A new model and analytical solution for heat transfer in the heating section of energy tunnels considering the insulation layer

Energy tunnels in cold regions represent an innovative integration of ground-source heat pump systems with tunnel lining technology. Harnessing geothermal energy to offer frost protection and warmth to the tunnel lining provides the dual benefits of environmental sustainability and economic efficiency. To evaluate the heating effect of energy tunnels in cold regions, a new semicircular heat transfer model is proposed in this paper; it describes the temperature field distribution of the tunnel lining and the surrounding rock. The analytical solution of the model was obtained using the superposition principle and the Laplace transform method, and its accuracy was verified through indoor model tests. The model was then used to analyze the effects of varying insulation thicknesses and different thermal conductivities of the insulation on the temperatures of the tunnel lining and surrounding rock. The findings reveal that the zone of temperature influence, using ground heat exchangers (GHEs) system, is approximately 0.5 times the diameter of the tunnel from the heat source. Besides, reducing the thermal conductivity of the insulation layer has a similar effect to increasing its thickness, and in tunnel lining GHEs systems, both lower thermal conductivity and greater thickness of the insulation layer lead to greater heat accumulation at the lining interface. Therefore, when designing energy tunnels in cold regions, it is essential to consider the thickness and type of insulation layer according to actual conditions.