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Fundamental Issues and Canonical Flows

Thermal Instability of Rivlin–Ericksen Elastico-Viscous Nanofluid Saturated by a Porous Medium

[+] Author and Article Information
Ramesh Chand

Department of Mathematics,
Government P.G. College Dhaliara,
Kangra (HP), India
e-mail: rameshnahan@yahoo.com

G. C. Rana

Department of Mathematics,
NSCBM Government P. G. College,
Hamirpur (HP), India
e-mail: drgcrana15@gmail.com

Contributed by the Fluids Engineering Division of ASME for publication in the Journal of Fluids Engineering. Manuscript received April 18, 2012; final manuscript received October 19, 2012; published online November 20, 2012. Assoc. Editor: Ali Beskok.

J. Fluids Eng 134(12), 121203 (Nov 20, 2012) (7 pages) doi:10.1115/1.4007901 History: Received April 18, 2012; Revised October 19, 2012

Thermal instability in a horizontal layer of Rivlin–Ericksen elastico-viscous nanofluid in a porous medium is considered. A linear stability analysis based upon normal mode analysis is used to find a solution of the fluid layer confined between two free boundaries. The onset criterion for stationary and oscillatory convection is derived analytically and graphs have been plotted by giving numerical values to various parameters to depict the stability characteristics. The effects of the concentration Rayleigh number, Vadasz number, capacity ratio, Lewis number, and kinematics viscoelasticity parameter on the stability of the system are investigated. Regimes of oscillatory and nonoscillatory convection for various parameters are derived and discussed in detail. The sufficient conditions for the nonexistence of oscillatory convection have also been obtained.

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References

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Figures

Grahic Jump Location
Fig. 1

Physical configuration

Grahic Jump Location
Fig. 2

Variation of Rayleigh number Ra with wave number a for different values of Lewis number

Grahic Jump Location
Fig. 3

Variation of Rayleigh number Ra with wave number a for different values of concentration Rayleigh number

Grahic Jump Location
Fig. 4

Variation of Rayleigh number Ra with wave number a for different values of porosity parameter

Grahic Jump Location
Fig. 5

Variation of Rayleigh number Ra with wave number a for different values of modified diffusivity ratio

Grahic Jump Location
Fig. 6

Variation of oscillatory Rayleigh number Ra with wave number a for different values of Vadasz number

Grahic Jump Location
Fig. 7

Variation of oscillatory Rayleigh number Ra with wave number a for different values of kinematic viscoelasticity parameter

Grahic Jump Location
Fig. 8

Variation of oscillatory Rayleigh number Ra with wave number a for different values of capacity ratio

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