Analysis of the frost growth on a flat plate by simple models of saturation and supersaturation

When humid air comes in contact with a cold surface maintained below the freezing temperature, heat and mass transfer occur and a frost layer begins to grow. Simple models for the growth of the frost layer on a flat plate are presented and they focus on diffusion and phase change inside the porous media. A simple model was built on the assumption that the water-vapor concentration at the frost surface is saturated, and that the gradient of vapor pressure is the same as the value obtained from the Clausius-Clapeyron equation. It was found that initial porosity of the frost layer affected the characteristics of frost growth. In order to solve the inconsistency of the diffusion resistance of water-vapor in the region of high porosity, the model was modified with the assumption that the concentration of water-vapor at the frost surface was in supersaturation. Two parameters controlling the densification and thickness growth of the frost layer were obtained.