Mathematical modeling of non-stationary heat exchange process and determination of air temperature changes in underground ventilation tract

The article discusses the issues of mathematical modeling of non-stationary heat exchange processes when air moves through an underground ventilation duct. To solve the process of unsteady heat transfer during air movement in a straight cylindrical underground channel, many scientists around the world conducted research and they obtained certain solutions to this problem. Analytical solutions for changes in supply air temperature in underground ventilation ducts were obtained by K. Van Heerden, E.V. Stefanov. The air temperature at the outlet of the channel without distortion reproduces changes in the air temperature at the inlet, but with some time lag and a change in the absolute value, therefore it is advisable to consider non-stationary heat exchange in single underground channels with a variable air temperature at the inlet, which makes it possible to identify the parameters of the supply underground ventilation ducts. The efficiency of air cooling and heating processes becomes effective at an air speed of 10 m/s, which corresponds to a slight change in air temperature. Changes in the temperature of the air moving in the channel in all cases will be determined by the magnitude of the temperature difference between the media exchanging heat, the time of thermal interaction of the supply air with the soil, and the size of the heat exchange surface. Based on the given mathematical equations, a computer program was developed and as a result a spectrum of graphs was obtained. These graphs of computer models allow scientific analysis of the studied physical processes of heating and cooling of air.