Exact solutions of solid-liquid phase-change heat transfer when subjected to convective boundary conditions

A closed-form expression is presented to find the location of solid-liquid interface motion in convection-dominated solidification and melting problems. In this regard, the solutions are expressed in terms of the generalized representations of error functions, E (u, v) and F (u, v), which are useful to heat-conduction problems with convective-type boundary conditions. It is demonstrated that for constant surface temperature, the interface solution reduces to the classical Neumann solution.