Short-time analysis of vertical boreholes, new analytic solutions and choice of equivalent radius

In the classical methods to analyze ground heat exchanger, the thermal capacity of the boreholes is often neglected. In recent years, several models have been proposed to take into account this effect that can be important for better design. We have presented in our previous paper, an analytical model that can take into account the thermal mass of the backfill material. However, this model did not take into account the thermal capacity of the heat transfer fluid inside the pipes. In recent years, some semi-analytical models were proposed to take this effect into account. In this paper, we give the full analytical solution of this problem. Analytical models have the advantage to easily generate results for different configurations and time scales. When applied to real boreholes, these models use the concept of equivalent radius. This choice is not unique and the influence of the choice of this radius will also be discussed in this paper.