# Lund University Publications

## LUND UNIVERSITY LIBRARIES

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

and (2018) In Energies 11(1).
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... (More)

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.

(Less)
author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Borehole thermal resistance, Boreholes, Calculation, Ground source heat pump (GSHP) systems, Internal thermal resistance, Multipole method, Second-order, Third-order
in
Energies
volume
11
issue
1
article number
en11010214
publisher
MDPI AG
external identifiers
• scopus:85054925820
ISSN
1996-1073
DOI
10.3390/en11010214
language
English
LU publication?
yes
id
c0f3b364-4311-4999-ac54-43792558c693
2018-11-09 09:16:12
date last changed
2021-10-06 03:33:18
```@article{c0f3b364-4311-4999-ac54-43792558c693,
abstract     = {<p>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.</p>},
author       = {Claesson, Johan and Javed, Saqib},
issn         = {1996-1073},
language     = {eng},
number       = {1},
publisher    = {MDPI AG},
series       = {Energies},
title        = {Explicit multipole formulas for calculating thermal resistance of single u-tube ground heat exchangers},
url          = {http://dx.doi.org/10.3390/en11010214},
doi          = {10.3390/en11010214},
volume       = {11},
year         = {2018},
}

```