Exploration of Coriolis Force on the Linear Stability of Couple Stress Fluid Flow Induced by Double Diffusive Convection

2019 ◽  
Vol 141 (12) ◽  
Author(s):  
S. B. Naveen Kumar ◽  
I. S. Shivakumara ◽  
B. M. Shankar
Keyword(s):  
Linear Stability ◽  
Coriolis Force ◽  
Couple Stress ◽  
Fluid Layer ◽  
Linear Instability ◽  
Neutral Curve ◽  
Couple Stress Fluid ◽  
Diffusive Convection ◽  
Convective Cells ◽  
Rayleigh Numbers

Abstract In this paper, the effect of Coriolis force is explored on convective instability of a doubly diffusive incompressible couple stress fluid layer with gravity acting downward. A linear stability analysis is used to obtain the conditions for the onset of stationary and oscillatory convection in the closed form. Being a multiparameter instability problem, results for some isolated cases have been presented to illustrate interesting corners of parameter space. It is found that the neutral curve for oscillatory onset forms a closed-loop which is separate from the neutral curve for stationary onset indicating the requirement of three critical thermal Rayleigh numbers to specify the linear instability criteria instead of the usual single value. Besides, the simultaneous presence of rotation and the addition of heavy solute to the bottom of the layer exhibit an intriguing possibility of destabilizing the system under certain conditions, in contrast to their stabilizing effect when they are present in isolation. The implication of couple stresses on each of the aforementioned anomalies is clearly brought out. The spatial wavelength of convective cells at the onset is also discussed.

The onset of convective instability in a triply diffusive fluid layer

1989 ◽  
Vol 202 ◽  
pp. 443-465 ◽  
Author(s):  
Arne J. Pearlstein ◽  
Rodney M. Harris ◽  
Guillermo Terrones
Keyword(s):  
Rayleigh Number ◽  
Linear Stability ◽  
Fluid Layer ◽  
Neutral Curve ◽  
Interesting Consequence ◽  
Stability Criteria ◽  
Neutral Curves ◽  
The Stability ◽  
Rayleigh Numbers ◽  
Periodic Bifurcation

The onset of instability is investigated in a triply diffusive fluid layer in which the density depends on three stratifying agencies having different diffusivities. It is found that, in some cases, three critical values of the Rayleigh number are required to specify the linear stability criteria. As in the case of another problem requiring three Rayleigh numbers for the specification of linear stability criteria (the rotating doubly diffusive case studied by Pearlstein 1981), the cause is traceable to the existence of disconnected oscillatory neutral curves. The multivalued nature of the stability boundaries is considerably more interesting and complicated than in the previous case, however, owing to the existence of heart-shaped oscillatory neutral curves. An interesting consequence of the heart shape is the possibility of ‘quasi-periodic bifurcation’ to convection from the motionless state when the twin maxima of the heart-shaped oscillatory neutral curve lie below the minimum of the stationary neutral curve. In this case, there are two distinct disturbances, with (generally) incommensurable values of the frequency and wavenumber, that simultaneously become unstable at the same Rayleigh number. This work complements the earlier efforts of Griffiths (1979a), who found none of the interesting results obtained herein.

scholarly journals Global Stability For Double-Diffusive Convection In A Couple-Stress Fluid Saturating A Porous Medium

2019 ◽  
Vol 41 (1) ◽  
pp. 13-20
Author(s):  
Shalu Choudhary ◽  
Keyword(s):  
Porous Medium ◽  
Couple Stress ◽  
Linear Instability ◽  
Couple Stress Fluid ◽  
Brinkman Number ◽  
Onset Of Convection ◽  
Instability Theory ◽  
Diffusive Convection ◽  
Solute Gradient ◽  
Double Diffusive

Abstract We show that the global non-linear stability threshold for convection in a double-diffusive couple-stress fluid saturating a porous medium is exactly the same as the linear instability boundary. The optimal result is important because it shows that linearized instability theory has captured completely the physics of the onset of convection. It is also found that couple-stress fluid saturating a porous medium is thermally more stable than the ordinary viscous fluid, and the effects of couple-stress parameter (F ) , solute gradient ( S f ) and Brinkman number ( D a ) on the onset of convection is also analyzed.

Flow analysis of biconvective heat and mass transfer of two-dimensional couple stress fluid over a paraboloid of revolution

2020 ◽  
Vol 34 (11) ◽  
pp. 2050110 ◽  
Author(s):  
Ahmed Zeeshan ◽  
Zeeshan Ali ◽  
Mohammad Rahimi Gorji ◽  
Farooq Hussain ◽  
S. Nadeem
Keyword(s):  
Boundary Layer ◽  
Couple Stress ◽  
Fluid Layer ◽  
Flow Analysis ◽  
Couple Stress Fluid ◽  
Two Dimensional ◽  
Nonlinear Odes ◽  
Similarity Transformations ◽  
Paraboloid Of Revolution ◽  
Stream Functions

In this paper, two-dimensional non-Newtonian couple stress fluid flow over the upper horizontal surface of a paraboloid (uhsp) (shaped like a submarine or any aerodynamical automobile) is investigated. At the freestream, a stretching of the fluid layer is assumed along with catalytic surface reaction which tends to induce the flow in the fluid-saturated domain. The problem is modeled by engaging laws of conservation for mass, momentum, heat and concentration. Velocity components are converted to stream functions and similarity transformations to reduce the dependent and independent variables in the partial differential equation describing the flow. Stream functions ideally satisfy continuity equation and transformation to reduce the PDEs to the system of coupled nonlinear ODEs. The numerical solution of these equations is obtained using the shooting-RKF method. The graphical results show that both the lateral and horizontal velocities decrease by increasing the couple stress material parameter and cause the temperature to rise. The thermal boundary layer decreases subject to the thickness parameter and has appositive effects on concentration boundary layer. Finally, numerical results have also been tabulated.

Sign in / Sign up

Export Citation Format

Share Document