Modelling the ground volume for numerically generating single borehole heat exchanger response factors according to the cylindrical source approach

Borehole heat exchangers (BHE) are the most common solution for ground coupled heat pumps (GCHP).The thermal interactions with ground and the GCHP performance are strictly related to a number of fac-tors, including the ground properties, the BHE field geometry, the sequence and strength of heat loadsrequired by the building. A typical assumption to solve this problem is assuming the ground volumeas a purely conductive medium with constant properties: in such a way the transient Fourier equationcan be solved either analytically or numerically with a reasonable computational effort provided that asimple BHE geometry is considered. According to this approach suitable temperature response factorscan be calculated: they account for constant heat transfer rate conditions and they can be later applied tosuperposition techniques for simulating transient heat loads to/from the ground. In literature a numberof reference geometries and related temperature response factors for BHE modelling are available. Theyinclude the infinite and finite line source and the infinite cylindrical source, at imposed heat transfer rateor even imposed temperature. The aim of this paper is to develop a reliable numerical model for gener-ating temperature response factors for the single BHE according to different geometrical and boundaryconditions. A detailed analysis is carried out to recast the Fourier equation and to efficiently solve it withsuitable numerical parameters. The results are compared with literature analytical data and new insightsare provided to the temperature response factor approach for simulating GCHP systems.