Comparison of isothermal and isoflux g-functions for borehole-heat-exchanger fields

A new numerical approach to determine the g-function of a borehole field with the boundary condition of uniform temperature and time-constant mean heat flux at the surface of the boreholes is presented. The method is employed to compare the g-functions obtained by this boundary condition with those obtained by the usual condition of uniform and constant heat flux, for a single borehole and for a field of six boreholes placed in two lines. Boreholes with length 150 m, diameter 15 cm, buried depth 1.5 m and mutual distance 7.5 m, for the field, are considered. The results show that the difference between the two kinds of g-functions is less than 1.5 % for a single borehole, while it reaches 8.7 % for the borehole field, at high values of time. Finally, we show that the superposition of the effects of the single boreholes yields correctly the g-function of the field in the case of uniform heat flux, but overestimates the g-function in the case of uniform temperature and constant mean heat flux.