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Galerkin FEM simulation of natural convection in an annular porous medium-based solar collector system

Venkatadri, K; Anwar Bég, O; Bég, T A; Kuharat, S


K Venkatadri

T A Bég



Motivated by simulating emerging hybrid designs in annular solar direct absorber collectors, a theoretical and numerical study of natural convection in an annular hybrid porous medium solar collector is presented. An aspect ratio of 2 is considered where the annular geometry is twice the depth relative to the diameter. The non-dimensional conservation equations for Newtonian absorber fluid are solved in an axisymmetric coordinate system (R, Z) using the COMSOL finite element platform, which uses a Galerkin formulation. An optimized mesh is designed following a mesh independence test. Extensive visualization of the streamline, isotherm, and pressure contours is included over a range of Rayleigh (10 3 ≤ Ra ≤ 10 6) and Darcy number (0.0001 ≤ Da ≤ 0.1), e.g., (inverse permeability). Additionally, Nusselt number distributions at the inner cylindrical wall of the annulus are presented. Furthermore, cut-through semi-annular contour plots are displayed. Validation with previous studies for the geometrically mapped case of axisymmetric flow is also included. A strong decrement in the Nusselt number is induced by decreasing the Darcy number due to the lower permeability, which depletes thermal conduction in the porous medium and inhibits heat flux to the boundary. Heat transfer to the boundary is optimized at a high Darcy number (large permeability). With raising of Rayleigh number, i.e., significant thermal buoyancy, the Nusselt number is strongly enhanced, whereas isotherm magnitudes are suppressed. Complex transitions, e.g., dual vortex cell synthesis in isotherms, streamline and pressure distributions, are computed with variation in Darcy and Rayleigh numbers. The simulations establish a good foundation for future extensions to consider radiative heat transfer and other working fluids, including nanofluids and non-Newtonian fluids.


Venkatadri, K., Anwar Bég, O., Bég, T. A., & Kuharat, S. (2024). Galerkin FEM simulation of natural convection in an annular porous medium-based solar collector system. International Journal of Ambient Energy, 45(1),

Journal Article Type Article
Acceptance Date May 17, 2024
Online Publication Date Jun 9, 2024
Publication Date Jun 9, 2024
Deposit Date May 18, 2024
Publicly Available Date Jun 10, 2025
Publisher Taylor and Francis
Peer Reviewed Peer Reviewed
Volume 45
Issue 1
Keywords Solar annulus collector; Darcy porous medium; Rayleigh number; Galerkin finite element method (FEM), COMSOL Multiphysics; streamlines; Natural convection