Implication of cross-diffusion on the stability of double diffusive convection in an imposed magnetic field

Abstract

The effects of cross-diffusion on linear and weak nonlinear stability of double diffusive convection in an electrically conducting horizontal fluid layer with an imposed vertical magnetic field are investigated. The criterion for the onset of stationary and oscillatory convection is obtained analytically by performing the linear instability analysis. Several noteworthy departures from those of doubly diffusive fluid systems are unveiled under certain parametric conditions. It is shown that (i) disconnected closed convex oscillatory neutral curve separated from the stationary neutral curve exists requiring three critical thermal Rayleigh numbers to completely specify the linear instability criteria instead of a usual single critical value, (ii) an electrically conducting fluid layer in the presence of magnetic field can be destabilized by stable solute concentration gradient, and (iii) a doubly diffusive conducting fluid layer can be destabilized in the presence of magnetic field. It is demonstrated that small variations in the off-diagonal elements enforce discrepancies in the instability criteria. A weak nonlinear stationary stability analysis has been performed using a perturbation method and a cubic Landau equation is derived and the stability of bifurcating equilibrium solution is discussed. It is found that subcritical bifurcation occurs depending on the choices of governing parameters.

Magnetic and chemical reaction effects on double‐diffusive convection with the effect of heat and salt flux boundary conditions

“…For example, Jena et al, 4 Liu and Umavathi, 5 Umavathi and Mohite, 6 Agarwal et al, 7 Zhuang et al, 8 Liu et al, 9 Siddiqa et al, 10 Shankar et al, 11 Raghunatha and Shivakumara, 12 Altawallbeh, 13 Mahajan and Tripathi, 14 and counts into the books by Nield et al, 15 Straughan, 16 and Vafai 17 . Moreover, the convection with the chemical reaction and magnetic effects has been much attention by many authors, see, for example, Turkyilmazoglu et al, 18 Turkyilmazoglu, 19,20 Malashetty and Biradar, 21 Ghasemi et al, 22 Teamah et al, 23 Al‐Sulaimi, 24 Yu et al, 25 Israel‐Cookey et al, 26 Gautam and Narayana, 27 Deepika et al, 28 Ebiwareme and Israel‐Cookey, 29 Mishra and Kumar, 30 Mahajan and Tripathi, 31 and Shivakumara et al 32 Recently, Noon and Haddad 33 investigated the impacts of varying gravity and rotation that combined with the reaction effect on the double‐diffusive convection of the Darcy model in a porous material using the linear and nonlinear stability analysis when the layer heated from the bottom and salted from the above or below. The linear, parabolic, and exponential kinds of varying gravity functions are discussed.…”

Cross‐diffusion effects on the onset of double‐diffusive convection in a rotating vertical heterogeneous porous cylinder with vertical throughflow

“…They found, among other results, that the Soret number has both stabilizing and destabilizing effects depending on the numerical value, but the Dufour number always has a destabilizing influence on the fluid system. Raghunatha and coworkers [28][29][30][31] investigated the cross-diffusion effect on the stability of a triple-diffusive Oldroyd-B fluid layer. Among other results, they concluded that the presence of cross-diffusion either stabilizes or destabilizes the fluid system depending on the strength of salt concentration as well as the elasticity of the fluid.…”