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Transient Multipole Expansion for Heat Transfer in Ground Heat Exchangers

Carlos Prieto, Massimo Cimmino

Article (2021)

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Abstract

A transient multipole method for short-term simulations of ground heat exchangers (GHEs) is presented. The two-dimensional unsteady heat equation over a GHE cross-section is separated into two problems: (i) a transient heat equation with homogeneous boundary conditions, and (ii) a steady-state heat equation with non-homogeneous boundary conditions. An eigenfunction expansion is proposed for the solution of the transient heat equation, where the treatment of boundary conditions is considered by a multipole expansion of the eigenfunctions. A singular value decomposition is applied to extract the eigenvalues of the problem. The solution of the steady-state heat equation is obtained from a multipole expansion. The proposed method is validated against reference results for the evaluation of the eigenvalues and for the steady-state temperature field. The complete transient solution is validated against finite element analysis simulations. The proposed method is meshless, and its accuracy is only dependent on the evaluation of eigenvalues and on the number of terms in each of the multipole expansions.

Uncontrolled Keywords

Transient Multipole Expansion; Ground Heat Exchangers; Eigenfunctions; Meshless Method

Subjects: 2100 Mechanical engineering > 2100 Mechanical engineering
Department: Department of Mechanical Engineering
Funders: CRSNG/NSERC
Grant number: RGPIN-2018-04471
PolyPublie URL: https://publications.polymtl.ca/5506/
Journal Title: Science and Technology for the Built Environment (vol. 27, no. 3)
Publisher: Taylor & Francis
DOI: 10.1080/23744731.2020.1845072
Official URL: https://doi.org/10.1080/23744731.2020.1845072
Date Deposited: 14 Dec 2020 10:25
Last Modified: 17 Nov 2022 09:38
Cite in APA 7: Prieto, C., & Cimmino, M. (2021). Transient Multipole Expansion for Heat Transfer in Ground Heat Exchangers. Science and Technology for the Built Environment, 27(3), 253-270. https://doi.org/10.1080/23744731.2020.1845072

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