Thermal boundary layer on a continuous moving plate with freezing

The growth of a solidified layer or "freeze coat" on the surface of a chilled continuous plate traveling steadily through a bath of warm liquid is investigated analytically. The behavior of the thermal boundary layer in the liquid flow field that is induced by the motion of the plate is modeled along with the process of heat conduction in the solid phase to determine the location of the freezing front. Using the method of similarity, axial variations of the freeze-coat thickness and the coefficient of local convective heat transfer from the liquid to the solid phase are obtained as functions of various controlling parameters of the system. It is found that, while the shape of the freeze coat depends strongly on the local convective heat flux, the flow is, in turn, heavily influenced by the variation of the solid/liquid interface location. Because of this mutual interaction between the phase change process and the flow, the local convective heat-transfer coefficient at the freezing front is considerably larger than the corresponding value for the case of forced convection over a continuous moving plate without freezing. The effect of flow/freezing interaction is found to be quite pronounced, especially when the liquid Prandtl number is large and the freeze coat grows rapidly in the axial direction.