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Couple stress effects on the stability of three‐component convection‐diffusion in a porous layer
Author(s) -
Raghunatha K. R.,
Shivakumara I. S.,
Pallavi G.
Publication year - 2021
Publication title -
heat transfer
Language(s) - English
Resource type - Journals
eISSN - 2688-4542
pISSN - 2688-4534
DOI - 10.1002/htj.22017
Subject(s) - convection , rayleigh number , thermal diffusivity , mechanics , instability , diffusion , nonlinear system , stress (linguistics) , thermodynamics , linear stability , physics , natural convection , linguistics , philosophy , quantum mechanics
In this study, the stability (linear and weak nonlinear) of triple‐diffusive convection in a couple stress fluid‐saturated porous layer has been studied. A normal mode analysis yields an exact dispersion equation of fourth degree, and the criterion for the onset of stationary and oscillatory convection is obtained accordingly. The numerical computations are carried out for diffusivity elements experimentally determined for an aqueous NaCl‐KCl‐Sucrose system. Contrary to the double‐diffusive couple stress fluid system, it is found that (i) oscillatory convection occurs even if the diffusivity ratios are greater than unity and (ii) a disconnected heart‐shaped oscillatory neutral curve exists for certain choices of physical parameters, demonstrating the requirement of three critical values of Darcy‐Rayleigh number to specify the linear instability criteria. The impact of a couple stress parameter on some of these unusual behaviors is emphasized. The cubic Landau equations are derived by performing a weak nonlinear stability analysis and the stability of stationary and oscillatory bifurcating solutions is discussed. The heat and mass transfer for stationary and oscillatory convection modes is presented, and the influence of the couple stress parameter on the same is analyzed.