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

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

Al-Khoury, Rafid (TU Delft Applied Mechanics)
Bni Lam, N.H.N. (Universiteit Antwerpen)
Musivand Arzanfudi, M. (TU Delft Applied Mechanics; DIANA FEA)
Saeid, S. (TU Delft Reservoir Engineering)

2020

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.

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

http://resolver.tudelft.nl/uuid:a7f05e8b-cf08-4923-b7a9-05ff817a50fc

https://doi.org/10.1016/j.ijheatmasstransfer.2020.120517

0017-9310

International Journal of Heat and Mass Transfer, 163

Institutional Repository

journal article

© 2020 Rafid Al-Khoury, N.H.N. Bni Lam, M. Musivand Arzanfudi, S. Saeid