Calculation model and analytical solution of heat transfer in filling body of deep mines

Heat hazards are becoming increasingly severe for underground mines worldwide, especially for deep mines using the cemented paste backfill (CPB) technology. In order to solve the heat transfer calculation problem, a one-dimensional unsteady state heat transfer model with internal heat source was established for filling body of deep mines. In this model, the cement hydration in CPB was considered as an internal heat source. Using the Green’s function method, the heat transfer equation was solved, and the analytical expression of the temperature field of filling body of deep mines was derived. Specifically, the impacts of initial condition, boundary condition and the cement hydration heat on the temperature distribution were combined based on the principle of superposition, through which the final analytical formula was derived. The resulting theoretical formula revealed that the temperature distribution in CPB was a function of location, Biot number (Bi) and Fourier number (FO). The engineering simplified calculation formula of filling body of deep mines was derived, which provides a fast, accurate and effective method for calculating the temperature field distribution and heat transfer of the filling body. The analysis results show that: as the displacement of the filling body increases, the temperature gradually decreases. The temperature at the top of the body is close to the airflow temperature of the working face.