Efficient finite element formulation for geothermal heating systems. Part II: transient

This paper presents an extension to the work presented in Part I of this series of two articles to the transient case. Emphasis is placed on the development of a new model for heat flow in a double U-shape vertical borehole heat exchanger and its thermodynamic interactions with surrounding soil mass. The discretization of the spatial-temporal domain of the heat pipe model is done by the use of the space–time finite element technique in conjunction with the Petrov–Galerkin method and the finite difference method. The paper shows that the proposed model and the choice of the discretization technique, in addition to the utilization of a sequential numerical algorithm for solving the resulting system of non-linear equations, have contributed in reducing significantly the required number of finite elements necessary for describing geothermal heating systems. Details of the mathematical derivations and comparison to experimental data are presented