Fig. 2

a 2D model of a BHE tube using cylindrical coordinates—the vertical symmetry axis is at x = 0. The colors denote units with different physical properties. For example, the inner pipe (P), the pipe walls and the BHE’s cement (C) (from left to right) are shown in blue colors between x = 0 and x = 0.07 m. Layers 1 to 6 denote different geological units with thermal conductivities of 1.89, 2.6, 2.83, 3.41, 2.97 and 3.4 W m⁻¹ K⁻¹, respectively. b The dashed and dotted black lines show the simulated temperatures at the outer surfaces of the inlet and outlet tubes, respectively. The solid black line shows the undisturbed temperature