Effective Thermal Conductivity of Frost

Abstract

If a temperature gradient exists in a frost layer energy is transferred from the warm to the cold side by molecular conduction, by water vapor diffusion, by radiation and occasionally by natural convection of the pore gas. A theoretical and experimental study has been carried out on the influence of these different transport mechanisms on the total energy flux in frost. This total energy flux can be represented by an effective thermal conductivity. An order of magnitude estimate and experiments on the temperature dependence of the thermal conductivity of frost indicate that radiation can be neglected. Natural convection cannot occur in horizontal frost layers forming opposite to the gravity vector. Furthermore, in other cases the contribution of natural convection in practically existing frost layers is normally negligible. There are, however, some uncertainties which should be studied by special experiments. The equivalent diffusion conductivity is mainly a function of the local temperature and the frost density. Measurements of the diffusion resistance in frost yield an equation for the diffusion heat flux. Its effect on the total heat flux reaches ratios of about 35% at 0°C and decreases rapidly with decreasing temperature and increasing density. Experimental data for pure molecular conduction are presented. Furthermore a simple pore model is defined with one parameter to be fitted to such data. The respective relationship for the conductivity due to conduction is in relatively good agreement with data of different authors.