Developing Laminar Mixed Convection With Solidification in a Vertical Channel

Solidification of both high and low Prandtl number fluids (n-octadecane and aluminum) is considered for downward, mixed convection in the entrance region between vertical parallel plates symmetrically cooled below the fusion temperature. A continuum model is used to formulate a set of steady, two-dimensional partial differential equations, which include the influences of both axial diffusion and thermal buoyancy. The equations are solved using a fully elliptic, control-volume-based finite-difference scheme. Results reveal that, for a given phase change system, conditions are uniquely determined by a Grashof-to-Reynolds number ratio, Gr/Re, a Peclet number Pe, and a characteristic dimensionless temperature. Limiting cases involving both large and small values of Pe have been considered, and the effect of Gr/Re on thermally induced flow reversal in the fluid core has been determined.