Analytical solution of heat transfer for energy soldier piles considering convection at the ground surface and internal wall of underground space

This paper presents a new 2-D heat transfer model for the energy soldier pile wall-internal structural wall during the operation and maintenance period of the internal building. Both the convection at the ground surface and the internal wall boundary convection effects are considered. The analytical solution to the problem is obtained by using the separation variable method and is compared with numerical solutions and an existing analytical solution to verify the correctness of the solution. The effects of the convection coefficient, thickness of overlying soil, and soil thermal conductivity on heat transfer are analyzed. Results show that the dimensionless temperature rise decreases with increasing internal/external convection heat transfer coefficient, increasing thickness of overlying soil, and decreasing soil thermal conductivity. For different times of operation, the temperature below the dimensionless depths of 2.1/6.6/9.5 (for the soil side) and 3.4/7.5/10.0 (for the underground space side) is mainly controlled by the heat source. For the summer conditions, the average air temperature is higher than the average pile-soil temperature, it is the ambient temperature that dominates, not the convection coefficient. The depths of ground convection effects corresponding to thicknesses of less than 1.0 m on the 30th day of operation are concentrated at depths of about 10.0. Under the premise of ensuring structural and engineering safety, using the smaller thickness of overlying soil has a better effect on both heat flux and temperature rise.