The Problem of Heat and Mass Transfer in Melting Snow and Ice Cover Taking into Account The External Heat Flow

Based on the Muskat-Leverett two-phase filtration equations, a model problem of water and air movement in melting snow is considered, taking into account the external heat flow. The maximum principle and the finite-velocity lemma for perturbations are proven for water saturation. An algorithm for numerically studying the self-similar problem is presented. Calculations of the temperature and water saturation distributions by depth are presented. The significant influence of the specified flux at the boundary and the thermal conductivity coefficient on the temperature field in the snow layer is demonstrated, which is important for predicting melting and hydrothermal processes in snow and ice covers. A theorem on the existence of a weak solution to this problem is formulated. A literature review is provided on mathematical models of multiphase filtration in porous media, taking into account phase transitions (melting, sublimation) and external heat fluxes.