The effects of heat generation and wall interaction on freezing and melting in a finite slab

The processes of freezing and melting occurring in a heat-generating slab bounded by two semi-infinite cold walls is studied numerically. The method of collocation is employed to solve the various sets of governing equations describing the unsteady behavior of the system during different periods of time. Depending on the rate of internal heat generation and the thermal properties of the wall and the slab, several changes may take place in the system. These changes, as indicated by the transient locations of the solid-liquid interface, include transitions from freezing directly to melting, from freezing to cooling without phase change, from cooling to heating without phase change, and from heating to melting. Numerical predictions of the occurrence of these transitions, the rates of freezing and melting, and the duration of the transients are obtained as functions of several controlling dimensionless parameters of the system. Comparison is made with the case of a heat-generating sphere to further explore the effect of system geometry.