A Mathematical Model for the Analysis of the Flow and Heat Transfer Problem in U-shaped Geothermal Exchangers

We propose a mathematical model for U-shaped geothermal heat exchangers based on the unsteady Navier-Stokes problem. In the numerical solution of this problem, we divide the exchanger into two computational domains: the rectilinear pipes, where the temperature field is computed analytically, and the U-curved pipe, where solutions of both the flow and the heat exchange are calculated by a numerical procedure based on Galerkin finite elements method. Results of some numerical simulations are provided and used to study the performance of geothermal exchangers by assessing the effective energy produced. These results consider also a validation analysis with experimental measurements obtained from a real geothermal exchanger.