A numerical model has been developed to numerically approximate the rate of ice crystal growth in a falling film flowing down a cooled vertical plate for assumed laminar flow. The governing energy equation contains the phase-change energy as a source term. Enhancement of heat transfer due to ice crystal and fluid interactions is accounted for in the use of effective values (thermal conductivity, viscosity, thermal diffusivity, and specific heat), as functions of volumetric concentration of ice in the falling film. Nusselt numbers and overall heat transfer coefficients between the film and cooled plate and ice crystal growth rates were calculated for different film thicknesses, initial ice crystal diameters, and Stefan numbers. Nusselt number and ice crystal growth rate were found to be dependent upon film thickness (flow rate), initial ice number concentration, and Stefan number. Quantitative comparisons of calculated heat transfer coefficients to some previous experimental data show reasonable agreement.

KEYWORDS: models, ice, streamline flow, changing physical state, energy storage, cooling, heat transfer coefficient, comparing, calculating, heat flow, Nusselt number, crystallisation.