Mathematical modeling of the heat-exchange process in a quarry bench in permanently frozen rock

The problem is one of determining the temperature field of a bench with the existence of additional auxiliary measures thermal insulation of a certain section of the bench and the installation of seasonal-cooling units (SCU). It is known that SCU are most effective if they are deployed with a sufficient density [1]. Proceeding from the geometric shape of the quarries and technical considerations, let us examine the tiered deployment of SCU. It is obvious that, beginning with a certain distance between cooling units, a row of SCU begins to create a temperature field similar to that surrounding a plate of the same productivity, which is situated in the plane of deployment of the row of SCU. It will be entirely correct, therefore, to examine not the three-dimensional, but the two-dimensional problem. Let us make the following assumptions: the temperature of the coolant (air) throughout the entire depth of the SCU is constant [2], and is