Analytical solution for the simulation of ground thermal conditions around planar trench collectors

• 3D analytical model for planar trench collectors for dimensioning purposes. • The model comprises the finite plane source, seasonal fluctuations and the collector resistance. • The analytical model is verified with numerical simulations and validated with experimental measurements. • computationally optimised solution of the finite plane source. Vertical planar installations in shallow ground are uncommon technological variants for geothermal heat supply. Still, they are of increasing interest when depth and space restrictions do not allow the drilling of boreholes or the installation of horizontal collectors. This work is dedicated to plate-shaped closed-loop heat exchangers that are installed in trenches at a few meters depth. A novel three-dimensional analytical model is presented that accounts for the thermal properties as well as seasonal temperature variation in the ground. The model represents the trench collector as a finite plane source with a specific thermal resistance to simulate the mean temperature of the circulating heat carrier fluid. Both, a detailed dimensional analysis and a successful comparison to numerical simulation are presented. Even though only conductive heat transport is simulated, the model could be validated to the conditions observed at an experimental field site with a trench collector installed at Biberach, Germany. The presented analytical method can serve as an ideal tool for the fast dimensioning of vertical planar heat collectors in practice, and it represents a fundamental framework for the integration of advection or latent heat transfer in frozen ground.