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 …