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

VL - 97

SP - 145

EP - 154

JO - Renewable Energy

JF - Renewable Energy

SN - 0960-1481

ER -