Two-dimensional solidification in a corner

Analytical and numerical techniques are used to study the solidification of 1/2 pi and 3/2 pi wedges of liquid, which, are initially at their fusion temperature. An enthalpy method is used to obtain numerical solutions to these problems and the results are compared with asymptotic solutions for large and small Stefan numbers (the Stefan number being defined as the ratio of latent to sensible heats). The new solutions for small Stefan numbers are shown to provide surprisingly good approximations, especially for the 3/2 pi wedge. New results for heat transfer in a wedge (in the absence of a change of phase) are derived and applied in the asymptotic analysis, as are new conservation laws for the Stefan problem.