A computer simulator with a global model of heat transfer during crystal growth of Si for solar cells is developed. The convective, conductive, and radiative heat transfers in the furnace are solved together in a coupled manner using the finite volume method. A three-dimensional (3D) global heat transfer model with 3D features is especially made suitable for any crystal growth, while the requirement for computer resources is kept permissible for engineering applications. A structured/unstructured combined mesh scheme is proposed to improve the efficiency and accuracy of the simulation. A dynamic model for the melt-crystal (mc) interface is developed to predict the phase interface behavior in a crystal growth process. Dynamic models for impurities and precipitates are also incorporated into the simulator. Applications of the computer simulator to Czochralski (CZ) growth processes and directional solidification processes of Si crystals for solar cells are introduced. Some typical results, including the turbulent melt flow in a large-scale crucible of a CZ-Si process, the dynamic behaviors of the mc interface, and the transport and distributions of impurities and precipitates, such as oxygen, carbon, and SiC particles, are presented and discussed. The findings show the importance of computer modeling as an effective tool in the analysis and improvement of crystal growth processes and furnace designs for solar Si material.