An Analytical Model for Transient Heat Transfer with a Time-Dependent Boundary in Solar- and Waste-Heat-Assisted Geothermal Borehole Systems: From Single to Multiple Boreholes

With the increasing engineering applications of geothermal borehole heat exchangers (BHEs), accurate and reliable mathematical models can help advance their thermal design and operations. In this study, an analytical model with a time-dependent heat flux boundary condition on the borehole wall is de...

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Autores principales:	Mohammed A. Hefni, Minghan Xu, Ferri Hassani, Seyed Ali Ghoreishi-Madiseh, Haitham M. Ahmed, Hussein A. Saleem, Hussin A. M. Ahmed, Gamal S. A. Hassan, Khaled I. Ahmed, Agus P. Sasmito
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	borehole heat exchanger (BHE) geothermal energy solar-assisted geothermal waste-heat-assisted geothermal thermal energy storage analytical model Technology T Engineering (General). Civil engineering (General) TA1-2040 Biology (General) QH301-705.5 Physics QC1-999 Chemistry QD1-999
Acceso en línea:	https://doaj.org/article/09993cb8ac2e40fd91e79abdd7635665
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spelling	oai:doaj.org-article:09993cb8ac2e40fd91e79abdd76356652021-11-11T15:23:34ZAn Analytical Model for Transient Heat Transfer with a Time-Dependent Boundary in Solar- and Waste-Heat-Assisted Geothermal Borehole Systems: From Single to Multiple Boreholes 10.3390/app1121103382076-3417https://doaj.org/article/09993cb8ac2e40fd91e79abdd76356652021-11-01T00:00:00Zhttps://www.mdpi.com/2076-3417/11/21/10338https://doaj.org/toc/2076-3417With the increasing engineering applications of geothermal borehole heat exchangers (BHEs), accurate and reliable mathematical models can help advance their thermal design and operations. In this study, an analytical model with a time-dependent heat flux boundary condition on the borehole wall is developed, capable of predicting the thermal performance of single, double, and multiple closed-loop BHEs, with an emphasis on solar- and waste-heat-assisted geothermal borehole systems (S-GBS and W-GBS) for energy storage. This analytical framework begins with a one-dimensional transient heat conduction problem subjected to a time-dependent heat flux for a single borehole. The single borehole scenario is then extended to multiple boreholes by exploiting lines of symmetry (or thermal superposition). A final expression of the temperature distribution along the center line is attained for single, double, and multiple boreholes, which is verified with a two-dimensional finite-element numerical model (less than 0.7% mean absolute deviation) and uses much lesser computational power and time. The analytical solution is also validated against a field-scale experiment from the literature regarding the borehole and ground temperatures at different time frames, with an absolute error below 6.3%. Further, the thermal performance of S-GBS and W-GBS is compared for a 3-by-3 borehole configuration using the analytical model to ensure its versatility in thermal energy storage. It is concluded that our proposed analytical framework can rapidly evaluate closed-loop geothermal BHEs, regardless of the numbers of boreholes and the type of the heat flux on the borehole wall.Mohammed A. HefniMinghan XuFerri HassaniSeyed Ali Ghoreishi-MadisehHaitham M. AhmedHussein A. SaleemHussin A. M. AhmedGamal S. A. HassanKhaled I. AhmedAgus P. SasmitoMDPI AGarticleborehole heat exchanger (BHE)geothermal energysolar-assisted geothermalwaste-heat-assisted geothermalthermal energy storageanalytical modelTechnologyTEngineering (General). Civil engineering (General)TA1-2040Biology (General)QH301-705.5PhysicsQC1-999ChemistryQD1-999ENApplied Sciences, Vol 11, Iss 10338, p 10338 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	borehole heat exchanger (BHE) geothermal energy solar-assisted geothermal waste-heat-assisted geothermal thermal energy storage analytical model Technology T Engineering (General). Civil engineering (General) TA1-2040 Biology (General) QH301-705.5 Physics QC1-999 Chemistry QD1-999
