Mathematical model to analyze the flow and heat transfer problem in U-shaped geothermal exchangers

In this study, 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: rectilinear pipes where the temperature field is computed analytically, and a U-curved pipe where solutions for both the flow and heat exchange are calculated using a numerical procedure based on the Galerkin finite elements method. The results of some numerical simulations are provided and used to study the performance of geothermal exchangers by assessing the effective energy produced. We also present a validation analysis based on experimental measurements obtained from a real geothermal exchanger.