Theoretical Prediction of the Number of B&#xE9;nard Cells in Low-Porosity Cylindrical/Rectangular Enclosures Saturated by a Fast Chemically Reacting Fluid
Bénard cells; chemically reactive fluid; cylindrical and rectangular enclosures; Darcy–Bénard convection; linear stability analysis
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, (Formula presented.), was obtained. An analytical expression for the number of cells that manifest in a given enclosure, at the onset of convection, was derived from (Formula presented.). The connection between the stabilizing and destabilizing effects of various parameters and the size or the number of B&#xE9;nard 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. 2023 by the authors.
Lakshmi K.M.; P&#xE9;rez L.M.; Siddheshwar P.G.; Laroze D.
Sustainability (Switzerland), Vol-15, No. 15
Multidisciplinary Digital Publishing Institute (MDPI)
https://doi.org/10.3390/su151511999 https://www.scopus.com/inward/record.uri?eid=2-s2.0-85167923345&doi=10.3390%2fsu151511999&partnerID=40&md5=feb4aeb26b46eb2c20e159393f91840d
Lakshmi K.M., Department of Mathematics, School of Physical Sciences, Central University of Karnataka, Kalaburagi, 585367, India; Pérez L.M., Departamento de Física, FACI, Universidad de Tarapacá, Casilla 7D, Arica, 1000000, Chile; Siddheshwar P.G., Centre for Mathematical Needs, Department of Mathematics, CHRIST (Deemed to be University), Hosur Road, Bengaluru, 560029, India; Laroze D., Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 7D, Arica, 1000000, Chile