Phase change heat conduction in general orthogonal curvilinear coordinates

The approximate method of London and Seban for predicting the solidification rate and for melting in or around slabs, cylinders, and spheres has been reformulated in general orthogonal curvilinear coordinates. Closed-form solutions are presented for the rate of phase change and temperature drop as a function of a nondimensional time, STeFo (product of Stefan and Fourier numbers), for various geometries including elliptic cylinders, spheroids of varying eccentricites, and bicylindrical problems. Both convection and flux boundary conditions which can vary with time are considered. The effect of Biot number on phase change times and the resulting boundary temperature are presented in graphical form for some of the geometries considered. The method's degree of approximation is investigated by comparison with published analytical results. The approximate applicability of the equations to some special phase change conduction problems is demostrated.