EFFECTS OF INTERNAL RADIATIVE-TRANSFER ON NATURAL-CONVECTION AND HEAT-TRANSFER IN A VERTICAL CRYSTAL-GROWTH CONFIGURATION

The paper examines the effect of internal radiation on the process of growing a single crystal. A two-dimensional model of the vertical growth configuration is used to simulate the vertical Bridgman method. The differential approximation is used to model radiative transfer on the spectral basis and account for interactions within the crystal and the melt. Boundary conditions for semitransparent crystals which cover the range from opaque to transparent are developed. The governing model equations are solved numerically using a finite-difference method. The solutions show the notable reduction of the temperature difference near the crystal-melt interface and of the intensity of natural convection in the melt with the decrease in the opacity of the crystal. Radiation from the sidewall is found to be a factor in influencing the natural convection flow structure in the melt. The calculations show that there is relatively little difference between the spectral-band predictions and the gray model results based on the geometric mean absorption coefficient. The results obtained indicate the necessity to consider internal radiative transfer for improving the accuracy of models to simulate single crystal growth. © 1990.