Second-order Multipole Formulas for Thermal Resistance of Single U-tube Borehole Heat Exchangers
Paper in proceeding, 2017

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.

Multipole method

Internal thermal resistance

Second-order multipole formulas

Borehole thermal resistance

Ground heat exchanger


Saqib Javed

Chalmers, Civil and Environmental Engineering, Building Services Engineering

Johan Claesson

Chalmers, Civil and Environmental Engineering, Building Technology

Proceedings of the IGSHPA Technical/Research Conference and Expo 2017, March 14-16, Denver

Subject Categories

Energy Engineering

Geotechnical Engineering

Energy Systems



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