Melt Flow and Characteristic Dimensions of Dendrite in Unidirectional Solidification

Abstract

The effect of melt flow, coming to dendrite tip, is studied analytically on the morphology of needle dendrite during unidirectional growth. The melt flow around the paraboloid body is analyzed under Oseen approximation for Navier-Stokes flow equation. Solutions of diffusion equation for temperature and solute distribution are studied under melt flow. The tip radius of curvature of needle dendrite is predicted by perturbation analysis just before for the growth of secondary arms of the needle. It is shown that the melt flow decreases the tip radius of curvature of dendrite and the effect becomes significant in low growth rate. The predicted radius is compared with experimental one and the correspondence between them is fairly well.