A mathematical model for predicting the densification and growth of frost on a flat plate

Frost deposition on a cold surface exposed to a warm moist air flow is simulated using a one-dimensional, transient formulation based on the local volume averaging technique. The spatial distribution of the temperature, ice-phase volume fraction (related to frost density), and rate of phase change within the frost layer are predicted. The time variation of the average frost density, frost thickness and heal flux at the cold surface shows a good agreement with the experimental data some distance downstream of the leading edge of a cold flat plate, providing that the proper transport properties are used. The results indicate that the local effective vapor mass diffusivity is up to seven times larger than the molecular diffusivity of water vapor in air as expressed by Fick's first law for frost temperatures between 264 and 272 K. This result is comparable with data measured for water vapor diffusion in snow.