Convection effects on radial segregation and crystal melt interface in vertical Bridgman growth

We analytically study the influence of convection caused by horizontal heat transfer through the sides of a vertical Bridgman apparatus. We consider the case when the heat transfer across the side walls is small so that the resulting interfacial deformation and fluid velocities are also small. This allows us to linearize the Navier-Stokes equations and express the interfacial conditions about a planar interface through a Taylor expansion. Using a no tangential stress conditions on the side walls, asymptotic expressions for both the interfacial slope, and radial segregation at the crystal-melt interface are obtained in closed form in the limit of large thermal Rayleigh number. It is suggested that these can be reduced by appropriately controlling a specific heat transfer property at the edge of the insulation zone in the solid side.