A model of the thermal conductivity of porous water ice at low gas pressures

This study is concerned with energy transfer in porous water ice at large Knudsen numbers of the sublimated gas. We present a formula for the effective thermal conductivity, λ eff, which is found to be valid for a wide range of material parameters, in particular also for high porosity materials, where other expressions for λ eff published in the literature lose their validity. It is found that above ∼ 190 K λ eff increases strongly with temperature and depends mainly on the average grain size, while at low temperatures it is primarily controlled by the value of the Hertz-factor. The influence of the porosity is relatively weak. The reliability of our expression for λ eff has been checked by comparing computed temperature profiles with the temperature recordings of comet simulation experiments. The predicted temperatures are in good agreement with the experimental results. Finally, our model is applied to a typical surface layer of a cometary nucleus. A strong temperature dependence of the effective thermal conductivity in cometary water ice is predicted.