Natural convection in a horizontal annular sector containing heat-generating porous medium
International Journal of Numerical Methods for Heat & Fluid Flow
ISSN: 0961-5539
Article publication date: 7 June 2021
Issue publication date: 3 January 2022
Abstract
Purpose
The purpose of this work is to propose the generalized integral transform technique (GITT) for the investigation of two-dimensional steady-state natural convection in a horizontal annular sector containing heat-generating porous medium.
Design/methodology/approach
GITT was used to investigate steady-state natural convection in a horizontal annular sector containing heat-generating porous medium. The governing equations in stream function formulation are integral transformed in the azimuthal direction, with the resulting system of nonlinear ordinary differential equations numerically solved by finite difference method. The GITT solutions are validated by comparison with fully numerical solutions by finite difference method, showing excellent agreement and convergence with low computational cost.
Findings
The effects of increasing Rayleigh number are more noticeable in stream function, whereas less significant for temperature. With decreasing annular sector angle from π to π/6, a reduction in the maximum temperature and stream function was noticed. While the two counter-rotating vortical structure is common for all annular sector angles investigated, the relative size of the two vortices varies with decreasing sector angle, with the vortex near the outer radius of the cavity becoming dominant. The annular sector angle affects strongly the maximum temperature and the partition of heat transfer on the inner and outer surfaces of the annular sector with heat-generating porous medium.
Originality/value
The strong effects of the annular sector angle on natural convection in annular sectors containing heat-generating porous medium are investigated for the first time. The proposed hybrid analytical–numerical approach can be applied in other convection problems in cylindrical or annular configurations, with or without porous medium. It shows potential for applications in practical convection problems in the nuclear and other industries.
Keywords
Acknowledgements
The authors are grateful to the funding agencies for the financial support.
Citation
Machado dos Santos, B., de Sá, L.S.S. and Su, J. (2022), "Natural convection in a horizontal annular sector containing heat-generating porous medium", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 32 No. 1, pp. 387-403. https://doi.org/10.1108/HFF-01-2021-0002
Publisher
:Emerald Publishing Limited
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