Temperature distribution in a field of long Borehole Heat Exchangers (BHEs) subjected to a monthly averaged heat flux

A method to evaluate the long-term temperature distribution in a field of long Borehole Heat Exchangers (BHEs) subjected to a monthly averaged heat flux is presented, under the assumption that the effects of the groundwater flow are negligible. Each BHE is considered as a cylindrical heat source with diameter D and length L. For each ratio L/D and dimensionless radial distance r/D, the g-function (time-dependent dimensionless temperature, averaged along the BHE length, due to a uniform and constant heat load) is determined by finite-element simulations and written in polynomial form through accurate interpolations, in a very broad range of values of the dimensionless time. Tables of the coefficients of the polynomial functions are provided. The g-functions are then used to determine the time evolution of the mean dimensionless temperature at the interface BHE-ground, averaged among BHEs, for some BHE fields subjected to a monthly averaged heat load.