The analysis of transient heat conduction for ground heat exchangers using analytical and numerical methods
The two dimensional transient heat conduction surrounding ground heat exchangers in clay soils is investigated analytically and numerically using finite element methods. The study is directed towards the application of the ground heat exchangers in a central solar heating plant with seasonal storage (CSHPSS). The analytical solution to the transient heat conduction for both the borehole and the U-tube configurations are presented.
The analytical solution to the transient heat conduction in the hollow cylinder geometry is derived in cylindrical coordinates using the separation of variables method. The results of this solution are used to validate the finite element models of the borehole geometry. The procedures for developing the finite element models are included. The finite element modeling was extended to the geometry of the U-tube ground heat exchanger. Results are presented for the transient heat exchange performance of the U-tube for variations in geometry, material properties, and boundary conditions.
The solution of the heat conduction in a circular region with two internal point sources of energy generation is derived in cylindrical coordinates to approximate the heat transfer for the U-tube geometry. The temperature profiles of the analytical solution compared closely to the finite element model of the U-tube geometry despite the inherent differences of the two models.
The finite element models were further used to demonstrate that the geometry of the borehole can be used to approximate the transient thermal performance of a U-tube ground heat exchanger. The heat exchange performance of the two configurations compared closely over time beyond a short initial transient period.