Lattice Boltzmann simulation of thermo-magnetic natural convection in an enclosure partially filled with a porous medium

Beg, OA; Venkatadri, K

Abstract

Motivated by emerging magnetized hybrid fuel cell applications, a theoretical analysis
of incompressible magnetohydrodynamic (MHD) non-Darcian thermogravitational convection
in a square enclosure partially filled with a highly permeable medium in presence of transverse
magnetic field is presented. The enclosure is filled with magnetized Newtonian fluid. A nonDarcy model is utilized for the porous region featuring both Darcian linear drag and second
order Forchheimer drag components with Brinkman no-slip at the walls. The horizontal (i.e.,
bottom and Top) wall boundaries are considered adibatic and impermeable, while the side walls
(hot and cold walls) are maintained with different thermal values. The Lattice Boltzmann
method (LBM) is implemented to employ the governing momenta and thermal conservation
equations with appropriate end conditions. The divergence of the non-linear system is avoided
by introducing convergence criteria factors. A grid independence test is included for validation
of the D2Q9-LBM code accuracy. Further validation with earlier studies in the absence of
Hartmann number (Ha) is included. A parametric examination of the impact of Hartmann
number (0 < Ha < 50), Darcy number (0.0001 < Da < 0.1), and Rayleigh number (103 < Ra <
106
) on temperature contours and streamline patterns for Helium gas (Prandtl number (Pr) =
0.71) is conducted. The heat flux distributions on the side walls and centre-line velocity are
also computed. With greater Darcy number and Rayleigh number, Nusselt number is boosted
at the left hot wall and the right cold wall. However, Nusselt number increases as one descends the hot wall towards the lower adiabatic boundary whereas for it increases as one ascends the
cold wall towards the upper adiabatic boundary.

Citation

Beg, O., & Venkatadri, K. (2022). Lattice Boltzmann simulation of thermo-magnetic natural convection in an enclosure partially filled with a porous medium. Waves in Random and Complex Media, https://doi.org/10.1080/17455030.2022.2157516

• Journal Article Type: Article
• Acceptance Date: Dec 6, 2022
• Online Publication Date: Dec 20, 2022
• Publication Date: Dec 20, 2022
• Deposit Date: Jan 3, 2023
• Publicly Available Date: Dec 21, 2023
• Journal: Waves in Random and Complex Media
• Print ISSN: 1745-5030
• Publisher: Taylor and Francis
• DOI: https://doi.org/10.1080/17455030.2022.2157516
• Publisher URL: https://doi.org/10.1080/17455030.2022.2157516
• Additional Information: Additional Information : This is an Accepted Manuscript of an article published by Taylor & Francis in Waves in Random and Complex Media on December 20th 2022, available at: http://www.tandfonline.com/10.1080/17455030.2022.2157516