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Linear and energy stability analyses of onset of Darcy-Bénard convection due to combustion

P.G. Siddheshwar, Reena Nandal

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 26 November 2024

Issue publication date: 27 January 2025

31

Abstract

Purpose

This paper aims to perform a linear and nonlinear analysis of the stability of a chemically reacting Newtonian fluid in a Darcy porous medium. The purpose of selecting both analyses is to investigate the probability of subcritical instability resulting from combustion.

Design/methodology/approach

The chemical reaction problem in a Darcy porous medium with Arrhenius kinetics is considered. The effect of the Frank-Kamenetskii number on the linear and nonlinear stability is analysed. The critical eigenvalue is obtained numerically by the Chebyshev pseudospectral method for both analyses.

Findings

The inference from the two analyses is that in the presence of combustion, the situation in the Darcy−Bénard convection problem can lead to subcritical instability. It is found that the value of the critical Frank-Kamenetskii number keeps on changing as the lower boundary temperature changes, beyond the critical value of the Frank-Kamenetskii number where the system splits, going from a steady condition to an explosive state.

Originality/value

The Chebyshev pseudospectral approach has been applied to address the combustion problem in this research. The normal mode methodology and energy method are used for linear and nonlinear analyses, and the effects of nonlinear factors are examined by comparing the outcomes.

Keywords

Acknowledgements

Ethical approval: No experiments involving humans or animals were conducted by the author for this research work.

Funding statement: No funding agency provided financial assistance for this research.

Citation

Siddheshwar, P.G. and Nandal, R. (2025), "Linear and energy stability analyses of onset of Darcy-Bénard convection due to combustion", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 35 No. 1, pp. 119-139. https://doi.org/10.1108/HFF-03-2024-0212

Publisher

:

Emerald Publishing Limited

Copyright © 2024, Emerald Publishing Limited

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