TY - JOUR
T1 - Transient heat conduction in an infinite medium subjected to multiple cylindrical heat sources
T2 - An application to shallow geothermal systems
AU - BniLam, Noori
AU - Al-Khoury, Rafid
PY - 2016/11/1
Y1 - 2016/11/1
N2 - 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.
AB - 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.
KW - Borehole heat exchanger BHE
KW - Cylindrical heat source
KW - FFT
KW - Geothermal system
KW - Heat equation
KW - Modified bessel series
UR - http://www.scopus.com/inward/record.url?scp=84973176753&partnerID=8YFLogxK
U2 - 10.1016/j.renene.2016.05.069
DO - 10.1016/j.renene.2016.05.069
M3 - Article
AN - SCOPUS:84973176753
SN - 0960-1481
VL - 97
SP - 145
EP - 154
JO - Renewable Energy
JF - Renewable Energy
ER -