Planar or radial freezing with solid-solid transitions and convective heating atthe solid-liquid interface

Numerical solutions have been carried out for planar or radial freezing on a cooled wall or cylinder maintained at a uniform temperature lower than the fusion temperature. The solutions were obtained by using an implicit/explicit method developed in the preceding paper in this issue. Results are presented for the frozen layer thick-ness, the instantaneous heat flux at the cooled surface, and the time-integrated heat transfer at the surface, all as a function of time from the beginning of the freezing period. These quantities are normalized in various ways to illuminate their short-time and long-time behaviors and to enable comparisons between planar and radial freezing. Convection at the solid-liquid interface had virtually no effect on the freezing process at short times, but at longer times the convection significantly slowed the freezing and ultimately terminated it. Solid-solid transitions tended to slow the freezing and also to increase the heat transfer at the cooled surface.