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Energies 2018, 11(1), 214; https://doi.org/10.3390/en11010214

Explicit Multipole Formulas for Calculating Thermal Resistance of Single U-Tube Ground Heat Exchangers

1
Building Physics, Lund University, Lund 221 00, Sweden
2
Building Services Engineering, Chalmers Technical University, Gothenburg 412 96, Sweden
Presented at the IGSHPA Technical/Research Conference and Expo, Denver, CO, USA, 14–16 March 2017.
*
Author to whom correspondence should be addressed.
Received: 30 November 2017 / Revised: 10 January 2018 / Accepted: 10 January 2018 / Published: 16 January 2018
(This article belongs to the Special Issue Geothermal Heating and Cooling)
View Full-Text   |   Download PDF [1738 KB, uploaded 16 January 2018]   |  

Abstract

Borehole thermal resistance is both an important design parameter and a key performance characteristic of a ground heat exchanger. Another quantity that is particularly important for ground heat exchangers is the internal thermal resistance between the heat exchanger pipes. Both these resistances can be calculated to a high degree of accuracy by means of the well-known multipole method. However, the multipole method has a fairly intricate mathematical algorithm and is thus not trivial to implement. Consequently, there is considerable interest in developing explicit formulas for calculating borehole resistances. This paper presents derivation and solutions of newly derived second-order and higher-order multipole formulas for calculating borehole thermal resistance and total internal thermal resistance of single U-tube ground heat exchangers. A new and simple form of the first-order multipole formula is also presented. The accuracy of the presented formulas is established by comparing them to the original multipole method. The superiority of the new higher-order multipole formulas over the existing formulas is also demonstrated. View Full-Text
Keywords: borehole thermal resistance; internal thermal resistance; multipole method; ground source heat pump (GSHP) systems; boreholes; calculation; second-order; third-order borehole thermal resistance; internal thermal resistance; multipole method; ground source heat pump (GSHP) systems; boreholes; calculation; second-order; third-order
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Claesson, J.; Javed, S. Explicit Multipole Formulas for Calculating Thermal Resistance of Single U-Tube Ground Heat Exchangers. Energies 2018, 11, 214.

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