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ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

Onset of Oscillatory Convection of a Chemically Reacting Fluid with Rigid Horizontal Boundaries

Discontinuity, Nonlinearity, and Complexity 13(2) (2024) 217--227 | DOI:10.5890/DNC.2024.06.001

G. Shiva Kumar Reddy, Ragoju Ravi

Department of Mathematics, National Institute of Technology Goa, Goa, India

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Abstract

A linear stability analysis determining the onset of convection of a chemically reacting fluid in a horizontal layer with rigid boundaries is performed. The governing dimensionless equations are solved using the normal modes, which leads to an eigenvalue problem for the onset of convection. The effects of the solute Rayleigh number, Prandtl number, Lewis number, and Damkohler number on the stability of the system are investigated. We find that the Damkohler number has a contrasting effect on stationary and oscillatory instability. The frequency decreases with $\chi $, but increases with $Le $ and $Pr$. The effect of increasing the Prandtl number is to advance the onset of convection. The Lewis number has a destabilizing effect on the onset of oscillatory convection.

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