Steady Dendritic Growth from Melt with Convective Flow
We now consider a more general system of dendritic growth, in which convective flow is generated by all kinds of sources, such as density change during phase transition, enforced uniform flow in the far field, and buoyancy effect in gravitational field. We still adopt the moving paraboloidal coordinate system (ξ, η, θ) fixed at the dendrite tip as defined in the last chapter (See Fig. 3.1). We let u(ξ, η, θ, t) = (u, v, w) represent the relative velocity field in the liquid state. Here, (u, v) are the components of the relative velocity along ξ- and η-direction, respectively, in the moving frame at the instant t. Furthermore, let Ω = ∇x u denote the vorticity; η s(ξ, θ, t) denote the interface shape function; T and T s denote the temperature field in the melt and in the solid state, respectively. The subscript ‘S’ refers to the solid state. The governing equations for the dendritic growth process now consist of the fluid dynamical equations and the heat conduction equation.
KeywordsConvective Flow Dendritic Growth Heat Conduction Equation Buoyancy Effect Fluid Dynamical Equation
Unable to display preview. Download preview PDF.