<abstract xmlns="http://www.w3.org/1999/xhtml">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 (<italic>F</italic> ) , solute gradient ( <italic>S f</italic> ) and Brinkman number ( <italic>D a</italic> ) on the onset of convection is also analyzed.</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.

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

Studia Geotechnica et Mechanica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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...

D_a	x_ce	R_cef
0.01	0.5684	1897.1
0.02	0.5682	1001.9
0.03	0.5679	7017
0.04	0.5676	5532
0.05	0.5673	4636
0.06	0.5671	405.2
0.07	0.5668	365.0
0.08	0.5665	330.6
0.09	0.5663	305.7
0.10	0.5660	285.8
0.11	0.5667	269.5

F₁	x_ce	R _cef
01	0.9636	307.90
2	0.6154	661.40
3	0.5682	1001.9
4	0.5483	1340.8
5	0.5374	1679.0
6	0.5305	2017.0
7	0.5258	23537
8	0.5223	2696.0
9	0.5197	3030.3
10	0.5176	3367.9
	0.5159	3705.6

S	$R_{c e f} (\begin{matrix} F_{1} = 1 \\ x_{c e} = 0.6164 \end{matrix})$ ${{R}_{cef}}\left( \begin{align}& {{F}_{1}}=1 \\ & {{x}_{ce}}=0.6164 \\ \end{align} \right)$	$R_{c e f} (\begin{matrix} F_{1} = 2 \\ x_{c e} = 0.5682 \end{matrix})$ ${{R}_{cef}}\left( \begin{align}& {{F}_{1}}=2 \\ & {{x}_{ce}}=0.5682 \\ \end{align} \right)$	$R_{c e f} (\begin{matrix} F_{1} = 3 \\ x_{c e} = 0.5483 \end{matrix})$ ${{R}_{cef}}\left( \begin{align}& {{F}_{1}}=3 \\ & {{x}_{ce}}=0.5483 \\ \end{align} \right)$
100	661.4	1001.9	1340.8
200	761.4	1101.9	1440.8
300	861.4	1201.9	1540.8
400	961.4	1301.9	1640.8
500	1061.4	1401.9	1740.8
600	1161.4	1501.9	1840.8
700	271.4	1601.9	1940.8
800	1361.4	1701.9	2040.8
900	1461.4	1801.9	2140.8

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

Article Category: Research Article

Published Online: Apr 08, 2019

Page range: 13 - 20

Received: Jul 06, 2018

Accepted: Dec 03, 2018

DOI: https://doi.org/10.2478/sgem-2018-0044

Keywords
couple-stress parameter, solute gradient, Brinkman number

© 2018 Shalu Choudhary, Sunil, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Figure 1

Figure 2

Figure 3

Figure 4

The variation in the fluid-based critical thermal Rayleigh number R cef with the couple-stress parameter (Da ) for F1=2, Vr=1 and Sf = 100.

The variation in the fluid-based critical thermal Rayleigh number Rcef with the couple-stress parameter F1 for Da=0.02, Vr =1 and Sf = 100.

The variation in the fluid-based critical thermal Rayleigh number R cef with the solute gradient (Sf) for Da, Vr =1.

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

Article Category: Research Article

Published Online: Apr 08, 2019

Page range: 13 - 20

Received: Jul 06, 2018

Accepted: Dec 03, 2018

DOI: https://doi.org/10.2478/sgem-2018-0044

Keywordscouple-stress parameter, solute gradient, Brinkman number

© 2018 Shalu Choudhary, Sunil, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Figure 1

Figure 2

Figure 3

Figure 4

The variation in the fluid-based critical thermal Rayleigh number R cef with the couple-stress parameter (Da ) for F1=2, Vr=1 and Sf = 100.

The variation in the fluid-based critical thermal Rayleigh number Rcef with the couple-stress parameter F1 for Da=0.02, Vr =1 and Sf = 100.

The variation in the fluid-based critical thermal Rayleigh number R cef with the solute gradient (Sf) for Da, Vr =1.

Keywords
couple-stress parameter, solute gradient, Brinkman number