A computational model has been developed for the Bridgman growth process of beta-NiAl crystal. The model accounts for heal transfer in the whole furnace system. including the encapsulated fluid between the heater and the ampoule, conjugate heat transfer around and within the ampoule, and phase change dynamics between melt and crystal. To handle the geometrical and physical complexities of the crystal growth processes, a two-level approach has been developed. At the global furnace level, combined convection/conduction/radiation calculations with realistic geometrical and thermal boundary conditions are made inside the whole system. Refined calculations are then made within the ampoule, with the boundary conditions supplied by the global furnace simulations. The present multi-level model can help improve the predictive capabilities for crystal growth techniques by optimizing the use of the computing resources; it allows one to probe the effects of different physical and geometrical variables on the crystal quality.