Influence of gravity on thermocapillary convection in floating zone melting of silicon

It was found that the finite difference equations used by Chang and Wilcox for the fluid adjacent to the free melt surface satisfy only the boundary conditions and not the Navier-Stokes differential equation. A new formulation was made which satisfies both. This eliminated the anomalous additional vortex center in the cell generated by electron bem heating. The influence of gravity was investigated as a function of zone size and temperature gradient at a constant zone travel rate of 5 cm/h with electron-beam heating and zone diameter = zone length. The change in vorticity at the freezing interface depends on Gr 6/M, and is proportional to the 5 2 power of zone diameter and the 3 4 power of the maximum superheating in the zone.