Finite cylinder-source model for energy pile heat exchangers: Effect of buried depth and heat load cyclic variations

A solution to the finite cylinder-source model for the ground heat exchangers at a different buried depths that takes into account the heat capacity inside them and allows arbitrary heat rate changes is presented. Analytical expressions for the average ground temperature are derived by integrating the exact solutions over the cylinder-source depth for vertical and time-dependent changes of heat rate. The influence of buried depth variations on thermal response to a constant and uniform mean heat rate of the cylinder-source is examined by the integral mean temperature method in a self-consistent approach. In addition, approximate expressions for steady-state average temperature are derived for periodic heat rate in the long-time limit.