FORCED-CONVECTION HEAT-TRANSFER DURING DENDRITIC CRYSTAL-GROWTH - LOCAL SOLUTIONS OF NAVIER-STOKES EQUATIONS

Abstract

Numerical local solutions are obtained to the Navier-Stokes equations and energy equation for the region near the tip of a needle crystal growing in the presence of a forced flow in a melt of succinonitrile. The Navier-Stokes solution for P is essential identical with solutions using the Oseen viscous flow and Stokes flow approximation if the fluid Peclet number (Pe) is less than about 2. However, as Pe is increased, the solutions of the Stokes and Oseen viscous flow approximation overpredict the crystal Peclet number (P). The forced convection solution can be approximated by a power law form such that P = 1.26 St1.06 Pe0.20 for 0.1 < Pe < 2.0. These forced convection solutions predict that the controlling mode of heat transfer changes when the growth velocity of the crystal is about the same as the convective velocity.