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

Author:

Lakshmi Kanakapura M.1ORCID,Pérez Laura M.2ORCID,Siddheshwar Pradeep G.3ORCID,Laroze David4ORCID

Affiliation:

1. Department of Mathematics, School of Physical Sciences, Central University of Karnataka, Kalaburagi 585367, India

2. Departamento de Física, FACI, Universidad de Tarapacá, Casilla 7D, Arica 1000000, Chile

3. Centre for Mathematical Needs, Department of Mathematics, CHRIST (Deemed to be University), Hosur Road, Bengaluru 560029, India

4. Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 7D, Arica 1000000, Chile

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, Rac, was obtained. An analytical expression for the number of cells that manifest in a given enclosure, at the onset of convection, was derived from Rac. 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.

Funder

ANID through Convocatoria Nacional Subvención a Instalación en la Academia Convocatoria Año 2021

Publisher

MDPI AG

Subject

Management, Monitoring, Policy and Law,Renewable Energy, Sustainability and the Environment,Geography, Planning and Development,Building and Construction

Reference30 articles.

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2. Chemically driven convection. A simple model;Diewald;Chem. Phys. Lett.,1993

3. Interaction between chemical reaction and natural convection in porous media;Gatica;Chem. Eng. Sci.,1989

4. On the classification of buoyancy-driven chemo-hydrodynamic instabilities of chemical fronts;DHernoncourt;Chaos,2007

5. A bifurcation study of chemically driven convection in a porous medium;Nandakumar;Chem. Eng. Sci.,1992

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