For the design and prediction of thermal behaviour of energy piles the reliable computational evaluation of time-dependent temperature distribution is required. Some knowledge of analytical solutions, leading to some numerically feasible integration schemes, is welcome. This paper demonstrates such approach on certain model problems with finite cylinder heat sources, generalizing existing results, working with various infinite heat sources, or with finite line ones.
Topics
Knowledge
REFERENCES
1.
2.
Abu H.
Abuel-Naga
, M. I. N.
Raouf
, A. M. I.
Raouf
and A. G.
Nasser
, “Energy piles: current state of knowledge and design challenges
,” Environmental Geotechnics
2
(2015
), 195
–210
.3.
Val J.
Vala
and P.
Jarošová
, “Optimization approaches to some problems of building design
,” Applications of Mathematics
63
(2018
), 305
–331
.4.
Ora J.
Oravec
and O.
Š ikula
, “Computational domain optimization for numerical modelling of energy piles
,” Juniorstav – 22th Student Conference in Brno (2020), Proceedings
(Brno University of Technology
2020
), 836
–841
.5.
Fad J.
Fadejev
, R.
Simson
, J.
Kurnitski
and F.
Haghighat
, “A review on energy piles design, sizing and modelling
,” Energy
122
(2017
), 390
–407
.6.
Zha X.
Zhang
, T.
Zhang
Y.
Jiang
and B.
Li
, “Improvement on an analytical finite line source model considering complex initial and boundary conditions: Part 1, model development and validation
,” Energy and Buildings
198
(2019
), 1
–10
.7.
Ing L. R.
Ingersoll
, O. J.
Zobel
and A. C.
Ingersoll
, Heat and Conduction: With Engineering, Geological, and Other Applications
(Madison
: Wisconsin University Press
1954
).8.
Car H. S.
Carslaw
and J. C.
Jaeger
, Conduction of Heat in Solids
(Oxford
: Clarendon Press
1959
).9.
Sim I.
Simões
, A.
Tadeu
and N.
Simões
, “Green's functions for heat conduction for unbounded and bounded rectangular spaces: time and frequency domain solutions
,” Hindawi: Journal of Applied Mathematics
(2016
), 6439710/1
–22
.10.
Cla J.
Claesson
and P.
Eskilson
, “Conductive heat extraction to a deep borehole: thermal analyses and dimensioning rules
,” Energy
13
(1988
), 509
–527
.11.
BanM T. V.
Bandos
, Á.
Montero
, E.
Fernández
, J. L. G.
Santander
, J. M.
Isidroa
, J.
Pérez
, P. J. Fernández
de Córdoba
and J. F.
Urchuegúıa
, “Finite line-source model for borehole heat exchangers: effect of vertical temperature variations
,” Geothermics
38
(2009
), 263
–270
.12.
LiM M.
Li
and A. C. K.
Lai
, “Analytical model for short-time responses of ground heat exchangers with U-shaped tubes: model development and validation
,” Applied Energy
104
(2013
), 510
–516
.13.
Man Y.
Man
, H.
Yang
, N.
Diao
, J.
Liu
and Z.
Fang
, “A new model and analytical solutions for borehole and pile ground heat exchangers
,” International Journal of Heat and Mass Transfer
53
(2010
), 2593
–2601
.14.
BanC T. V.
Bandos
, A.
Campos-Celador
, L. M.
López-González
and J. M.
Sala-Lizarraga
, “Finite cylinder-source model for energy pile heat exchangers: effects of thermal storage and vertical temperature variations
,” Energy
78
(2014
), 639
–648
.15.
Gha O.
Ghasemi-Fare
and P.
Basu
, “A practical heat transfer model for geothermal piles
,” Energy and Buildings
66
(2013
), 470
–479
.16.
Jha B. K.
Jha
and M. O.
Oni
, “An analytical solution for temperature field around a cylindrical surface subjected to a time dependent heat flux: an alternative approach
,” Alexandria Engineering Journal
57
(2018
), 927
–929
.17.
Sha X.
Shang
, J.
Wang
and X.
Yang
, “Fractal analysis for heat extraction in geothermal system
,” Thermal Science
21
(2017
), S25
–S31
.18.
Yan S.-Y. Yang
and
, H.-D. Yeh
, “Modeling heat extraction from hot dry rock in a multi-well system
,” Applied Thermal Engineering
29
(2009
), 1676
–1681
.19.
Koo S.
Koohi-Fayegh
and M. A.
Rosen
, “A review of the modelling of thermally interacting multiple boreholes
,” Sustainability
5
(2013
), 2519
–2536
.20.
Li Q.
Li
, L.
Chen
and L.
Qiao
, “Thermal effect on structural interaction between energy pile and its host soil
,” Hindawi: Advances in Materials Science and Engineering
(2017
), |p7121785/1–9.21.
And F. C.
Andrews
, Special Functions of Mathematics for Engineers
(New York
: McGraw-Hill
1992
).22.
Fie M.
Fiedler
, Special Matrices and Their Applications in Numerical Mathematics
(Boston
: Dordrecht
1986
).23.
Sil T. Da Silva Oliveira
Morais
and C. De Hollanda Cavalcanti
Tsuha
, “Energy pile and ground temperature response to heating test: a case study in Brazil
,” Bulgarian Chemical Communications
48
(2016
), 115
–119
.24.
Ng C. W. W.
Ng
, A.
Gunawan
, C.
Shi
, Q. J.
Ma
and H. L.
Liu
, “Centrifuge modelling of displacement and replacement energy piles constructed in saturated sand: a comparative study
,” Géotechnique Letters
6
, 34
–38
.
This content is only available via PDF.
© 2020 Author(s).
2020
Author(s)
