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

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Abstract

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.

Original languageEnglish
Article number120517
Number of pages10
JournalInternational Journal of Heat and Mass Transfer
Volume163
DOIs
Publication statusPublished - 2020

Keywords

  • Conduction-convection heat flow
  • Ground source heat pump
  • Heat flow in groundwater
  • Moving cylindrical heat source

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