The finite element software FIDAP is employed to study the temperature and velocity distribution and the interface shape during a large sapphire crystal growth process using a heat exchanger method (HEM). In the present study, the energy input to the crucible by the radiation and convection inside the furnace and the energy output through the heat exchanger is modeled by the convection boundary conditions. The effects of the various growth parameters are studied. It is found that the contact angle is obtuse before the solid-melt interface touches the sidewall of the crucible. Therefore, hot spots always appear in this process. The maximum convexity decreases significantly when the cooling-zone radius (R-C) increases. The maximum convexity also decreases significantly as the combined convection coefficient inside the furnace (h(1)) decreases.