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

Author

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  • Johan Claesson

    (Building Physics, Lund University, Lund 221 00, Sweden)

  • Saqib Javed

    (Building Services Engineering, Chalmers Technical University, Gothenburg 412 96, Sweden)

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.

Suggested Citation

  • Johan Claesson & Saqib Javed, 2018. "Explicit Multipole Formulas for Calculating Thermal Resistance of Single U-Tube Ground Heat Exchangers," Energies, MDPI, vol. 11(1), pages 1-17, January.
    • Handle: RePEc:gam:jeners:v:11:y:2018:i:1:p:214-:d:127184
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    References listed on IDEAS

    as
    1. Spitler, Jeffrey D. & Gehlin, Signhild E.A., 2015. "Thermal response testing for ground source heat pump systems—An historical review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 50(C), pages 1125-1137.
    2. Ana Vieira & Maria Alberdi-Pagola & Paul Christodoulides & Saqib Javed & Fleur Loveridge & Frederic Nguyen & Francesco Cecinato & João Maranha & Georgios Florides & Iulia Prodan & Gust Van Lysebetten , 2017. "Characterisation of Ground Thermal and Thermo-Mechanical Behaviour for Shallow Geothermal Energy Applications," Energies, MDPI, vol. 10(12), pages 1-51, December.
    3. Ma, WeiWu & Li, Min & Li, Ping & Lai, Alvin C.K., 2015. "New quasi-3D model for heat transfer in U-shaped GHEs (ground heat exchangers): Effective overall thermal resistance," Energy, Elsevier, vol. 90(P1), pages 578-587.
    4. Spitler, Jeffrey D. & Javed, Saqib & Ramstad, Randi Kalskin, 2016. "Natural convection in groundwater-filled boreholes used as ground heat exchangers," Applied Energy, Elsevier, vol. 164(C), pages 352-365.
    5. Javed, Saqib & Spitler, Jeffrey, 2017. "Accuracy of borehole thermal resistance calculation methods for grouted single U-tube ground heat exchangers," Applied Energy, Elsevier, vol. 187(C), pages 790-806.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

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    5. Joanna Piotrowska-Woroniak, 2021. "Determination of the Selected Wells Operational Power with Borehole Heat Exchangers Operating in Real Conditions, Based on Experimental Tests," Energies, MDPI, vol. 14(9), pages 1-21, April.
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    7. Christopher Vella & Simon Paul Borg & Daniel Micallef, 2020. "The Effect of Shank-Space on the Thermal Performance of Shallow Vertical U-Tube Ground Heat Exchangers," Energies, MDPI, vol. 13(3), pages 1-16, January.
    8. Coninx, Matthijs & Nies, Jarne De & Hermans, Louis & Peere, Wouter & Boydens, Wim & Helsen, Lieve, 2024. "Cost-efficient cooling of buildings by means of geothermal borefields with active and passive cooling," Applied Energy, Elsevier, vol. 355(C).
    9. Bi, Yuehong & Lyu, Tianli & Wang, Hongyan & Sun, Ruirui & Yu, Meize, 2019. "Parameter analysis of single U-tube GHE and dynamic simulation of underground temperature field round one year for GSHP," Energy, Elsevier, vol. 174(C), pages 138-147.
    10. Aminhossein Jahanbin & Giovanni Semprini & Andrea Natale Impiombato & Cesare Biserni & Eugenia Rossi di Schio, 2020. "Effects of the Circuit Arrangement on the Thermal Performance of Double U-Tube Ground Heat Exchangers," Energies, MDPI, vol. 13(12), pages 1-19, June.

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