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Transient heat conduction in an infinite medium subjected to multiple cylindrical heat sources: An application to shallow geothermal systems

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  • BniLam, Noori
  • Al-Khoury, Rafid

Abstract

In this paper, we introduce analytical solutions for transient heat conduction in an infinite solid mass subjected to a varying single or multiple cylindrical heat sources. The solutions are formulated for two types of boundary conditions: a time-dependent Neumann boundary condition, and a time-dependent Dirichlet boundary condition. We solve the initial and boundary value problem for a single heat source using the modified Bessel function, for the spatial domain, and the fast Fourier transform, for the temporal domain. For multiple heat sources, we apply directly the superposition principle for the Neumann boundary condition, but for the Dirichlet boundary condition, we conduct an analytical coupling, which allows for the exact thermal interaction between all involved heat sources. The heat sources can exhibit different time-dependent signals, and can have any distribution in space. The solutions are verified against the analytical solution given by Carslaw and Jaeger for a constant Neumann boundary condition, and the finite element solution for both types of boundary conditions. Compared to these two solutions, the proposed solutions are exact at all radial distances, highly elegant, robust and easy to implement.

Suggested Citation

  • BniLam, Noori & Al-Khoury, Rafid, 2016. "Transient heat conduction in an infinite medium subjected to multiple cylindrical heat sources: An application to shallow geothermal systems," Renewable Energy, Elsevier, vol. 97(C), pages 145-154.
    • Handle: RePEc:eee:renene:v:97:y:2016:i:c:p:145-154
    DOI: 10.1016/j.renene.2016.05.069
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    References listed on IDEAS

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    1. 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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    1. Liang, Yanzhong & Teng, Bailu & Luo, Wanjing, 2024. "A new semi-analytical model for studying the performance of deep U-shaped borehole heat exchangers," Renewable Energy, Elsevier, vol. 225(C).
    2. BniLam, Noori & Al-Khoury, Rafid, 2020. "Parameter identification algorithm for ground source heat pump systems," Applied Energy, Elsevier, vol. 264(C).

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