Convective instabilities induced by exothermic reactions occurring in a porous medium
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abstract
A pseudohomogeneous model is developed and used to analyze the onset of reaction-driven convection in an open rectangular box containing a porous medium. For exothermic reactions, the one-dimensional conduction state exhibits multiplicity as well as oscillatory behavior. Singularity theory is used to classify the different possible bifurcation diagrams of conduction states, along with their stabilities. Linear instability theory is used to determine the stability of the conduction states to convective perturbations. The dependence of both simple zero and Hopf bifurcation neutral stability curves on various problem parameters is presented. It is shown that the Lewis number, Le (ratio of thermal to mass diffusivity), has a pronounced effect on the stability boundaries. Increasing the value of Le, shifts the stationary stability boundary toward higher Rayleigh numbers (Ra). It is also shown that in the region of multiple conduction solutions, there exists a critical value of Lewis number, Le1 (resp., Le2) below which the entire ignited (resp., extinguished) conduction branch is stable to convective perturbations for 0<Ra<Rac, where Rac is the critical Rayleigh number at the extinction (resp., ignition) point. Moreover, depending on the value of Le, a branch of the neutral stability curve for simple bifurcation is found for negative values of Ra. The results indicate that oscillatory instability is more likely to occur for the case of liquids, while for gases only stationary instability is possible for a practical range of parameter values. Numerically computed global bifurcation diagrams of conductive and convective solutions along with flow patterns, isotherms, and concentration profiles are also presented.
