Solving Stefan’s Problem for Frozen Soil Using New Ecological Methods

The research considers the solution to Stefan’s problem—the determination of temperature fields and thermal conductivity in frozen soil. The authors examine the location of the boundary between frozen and condensed parts of the soil, where the form of the function representing the propagation rate of the freezing front is unknown over time. The authors model the influence of specific shapes of air flows and the quantity of these flows to resolve the indeterminate geometry of the frozen layer. The authors developed a novel numerical method to calculate Stefan’s problem of heat flow propagation, temperature field variations during changes in the aggregate state of the material, and Stefan’s problem at the boundary between two phases. This model was modified by introducing new boundary conditions and a new approach to forming the heat flow pattern within soil layers under the influence of rotating air flows. The authors compiled a set of programs to solve the system of differential equations representing heat conduction problems on the boundary of phase change in soil layers. The novelty of this research lies in the modeling of airflow systems, creating a new metric space of solutions for heat conduction problems, and the formation of phase transition boundaries in zones of airflow bifurcation. The speed and shape of the phase boundary change are determined by the imbalance of the rotating airflow. The creation of such flows in the area of laying technological systems for water and gas supply instills confidence in establishing correct temperature fields and the location of boundaries between frozen and condensed parts of the soil.