“…The melt-solid interface shapes of a silicon ingot in unidirectional solidification and casting processes were studied by Vizman et al [5] and Miyazawa et al [6,7]. The relative movement of various parts of furnace was considered in a global 3D time-dependent numerical simulation by Delannoy et al [8]. Two major types of casting furnaces, direct solidification system (DSS) and heat exchange method (HEM) system, have been compared from the aspects of thermal field, crystal quality and shear stress field by Wu et al [9].…”