Asymptotic analysis of a three-dimensional Bridgman furnace at large Rayleigh number

now know that the operation of a vertical Bridgman furnace, used for solidi fying a dilute binary alloy, may be optimized, in the sense of minimizing r adial material segregation, by a proper choice of the geometrical parameter s of the insulation zone that surrounds the crystal-melt interface. We have found [Phys. Fluids 9, 683 (1997)], as an extension of the work of Tanveer [Phys. Fluids 6, 2270 (1994)], that small surface tension reduces the radi al segregation but does not modify that optimization condition. Most previo us analyses have been done for axisymmetric ampoules. However, in a laborat ory setting, it may not be possible to assure axisymmetry, due to, say, azi muthal variations in the heat transfer or a small tilt of the ampoule axis. We find that nonaxisymmetric effects lead to optimization conditions simil ar to their axisymmetric counterparts. We include in the analysis geometric (Gibbs-Thomson) and concentration effects in melt temperature; the former effect decreases the segregation, and the latter increases segregation-for either axisymmetric or asymmetric thermal loading. We identify the mechanis m for the trend noted by other investigators in prior numerical work: even very small asymmetry causes large increases in crystalline segregation. (C) 1999 American Institute of Physics. [S1070-6631(99)02307-7].