Heat-source solutions to heat conduction in anisotropic media with application to pile and borehole ground heat exchangers

This work analyzes influence of anisotropy of anisotropic soil on the processes of heat transfer by ground heat exchangers used in ground-coupled heat pump systems. First, this paper uses the heat-source theory to develop several explicit exact solutions for heat conduction in anisotropic infinite or semi-infinite media with internal line, cylindrical-surface, or spiral-line sources. These solutions will reduce to common heat-source solutions for isotropic media. Next, these general solutions are applied to borehole ground heat exchangers and energy piles (or pile ground heat exchangers). Then, temperature responses of borehole and pile ground heat exchangers are examined in depth. Especially, the cylindrical-surface source model and the spiral-line source model are compared when applied to energy piles with spiral coils. An interesting result of this comparison is that these two models yield the almost same average temperature at the pile wall, implying these two models should be equivalent for modeling responses of energy piles with spiral coils. However, compared to the cylindrical-surface model, spiral-line model is physically reasonable but is computation-intense. Moreover, the theoretical analysis shows that anisotropy of the medium has little effect on the short-term performance of ground heat exchangers but influences the long-term temperature responses obviously.

► We derived solutions to heat conduction in anisotropic solids with heat sources. ► Anisotropy affects long-term behavior of ground heat exchanger (GHE) greatly. ► Cylindrical surface and spiral-line models are equivalent for modeling pile GHEs. ► Compared to cylindrical surface model, spiral-line model is computation-intensive.