Freezing and Thawing of Wet Soil from the Surface and Around the Underground Pipeline

Abstract

This paper reveals a method for an approximate solution to the heat exchange problem with a phase transition in a wet finely dispersed soil in an infinite one-dimensional axisymmetric region. Some artificial techniques help to replace non-monotonic functions with a certain combination of monotonic ones. Then it becomes possible to apply comparison theorems or integral inequalities to draw the boundaries of the solution. The solution has the form of a system of functions that alternately find a majorant of the desired solution from top to bottom. The solution error is the value known and controlled at each stage of the solution. The proposed method can be used in engineering calculations, as well as a reference for estimating the accuracy of numerical and approximation techniques.