Effect of Vadasz Number on Magnetoconvection in a Darcy Porous Layer with Concentration Based Internal Heating

In this research article, the effect of Vadasz number on magnetoconvection in a Darcy Porous Layer with concentration based internal heating is studied. The flow is governed by the Oberbeck-Boussineq model for Newtonian fluid. The stability analysis method based on the perturbation of infinitesimal amplitude is carried out using the normal mode analysis. The onset criterion for both the stationary and oscillatory convection on the stability of system is obtained. The analysis examines the effects of pertinent parameters on the stability of the system: magnetic field parameter, solutal Rayleigh number, Lewis number and Vadasz number. The result show that, internal heat parameter, and Lewis number, , hastens the onset of instability in the system, whereas magnetic field, , Vadasz number, and solutal Rayleigh number, delay the onset of instability.

From a steady plume to periodic puffs during confined carbon dioxide dissolution

In this paper, the stability of a laminar plume due to solutal convection is addressed from experimental, numerical and theoretical points of view. A topless vertical tube containing water is put in a pressure cell filled with carbon dioxide ( $\text{CO}_{2}$ ). The diffusion of $\text{CO}_{2}$ at the free surface creates a thin layer of heavy fluid underneath the surface. This unstable density gradient generates a steady laminar plume which goes downward through the entire tube. A quasi-steady flow settles in the tube, filling gradually the bottom of the tube with heavy fluid. During this laminar regime, the velocity of the plume slowly decreases due to the build-up of the background density gradient. Surprisingly, despite the decrease of the Reynolds number, the laminar plume suddenly destabilises via a varicose mode into periodic pulsed puffs after an onset time which depends on the height of the tube and on the solutal Rayleigh number $Ra$ . This periodic regime is followed by an aperiodic regime, which lasts until the complete saturation of the solution. The observed destabilisation is explained as a result of the interplay between the feedback of the global recirculating flow and the progressive density stratification of the background fluid. The wavelength, frequency, onset time and phase velocity of the instability are explored using particle image velocimetry (PIV) measurements over two decades of Rayleigh number. The characteristics of the instability appear to be almost independent of the Bond number but strongly dependent on the solutal Rayleigh number and the aspect ratio. The phase velocity is very close to the fluid velocity of the plume before the instability, which has been predicted in various works to scale as $Ra^{2/3}(\ln \,Ra)^{1/3}$ . The wavelength is close to 4.5 times the radius of the cylinder (independent of aspect ratio, Bond number and Rayleigh number) such that the frequency scales as the phase velocity. The onset time, which is proportional to the height of the cylinder, scales as $Ra^{-0.55}$ and depends on the Bond number. A simplified model inspired from Lorenz’ waterwheel is proposed to explain the destabilisation process after partial fill-up of the cylinder. Although very qualitative, the model captures the key features of the experimental observations.

On the Onset of Double-diffusive Convection in a Couple Stress Nanofluid in a Porous Medium

Double-diffusive convection in a horizontal layer of nanofluid in a porous medium is studied. The couple-stress fluid model is considered to describe the rheological behavior of the nanofluid and for porous medium Darcy model is employed. The model applied for couple stress nanofluid incorporates the effect of Brownian motion and thermophoresis. We have assumed that the nanoparticle concentration flux is zero on the boundaries which neutralizes the possibility of oscillatory convection and only stationary convection occurs. The dispersion relation describing the effect of various parameters is derived by applying perturbation theory, normal mode analysis method and linear stability theory. The impact of various physical parameters, like the couple stress parameter, medium porosity, solutal Rayleigh Number, thermo-nanofluid Lewis number, thermo-solutal Lewis number, Soret parameter and Dufour parameter have been examined on the stationary convection. It is observed that the couple stress parameter, thermo-nanofluid Lewis number, thermo-solutal Lewis number, Soret parameter and Dufour parameter have stabilizing effects on the stationary convection whereas the solutal Rayleigh number and Dufour parameter have very small effect on the system.