Dendritic Growth in Undercooled Melt with forced Convection: Theory.

Abstract

Analytical solutions for melt flow with Oseen viscous flow approximation are obtained for the Navier-Stokes equations in the region near the tip of a dendrite of which shape is approximated to be a paraboloid of revolution. Temperature is also analyzed in the presence of flow in a melt. A theory of dendritic growth is proposed with flow in the undercooled pure melt. Local equilibrium condition at the interface is applied in the theory. The predicted growth rate of the tip of dendrite as functions of the melt undrcooling with and without forced flow velocity is successfully compared with the experimental results for the pure succinonitrile.