# Explicit multipole formulas and thermal network models for calculating thermal resistances of double U-pipe borehole heat exchangers

Forskningsoutput: TidskriftsbidragArtikel i vetenskaplig tidskrift

### Standard

I: Science and Technology for the Built Environment, Vol. 25, Nr. 8, 2019, s. 980-992.

Forskningsoutput: TidskriftsbidragArtikel i vetenskaplig tidskrift

### RIS

TY - JOUR

T1 - Explicit multipole formulas and thermal network models for calculating thermal resistances of double U-pipe borehole heat exchangers

AU - Claesson, Johan

AU - Javed, Saqib

PY - 2019

Y1 - 2019

N2 - Double U-pipe boreholes are the second most used type of ground heat exchangers after single U-pipe boreholes. The borehole thermal resistance is a key design and performance parameter for the double U-pipe boreholes. Another parameter that is particularly important for double U-pipe boreholes is the internal thermal resistance between the U-pipes. There is, however, a general lack of methods that can be used to calculate the thermal resistances of the double U-pipe boreholes. This article presents explicit multipole formulas for calculating thermal resistances of double U-pipe boreholes with symmetrically positioned pipes. The presented formulas include zeroth- and first-order expressions for the borehole thermal resistance and the internal thermal resistance. The internal thermal resistance formulas cover various possible flow configurations of the heat carrier fluid in the double U-pipes. The accuracy of the presented zeroth- and first-order formulas is established by comparing them to the original 10th-order multipole method. The article also presents thermal network models for computing effective borehole thermal resistance of double U-pipe boreholes from the multipole resistances. Formulas for calculating effective borehole thermal resistance of double U-pipe boreholes are presented for two idealized cases of uniform heat flux and uniform average wall temperature along the borehole.

AB - Double U-pipe boreholes are the second most used type of ground heat exchangers after single U-pipe boreholes. The borehole thermal resistance is a key design and performance parameter for the double U-pipe boreholes. Another parameter that is particularly important for double U-pipe boreholes is the internal thermal resistance between the U-pipes. There is, however, a general lack of methods that can be used to calculate the thermal resistances of the double U-pipe boreholes. This article presents explicit multipole formulas for calculating thermal resistances of double U-pipe boreholes with symmetrically positioned pipes. The presented formulas include zeroth- and first-order expressions for the borehole thermal resistance and the internal thermal resistance. The internal thermal resistance formulas cover various possible flow configurations of the heat carrier fluid in the double U-pipes. The accuracy of the presented zeroth- and first-order formulas is established by comparing them to the original 10th-order multipole method. The article also presents thermal network models for computing effective borehole thermal resistance of double U-pipe boreholes from the multipole resistances. Formulas for calculating effective borehole thermal resistance of double U-pipe boreholes are presented for two idealized cases of uniform heat flux and uniform average wall temperature along the borehole.

U2 - 10.1080/23744731.2019.1620565

DO - 10.1080/23744731.2019.1620565

M3 - Article

AN - SCOPUS:85073575586

VL - 25

SP - 980

EP - 992

JO - Science and Technology for the Built Environment

JF - Science and Technology for the Built Environment

SN - 2374-4731

IS - 8

ER -