Short-term behavior of classical analytic solutions for the design of ground-source heat pumps

Over the years several methods have been proposed to simulate and design the earth heat exchanger for a ground-source heat pump (GSHP) system. Some of these methods are based on numerical techniques while others rely on analytic solutions. Among the latter, two classical solutions have been extensively used over the years, the infinite line source (ILS) solution and the infinite cylindrical source (ICS). These solutions were known to overestimate the fluid temperature when the time scale is important and are valid only in a time range between a minimum and a maximum value which are often adequate for must design applications. It is usually accepted that for small Fourier numbers, the ICS solution should be used instead of the ILS. This paper revisits the short-term behavior of these solutions and we arrive at different conclusions than those usually accepted in the literature if the Fourier number is based on the borehole radius, which is normally the case. The reasons for these discrepancies are discussed and several options are proposed.