Explicit multipole formula for the local thermal resistance in an energy pile-the line-source approximation
(2020) In Energies 13(20).- Abstract
This paper presents a closed-form quite handy formula for the local thermal resistance Rb between the temperature of the bulk heat-carrier fluid in the pipes, equally spaced on a concentric circle inside a circular energy pile, and the mean temperature at the periphery of the pile. The so-called multipole method is used to calculate the temperature field. An important improvement of the multipole method is presented, where Cauchy's mean value theorem of analytical functions is used. The formula for thermal resistance Rb0 for the zero-order approximation (J = 0), where only line heat sources at the pipes are used, is presented. The errors using zeroth-order approximation (J = 0) are shown to be quite small by comparisons with eight-order... (More)
This paper presents a closed-form quite handy formula for the local thermal resistance Rb between the temperature of the bulk heat-carrier fluid in the pipes, equally spaced on a concentric circle inside a circular energy pile, and the mean temperature at the periphery of the pile. The so-called multipole method is used to calculate the temperature field. An important improvement of the multipole method is presented, where Cauchy's mean value theorem of analytical functions is used. The formula for thermal resistance Rb0 for the zero-order approximation (J = 0), where only line heat sources at the pipes are used, is presented. The errors using zeroth-order approximation (J = 0) are shown to be quite small by comparisons with eight-order approximation (J = 8) with its accuracy of more than eight digits. The relative error for the local thermal resistance Rb0 for the zero-order approximation (J = 0) lies below 5% for a wide range of input parameter values. These ranges are judged to cover most practical cases of application. The smallest local thermal resistance Rbmin is, with some exceptions, obtained when the pipes lie directly in contact with the pile periphery. A neat formula for this minimum is presented.
(Less)
- author
- Claesson, Johan LU and Javed, Saqib LU
- organization
- publishing date
- 2020
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Energy piles, Ground source heat pump (GSHP), Local thermal resistance, Minimum thermal resistance, Multipole method, Pile foundations, Thermal piles
- in
- Energies
- volume
- 13
- issue
- 20
- article number
- 5445
- publisher
- MDPI AG
- external identifiers
-
- scopus:85093930269
- ISSN
- 1996-1073
- DOI
- 10.3390/en13205445
- language
- English
- LU publication?
- yes
- id
- 2dc975b7-d853-4821-996f-b4fcdf696251
- date added to LUP
- 2020-11-06 08:40:30
- date last changed
- 2022-04-19 01:47:49
@article{2dc975b7-d853-4821-996f-b4fcdf696251,
abstract = {{<p>This paper presents a closed-form quite handy formula for the local thermal resistance Rb between the temperature of the bulk heat-carrier fluid in the pipes, equally spaced on a concentric circle inside a circular energy pile, and the mean temperature at the periphery of the pile. The so-called multipole method is used to calculate the temperature field. An important improvement of the multipole method is presented, where Cauchy's mean value theorem of analytical functions is used. The formula for thermal resistance Rb0 for the zero-order approximation (J = 0), where only line heat sources at the pipes are used, is presented. The errors using zeroth-order approximation (J = 0) are shown to be quite small by comparisons with eight-order approximation (J = 8) with its accuracy of more than eight digits. The relative error for the local thermal resistance Rb0 for the zero-order approximation (J = 0) lies below 5% for a wide range of input parameter values. These ranges are judged to cover most practical cases of application. The smallest local thermal resistance Rbmin is, with some exceptions, obtained when the pipes lie directly in contact with the pile periphery. A neat formula for this minimum is presented.</p>}},
author = {{Claesson, Johan and Javed, Saqib}},
issn = {{1996-1073}},
keywords = {{Energy piles; Ground source heat pump (GSHP); Local thermal resistance; Minimum thermal resistance; Multipole method; Pile foundations; Thermal piles}},
language = {{eng}},
number = {{20}},
publisher = {{MDPI AG}},
series = {{Energies}},
title = {{Explicit multipole formula for the local thermal resistance in an energy pile-the line-source approximation}},
url = {{http://dx.doi.org/10.3390/en13205445}},
doi = {{10.3390/en13205445}},
volume = {{13}},
year = {{2020}},
}