Fluid flow, heat transfer, and solidification near tri-junctions

Steady, two-dimensional fluid flow and heat transfer are considered near tri-junctions at which solidification is occurring. Meniscus-defined configurations as well as closed configurations such as directional solidification are examined. The local wedge geometry admits separable solutions in plane polar coordinates. Over the class of functions which have bounded temperatures and velocities at the corner, local solutions, those which satisfy all local boundary conditions, and partial local solutions, those which satisfy all but the normal-stress boundary condition, are considered. The aim in this work is to describe local fluid flow and heat transfer in problems where solidification is occurring by identifying singularities in the heat flux and stress which are present at the tri-junction, determining the dependence of these singularities on the wedge angles, and determining when specific wedge geometries are selected. It is found that the locally dominant flow is that due to the expansion or contraction of the material upon solidification.