Computer simulations using the commercial code FIDAP, which is based on finite element techniques, were performed to investigate the effect of the shape of the crucible on the temperature distribution, velocity distribution and shape of the melt-crystal interface, during the application of the heat exchanger method (HEM) of growing sapphire crystals. Heat transfer from the furnace to the crucible and heat extraction from the heat exchanger can be modeled by the convection boundary conditions. Cylindrical crucibles with differently curved corners at their base are considered. The curved base of the crucible decreases the convexity of the melt-crystal interface and suppresses the appearance of "hot spots". A hemispherically shaped crucible base yields the lowest maximum convexity. The variation in convexity of the melt-crystal interface is less abrupt for a cylindrical crucible with curved corners at the base than one without curved corners. The effects of the thickness and the conductivity of the crucible are also addressed. The convexity of the melt-crystal interface decreases as the thickness of the crucible wall increases. The convexity also declines as the conductivity of the crucible increases. (C) 2004 Elsevier B.V. All rights reserved.