Numerical analysis of heat and momentum transfer in the growth of yttrium aluminum garnet crystals by the Czochralski method

The crystal growth of Yttrium Aluminum Garnet (doped with Neodynium) was studied mathematically. A finite difference mathematical model was used to generate temperature fields in the crystal and temperature and velocity fields in the melt. A method involving a false compressibility was used to aid convergence. Conduction in the crystal and melt and natural convection in the melt were taken into account. The process was simulated for three different crystal heights. It was found that the temperature remained in excess of 1600...