A spectral model for a moving cylindrical heat source in a conductive-convective domain

• Published in: International journal of heat and mass transfer Vol. 163; p. 120517
• Main Authors: Al-Khoury, Rafid, BniLam, Noori, Arzanfudi, Mehdi M., Saeid, Sanaz
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01-12-2020; Elsevier BV
• Subjects: Bessel functions; Boreholes; Boundary conditions; Conduction heating; Conduction-convection heat flow; Conductive heat transfer; Dirichlet problem; Fast Fourier transformations; Finite element method; Fourier series; Fourier transforms; Green's functions; Ground source heat pump; Groundwater flow; Heat exchangers; Heat flow in groundwater; Heat pumps; Mathematical models; Moving cylindrical heat source; Physical properties; Spectra; Thermodynamics; Moving cylindrical heat source; Heat flow in groundwater; Conduction-convection heat flow; Ground source heat pump
• ISSN: 0017-9310; 1879-2189
• DOI: 10.1016/j.ijheatmasstransfer.2020.120517

•Groundwater flow is an important design aspect for ground source heat pump systems.•Groundwater increases thermal interaction between boreholes and affects efficiency.•The conceptual model entails a convective domain passing a cylindrical heat source.•The governing heat equation is solved analytically using the spectral analysis.•Compared to other analytical models, the spectral model is robust and CPU efficient.
This paper introduces a spectral model for a moving cylindrical heat source in an infinite conductive-convective domain. This physical process occurs in many engineering and technological applications including heat conduction-convection in ground source heat pump systems, where the borehole heat exchangers likely go through layers with groundwater flow. The governing heat equation is solved for Dirichlet and Neumann boundary conditions using the fast Fourier transform for the time domain, and the Fourier series for the spatial domain. A closed form solution based on the modified Bessel functions is obtained for the Dirichlet boundary condition and an integral form for the Neumann boundary condition. Limiting cases of the moving cylindrical heat source to represent a moving line heat source are also derived. Compared to solutions based on the Green's function and the Laplace transform, the spectral model has a simpler form, applicable to complicated time-variant input signals, valid for a wide range of physical parameters and easy to implement in computer codes. The model is verified against the existing infinite line heat source model and a finite element model.