Dependence of thermal conductivity of snow on microstructure

A geometrical model, including different geometrical shapes influencing thermal conductivity of snow is proposed. The geometrical model has been assumed to comprise of unit cells having solid (ice) inclusion as an aggregation of spherical, cylindrical or cubical shapes with vertical connection, arranged in a cubic packing. From the geometrical model and one-dimensional heat transfer theory, the effective thermal conductivity has been computed. For this purpose, coupled one-dimensional heat transfer equations have been solved for steady-state condition to account for conduction in ice, conduction in air and latent heat transfer due to water vapour sublimation through air. The model demonstrates the dependency of thermal conductivity on density, grain-spacing, grain contact ratio and temperature. Spherical inclusions give highest conductivity while cubical inclusion estimates lowest value for the same density. Thermal conductivity has been found increasing sharply near to the packing density for all three shapes. Empirical model results and results obtained from existing microstructure based models have also been compared with the present model.

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