The behavior of a frozen layer (or “freeze coat”) on the surface of a chilled flat plate traveling with a constant velocity through a warm liquid bath is studied analytically. A perturbation technique is employed to solve the equations governing the shape and temperature of the freeze coat, taking full account of the axial variation of the plate temperature and heat convection from the warm liquid to the moving object. Unlike the case of an isothermal plate where the freeze-coat thickness increases monotonically along the axial direction, here the freeze coat is found to grow only within a limited distance from the inlet. Beyond this distance, the freeze coat begins to decay through remelting. The location at which remelting occurs and the maximum freeze-coat thickness are determined displaying the principal effects of three controlling dimensionless parameters. Criteria for selection of the optimum freeze-coating operation conditions are established and discussed.

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