# Explicit multipole formulas for calculating thermal resistance of single u-tube ground heat exchangers

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**Explicit multipole formulas for calculating thermal resistance of single u-tube ground heat exchangers.** / Claesson, Johan; Javed, Saqib.

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*Energies*, vol. 11, nr. 1, en11010214. https://doi.org/10.3390/en11010214

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*Energies*,

*11*(1), [en11010214]. https://doi.org/10.3390/en11010214

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*Energies*. 2018. 11(1). https://doi.org/10.3390/en11010214

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TY - JOUR

T1 - Explicit multipole formulas for calculating thermal resistance of single u-tube ground heat exchangers

AU - Claesson, Johan

AU - Javed, Saqib

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

KW - Borehole thermal resistance

KW - Boreholes

KW - Calculation

KW - Ground source heat pump (GSHP) systems

KW - Internal thermal resistance

KW - Multipole method

KW - Second-order

KW - Third-order

U2 - 10.3390/en11010214

DO - 10.3390/en11010214

M3 - Article

AN - SCOPUS:85054925820

VL - 11

JO - Energies

JF - Energies

SN - 1996-1073

IS - 1

M1 - en11010214

ER -