Numerical analysis which is based on finite element techniques, implicit Euler method and frontal solving algorithm was performed to study the effects of the crucible shape on the temperature of sapphire crystal and the shape of the melt/crystal interface in heat exchanger method. The computer simulation described here and effective to solving the heat transport phenomena with the transition of the interface shape from hemispherical to planar. In the work, various crucibles with differently shaped corners at their bottom are considered to improve the deflection of the melt/crystal interface. The shape of the crucible should be considered as one of the variables for the process optimization.