge number of 3D structured grids. To overcome this difficulty, a 2D/3D mixed discretization scheme is employed to reduce the requirement of computational resources [11,12]. The domains in the central area of the furnace, in which the configuration and heat transfer are nonaxisymmetric, are discretized in a 3D way. 

---