Mass transfer on and within a frost layer

Abstract

This paper investigates fundamental phenomena related to understanding of frost deposition and growth. The water vapor mass transfer rate from the air stream to a frost surface was tested and the results analyzed. The water vapor pressure at the frost surface was found to be supersaturated, and this phenomenon is explained using laminar concentration boundary layer analysis. A simple equation for calculating the supersaturated water vapor density at the frost surface was developed using boundary layer analysis, and it was compared to the experimental data. The comparison showed that the proposed equation for the water vapor supersaturation degree at the frost surface agrees well with the experimental data. The physical meaning of the tortuosity factor, which is related to mass diffusion within the frost layer, is mathematically explained, and published correlations were reviewed. It was found that some existing correlations are basically empirical curve fits that force agreement of the frost growth rate with the measured values. Further, these empirical curve fits do not satisfy the known physical bounds on the tortuosity factor. This deficiency further supports the existence of supersaturation at the frost surface. The effect of uncertainty in tortuosity factor on the heat transfer rate through a frost layer was quantitatively analyzed, and it was found that its uncertainty does not significantly affect the heat transfer rate through the frost layer in typical frosting conditions.