Two new analytical models for heat transport in ground-coupled heat pump system with heat loss at ground surface: A new meshless treatment of ground heat exchanger for reflecting heat capacity effect

Abstract

Existing boundary conditions or source terms specified at cylindrical ground heat exchangers (GHEs) in ground-coupled heat pump (GCHP) systems neglect the effect of GHE heat capacity. This study modifies a governing equation as a new meshless GHE treatment reflecting the effect by the product of a coefficient and temperature time derivative. Two new analytical models are developed for depicting heat transport in a GCHP system with heat loss at the ground surface. The two-zone model adopts two coupled governing equations describing heat transport in the GHE and soil formation zones. The single-zone model applies the new GHE treatment for the GHE zone with the governing equation for the formation zone. Analytical solutions of the models are derived; finite element solutions are built to release analytical solutions’ assumption of the same thermal property of the GHE and formation below the GHE. Results suggest the coefficient equals the half product of the GHE density, specific heat, and square of its radius divided by its thermal conductivity. Both analytical solutions agree to temperature within 6.2 % relative difference and 5 % for most time of a heating or cooling season, applicable to most GHEs. One finite element solution with the new meshless GHE treatment takes about 1 % of the computing time of acquiring the other finite element solution based on the governing equation and fine GHE discretization. The assumption causes 10.6 % relative error in temperature at the GHE bottom, but the error dramatically decreases below 5 % elsewhere. The present solution applies to a field GCHP experiment. In conclusion, this study may provide a better understanding of GCHP systems and useful approach for field applications.