Second-Order Multipole Formulas for Thermal Resistance of Single U-tube Borehole Heat Exchangers

Research output: Chapter in Book/Report/Conference proceedingPaper in conference proceeding


The borehole thermal resistance is both an important design parameter and a key performance characteristic of a borehole heat exchanger. Another quantity that is particularly important for deep borehole heat exchangers is the internal thermal resistance between the upward-flowing and downward-flowing fluid channels in the borehole. The multipole method is a well-known and robust method to compute both these thermal resistances. However, it has a fairly intricate mathematical algorithm and is thus not trivial to implement. Consequently, there is considerable interest in developing explicit multipole formulas. So far zeroth-order and first-order multipole formulas have been derived for cases where the two legs of the borehole are placed symmetrically in a borehole. This paper presents new explicit second-order multipole formulas, which provide significant accuracy improvements over the previous formulas.


Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Energy Systems
  • Energy Engineering
  • Other Engineering and Technologies


  • Borehole thermal resistance, Multipole method, Ground heat exchanger, Internal thermal resistance, Second-order multipole formulas
Original languageEnglish
Title of host publicationResearch Conference Proceedings, International Ground Source Heat Pump Association Conference & Expo, March 14-16, 2017
Publication statusPublished - 2017 Mar 14
Publication categoryResearch
EventResearch Conference Proceedings - IGSHPA Conference & Expo 2017 - Denver, United States
Duration: 2017 Mar 142017 Mar 16


ConferenceResearch Conference Proceedings - IGSHPA Conference & Expo 2017
CountryUnited States