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.
Highlights
Heat conduction-convection in an infinite domain subjected to a heat source may be regarded either a case with a moving source of heat through a conductive medium, or a case of a convective medium passing a heat source
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
Cimmino and Baliga [10] developed a computational model utilizing the control-volume finite element method (CVFEM), which is a hybrid between the finite element method and the finite volume method, for modeling heat flow in ground source heat pump systems under the effect of groundwater flow
Summary
Heat conduction-convection in an infinite domain subjected to a heat source may be regarded either a case with a moving source of heat through a conductive medium, or a case of a convective medium passing a heat source. Al-Khoury et al [3] and Nam. et al [19] utilized the finite element method to simulate heat flow in GSHP systems constituting layers with groundwater flow. Carslaw and Jaeger [9] were among the firsts to introduce analytical solutions to heat conductionconvection problems using the moving heat source/domain concept They provided analytical solutions to the moving infinite line heat source using the Green’s function method and to the moving infinite cylindrical heat source using the Laplace transform. Sutton et al [22] adopted the Green’s function solution for a moving infinite line source to simulate 2D heat flow in GSHP systems with groundwater flow. In this paper we depart from the Green’s function and the Laplace transform and introduce a spectral model for heat flow in a convective infinite domain passing a cylindrical heat source. Unlike the inverse Laplace transform, inverse calculation of the spectral model is rather straightforward due to the use of the inverse fast Fourier transform (IFFT) algorithm
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