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

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.