Finite cylinder-source model for energy pile heat exchangers: Effects of thermal storage and vertical temperature variations

A mean integral solution to the FCS (finite cylindrical source) model for ground heat exchangers that takes into account the heat capacity inside the borehole or foundation and allows estimation of temperature field for an arbitrary borehole configuration is presented as a single integral. Approximate expressions for the average temperature over a wide range of time values are derived analytically in the vicinity of both sides of the finite cylindrical surface of heat source. Exact and approximate results for the mean temperature are compared to those calculated at the mid-depth from the exact solution of the same FCS model.