On Thermally Interacting Multiple Boreholes with Variable Heating Strength: Comparison between Analytical and Numerical Approaches
AbstractThe temperature response in the soil surrounding multiple boreholes is evaluated analytically and numerically. The assumption of constant heat flux along the borehole wall is examined by coupling the problem to the heat transfer problem inside the borehole and presenting a model with variable heat flux along the borehole length. In the analytical approach, a line source of heat with a finite length is used to model the conduction of heat in the soil surrounding the boreholes. In the numerical method, a finite volume method in a three dimensional meshed domain is used. In order to determine the heat flux boundary condition, the analytical quasi-three-dimensional solution to the heat transfer problem of the U-tube configuration inside the borehole is used. This solution takes into account the variation in heating strength along the borehole length due to the temperature variation of the fluid running in the U-tube. Thus, critical depths at which thermal interaction occurs can be determined. Finally, in order to examine the validity of the numerical method, a comparison is made with the results of line source method.
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Bibliographic InfoArticle provided by MDPI, Open Access Journal in its journal Sustainability.
Volume (Year): 4 (2012)
Issue (Month): 8 (August)
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geothermal energy; vertical ground heat exchangers; numerical analysis; analytical analysis; variable heat flux;
Find related papers by JEL classification:
- Q - Agricultural and Natural Resource Economics; Environmental and Ecological Economics
- Q0 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - General
- Q2 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation
- Q3 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Nonrenewable Resources and Conservation
- Q5 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics
- Q56 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Environment and Development; Environment and Trade; Sustainability; Environmental Accounts and Accounting; Environmental Equity; Population Growth
- O13 - Economic Development, Technological Change, and Growth - - Economic Development - - - Agriculture; Natural Resources; Environment; Other Primary Products
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- Jun, Liu & Xu, Zhang & Jun, Gao & Jie, Yang, 2009. "Evaluation of heat exchange rate of GHE in geothermal heat pump systems," Renewable Energy, Elsevier, vol. 34(12), pages 2898-2904.
- Yang, Weibo & Shi, Mingheng & Liu, Guangyuan & Chen, Zhenqian, 2009. "A two-region simulation model of vertical U-tube ground heat exchanger and its experimental verification," Applied Energy, Elsevier, vol. 86(10), pages 2005-2012, October.
- Marcotte, D. & Pasquier, P., 2008. "On the estimation of thermal resistance in borehole thermal conductivity test," Renewable Energy, Elsevier, vol. 33(11), pages 2407-2415.
- Lee, C.K. & Lam, H.N., 2008. "Computer simulation of borehole ground heat exchangers for geothermal heat pump systems," Renewable Energy, Elsevier, vol. 33(6), pages 1286-1296.
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