A Finite Volume Simulation of Crystal Growth in Water Falling Films over a Cold Isothermal Surface

A numerical model of ice crystal growth in a cooled laminar falling film has been developed using a control volume technique. A source term has been included in the energy equation to represent the phase change energy. The effective values of thermal conductivity, viscosity, thermal diffusivity, and specific heat are considered as functions of the volumetric concentration of ice crystals in the falling film. Film temperature distributions and ice crystal diameters in the film are calculated numerically. It is found that the wall Nusselt number is a function of film thickness and is essentially independent of the Stefan number. The ice crystal growth rate was found to be primarily a function of the Stefan number and film thickness. The ice crystal Nusselt number and super-cooling of the solution are dependent on the Stefan number, while the Reynolds number (film thickness) has a lower influence on these parameters.