A transient natural convection heat transfer model for geothermal borehole heat exchangers

The effect of buoyancy-driven natural convection on the performance of ground-coupled heat exchangers of closed loop geothermal systems is investigated. The governing equations of continuity, momentum, and energy balance are derived, taking into account a porous ground medium fully saturated with liquid water. Boussinesq approximation is used to model the effect of buoyancy forces in water. A three-dimensional finite-volume discretization method over a structured mesh is used to solve the governing equations numerically. The performance of the ground-coupled heat exchanger system is assessed based on the rate of energy extraction and the outlet fluid temperature. The effects of hydraulic conductivity of the heat exchange medium and seasonal variations of heat load on the heat transfer phenomenon are studied. The results are evaluated by comparing them against the results of existing conduction-based heat transfer models. The influence of natural convection on the sustainable rate of heat extraction from a geothermal resource is underlined and interpreted.