A new analytical solution for horizontal geothermal heat exchangers with vertical spiral coils

• A new transient analytical solution for horizontal geothermal heat exchangers.
• A good agreement between the new analytical solution and a simulation solution.
• An on-site experiment has been conducted to validate this new analytical model.

Horizontal geothermal heat exchangers (HGHEs) with vertical spiral coils have been increasingly used in ground source heat pump (GSHP) systems. Research studies have been conducted using field tests and simulations trying to reveal the heat transfer mechanism of HGHEs with vertical spiral coils and to provide a good heat transfer performance. However, there is no analytical solution has been established for HGHEs with vertical spiral coils. Of particular interest is the temperature variation at the soil surface. The study presented in this paper proposes the development of a mathematical vertical ring-coil model used to describe the heat transfer process of HGHEs with vertical spiral coils. In this new model, the spiral heat exchanger is simplified as a series of ring coils that inject/extract heat in/from a semi-infinite medium. A single ring model in an infinite medium is first introduced. Using images and superposition, a multiple ring-coils analytical solution is then given. The significant influence on the heat transfer performance of HGHEs temperature variation of the ground surface is then considered. A periodically changed boundary condition is being taken into consideration in the modeling process. The validity of the model was examined by a field test and a 3-D simulation model. The analytical solutions may provide a desirable and better tool for the simulation/design HGHEs with vertical spiral coils.