Perturbative analysis of planar phase change processes with time-dependent temperature at the boundary

The perturbation method developed recently for analysis of planar phase change processes is extended to the case of time-dependent temperature boundary conditions. Approximate solutions uniformly valid in time are derived. The role of time scales, that of the driving signal and the (time-dependent) response time of the emerging phase, in the dynamics of a weakly nonlinear melting process is clarified. The short and long time asymptotics are studied in detail. The analytical results are compared with the numerical solution for the problem of melting in a semi-infinite slab induced by a periodically varying boundary condition.