Dimensionless analysis of the temperature field of surrounding rock in coalface with a finite volume method

Abstract

The thermal conductive mathematical model of surrounding rock was established in a moving coordinate in order to determine the temperature field of surrounding rock around coalface with a moving boundary. It was made possible to have a non-dimensional mathematical model by introducing dimensionless parameters such as Biot coefficient and Peclet coefficient. The dimensionless mathematical model was dispersed with a finite volume method, and then a computer code was developed for determining the temperature field of surrounding rock in coalface. Under the condition where the ratio of face width and semi mining height is 8/3 for example, the dimensionless temperature distribution of surrounding rock is obtained by assuming both the Biot coefficient and Peclet coefficient to be parallel. When the Biot coefficient and Peclet coefficient are assumed to be variants, the results reveal that the temperature increases with the increase of Peclet coefficient at a constant Biot coefficient, while the temperature decreases with the increase of Biot coefficient at a constant Peclet coefficient. Five kinds of working face are chosen for calculation with typical ratio of face width and semi mining height, and each variation curves of unstable heat transfer criterion with increasing Peclet coefficient are obtained with different values of the Biot coefficient, which reveals that the unstable heat transfer criterion increases with the increase of Biot coefficient and Peclet coefficient. The complex calculation of heat dissipating capacity is greatly simplified and the results are given universal significance. The unstable heat transfer criterion can be determined by a consulting graph, and this method provides critical parameters for forecasting air temperature and calculating chilling requirements in coalface.