| Abstract |
We present analytical solutions for the temperature around the borehole heat exchanger which account for: (I) finite length line-source; (II) natural vertical gradient of the ground temperature; (III) arbitrary changes of the ground surface temperature. We find that the time-dependent part of the solution decays as a power of the time approaching the steady state limit. The long-time limit and asymptotic approach to this limit differ from that predicted by the infinite line-source model for very large times. We present series for the temperature in time scaled by the longitudinal and the transverse borehole lengths that also enables to determine the thermal conductivity of the ground, that is a critical parameter in designing geothermal borehole, and clarifies the estimation of the duration of the thermal response test. |