On the theory of dendritic growth under convective heat and mass transfer in a binary alloy

Abstract

We consider a thermo-solutal growth of an anisotropic dendrite in a binary liquid with allowance for the convective heat and mass transfer mechanism at the dendrite surface. We obtain a new stability criterion for stable mode of dendritic evolution. Also in this work, a stable relation for the dendrite tip velocity and its tip diameter via the selection theory and undercooling balance is discussed. The undercooling balance and selection criterion allow us to obtain two nonlinear equations determining the crystal tip velocity and its tip diameter as functions of undercooling.