spellingShingle	borehole heat exchanger (BHE) geothermal energy solar-assisted geothermal waste-heat-assisted geothermal thermal energy storage analytical model Technology T Engineering (General). Civil engineering (General) TA1-2040 Biology (General) QH301-705.5 Physics QC1-999 Chemistry QD1-999 Mohammed A. Hefni Minghan Xu Ferri Hassani Seyed Ali Ghoreishi-Madiseh Haitham M. Ahmed Hussein A. Saleem Hussin A. M. Ahmed Gamal S. A. Hassan Khaled I. Ahmed Agus P. Sasmito An Analytical Model for Transient Heat Transfer with a Time-Dependent Boundary in Solar- and Waste-Heat-Assisted Geothermal Borehole Systems: From Single to Multiple Boreholes
description	With the increasing engineering applications of geothermal borehole heat exchangers (BHEs), accurate and reliable mathematical models can help advance their thermal design and operations. In this study, an analytical model with a time-dependent heat flux boundary condition on the borehole wall is developed, capable of predicting the thermal performance of single, double, and multiple closed-loop BHEs, with an emphasis on solar- and waste-heat-assisted geothermal borehole systems (S-GBS and W-GBS) for energy storage. This analytical framework begins with a one-dimensional transient heat conduction problem subjected to a time-dependent heat flux for a single borehole. The single borehole scenario is then extended to multiple boreholes by exploiting lines of symmetry (or thermal superposition). A final expression of the temperature distribution along the center line is attained for single, double, and multiple boreholes, which is verified with a two-dimensional finite-element numerical model (less than 0.7% mean absolute deviation) and uses much lesser computational power and time. The analytical solution is also validated against a field-scale experiment from the literature regarding the borehole and ground temperatures at different time frames, with an absolute error below 6.3%. Further, the thermal performance of S-GBS and W-GBS is compared for a 3-by-3 borehole configuration using the analytical model to ensure its versatility in thermal energy storage. It is concluded that our proposed analytical framework can rapidly evaluate closed-loop geothermal BHEs, regardless of the numbers of boreholes and the type of the heat flux on the borehole wall.
format	article
author	Mohammed A. Hefni Minghan Xu Ferri Hassani Seyed Ali Ghoreishi-Madiseh Haitham M. Ahmed Hussein A. Saleem Hussin A. M. Ahmed Gamal S. A. Hassan Khaled I. Ahmed Agus P. Sasmito
author_facet	Mohammed A. Hefni Minghan Xu Ferri Hassani Seyed Ali Ghoreishi-Madiseh Haitham M. Ahmed Hussein A. Saleem Hussin A. M. Ahmed Gamal S. A. Hassan Khaled I. Ahmed Agus P. Sasmito
author_sort	Mohammed A. Hefni
title	An Analytical Model for Transient Heat Transfer with a Time-Dependent Boundary in Solar- and Waste-Heat-Assisted Geothermal Borehole Systems: From Single to Multiple Boreholes
title_short	An Analytical Model for Transient Heat Transfer with a Time-Dependent Boundary in Solar- and Waste-Heat-Assisted Geothermal Borehole Systems: From Single to Multiple Boreholes
title_full	An Analytical Model for Transient Heat Transfer with a Time-Dependent Boundary in Solar- and Waste-Heat-Assisted Geothermal Borehole Systems: From Single to Multiple Boreholes
title_fullStr	An Analytical Model for Transient Heat Transfer with a Time-Dependent Boundary in Solar- and Waste-Heat-Assisted Geothermal Borehole Systems: From Single to Multiple Boreholes
title_full_unstemmed	An Analytical Model for Transient Heat Transfer with a Time-Dependent Boundary in Solar- and Waste-Heat-Assisted Geothermal Borehole Systems: From Single to Multiple Boreholes
title_sort	analytical model for transient heat transfer with a time-dependent boundary in solar- and waste-heat-assisted geothermal borehole systems: from single to multiple boreholes
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/09993cb8ac2e40fd91e79abdd7635665
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An Analytical Model for Transient Heat Transfer with a Time-Dependent Boundary in Solar- and Waste-Heat-Assisted Geothermal Borehole Systems: From Single to Multiple Boreholes

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