A new analytical model for short vertical ground heat exchangers with Neumann and Robin boundary conditions on ground surface

While ground surface conditions have been counted accurately in numerical models of ground heat exchangers (GHE) by defining a Neumann or Robin boundary condition, current analytical models of vertical GHE still commonly adopt a Dirichlet boundary condition. Using a new integral transform method, this paper developed a new analytical model of vertical GHE with three different (Dirichlet, Neumann, and Robin) top boundary conditions. The new model was validated analytically and numerically. Using the new model, the effect of different ground surface boundary conditions on temperature responses of vertical GHE is studied. As an example of application of the proposed model, a case study of soil borehole thermal energy storage (SBTES) systems where the borehole top is covered with insulation material was presented. Results show that the calculated average temperature along the depth of vertical GHE by using the Dirichlet boundary condition would be 14.1% and 8.5% less compared with using the Neumann and Robin boundary condition respectively in the long term. The percentages may in turn quantify the improvement in thermal energy storage by placing insulation cover over boreholes in practical engineering.