Theoretical Prediction of the Number of Bénard Cells in Low-Porosity Cylindrical/Rectangular Enclosures Saturated by a Fast Chemically Reacting Fluid

Kanakapura M. Lakshmi (), Laura M. Pérez, Pradeep G. Siddheshwar and David Laroze
Additional contact information
Kanakapura M. Lakshmi: Department of Mathematics, School of Physical Sciences, Central University of Karnataka, Kalaburagi 585367, India
Laura M. Pérez: Departamento de Física, FACI, Universidad de Tarapacá, Casilla 7D, Arica 1000000, Chile
Pradeep G. Siddheshwar: Centre for Mathematical Needs, Department of Mathematics, CHRIST (Deemed to be University), Hosur Road, Bengaluru 560029, India
David Laroze: Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 7D, Arica 1000000, Chile

Sustainability, 2023, vol. 15, issue 15, 1-19

Abstract: Many applications including chemical engineering and meteorology require the study of a chemically driven convection in cylindrical, as well as rectangular enclosures. The present paper reports a unified analysis of a chemically driven convection in densely packed porous cylindrical/rectangular enclosures saturated by a chemically reactive binary fluid mixture. Employing the degeneracy technique and the single-term Galerkin method involving Bessel functions in a linear stability analysis, an analytical expression for the critical Rayleigh number, R a c , was obtained. An analytical expression for the number of cells that manifest in a given enclosure, at the onset of convection, was derived from R a c . The connection between the stabilizing and destabilizing effects of various parameters and the size or the number of Bénard cells that manifest are described in detail. The results depicted that the chemical parameters related to the heat of reaction destabilize and the parameter depending inversely on the rate of the chemical reaction stabilizes the system. In the latter case, a greater number of smaller cells were formed in the system compared to the former case. Hence, we concluded that the chemically reactive fluid advances the onset of convection compared to the chemically non-reactive fluid. The results of a similar problem in rectangular enclosures of infinite horizontal extent and chemically non-reactive liquid-saturated porous medium were recovered as limiting cases. Thus, the present model presents a unified analysis of six individual problems.

Keywords: Darcy–Bénard convection; chemically reactive fluid; cylindrical and rectangular enclosures; Bénard cells; linear stability analysis (search for similar items in EconPapers)
JEL-codes: O13 Q Q0 Q2 Q3 Q5 Q56 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/2071-1050/15/15/11999/pdf (application/pdf)
https://www.mdpi.com/2071-1050/15/15/11999/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jsusta:v:15:y:2023:i:15:p:11999-:d:1210572

Access Statistics for this article

Sustainability is currently edited by Ms. Alexandra Wu

More articles in Sustainability from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().