Frosting occurs on heat exchangers in heat pumping and refrigeration applications when the surface temperature of the heat exchanger is below the freezing point of water. The accumulation of frost on the heat transfer surface increases pressure drop (fan power) and decreases heat transfer, because the frost layer has a low thermal conductivity much lower than that of the heat exchanger material, and it blocks the air flow. System efficiency is reduced by frost accumulation, and operation is complicated by the need to defrost the heat exchanger. Many factors including air temperature, humidity, and cold plate temperature are known to affect frost growth on heat transfer surfaces. In the present study, a model for frost growth on and densification on flat surfaces is presented. The mathematical model is developed by analytically solving the governing heat and mass diffusion equations with appropriate boundary conditions. For temperature, a convective boundary condition at the frost surface and a fixed cold plate temperature were used. However, for the water-vapor density, the condition at the frost surface is unknown. Unlike earlier saturation and supersaturation models, the current work is based on a specified heat flux obtained experimentally in order to find the density gradient at the surface. From the results, it can be shown that the water-vapor at the frost-air interface is supersaturated.
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