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Stability analysis of double-diffusive convection of Rivlin-Ericksen elastico-viscous nanofluid saturating a porous medium: a revised model

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Abstract

In the present paper we study the stability analysis of double-diffusive convection in a horizontal layer of an elastico-viscous nanofluid in a porous medium. The Rivlin-Ericksen fluid model is employed to describe the rheological behavior of the nanofluid. The dispersion relation describing the effect of various parameters is obtained by applying normal modes method and by using linear stability analysis. In this model we assume that the nanoparticle concentration flux is zero on the boundaries and we can give the values of temperature and concentration at the boundaries. The assumed boundary conditions neutralize the possibility of oscillatory convection and only stationary convection occurs. For stationary convection; it is observed that the Rivlin-Ericksen elastico-viscous nanofluid fluid behaves like an ordinary Newtonian nanofluid. The solutal-Rayleigh Number, thermo-nanofluid Lewis number, thermo-solutal Lewis number, Soret parameter and Dufour parameter have stabilizing effect on the stationary convection. A very good agreement is found between the present paper and earlier published results.

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Abbreviations

a :

Wave number

c:

Specific heat

d:

Thickness of the horizontal layer

DB :

Diffusion coefficient (m2/s)

DT :

Thermophoretic diffusion coefficient

F:

Kinematic visco-elasticity parameter

g:

Acceleration due to gravity (m/s2)

g :

Gravitational acceleration vector

k:

Thermal conductivity (w/mK)

Le:

Thermosolutal Lewis number

Ln:

Thermo-nanofluid Lewis number

NA :

Modified diffusivity ratio

NB :

Modified particle-density ratio

N CT :

Soret parameter

N TC :

Dufour parameter

p:

Pressure (Pa)

Pr:

Prandtl number

q :

Darcy velocity vector (m/s)

R D :

Thermal Darcy-Rayleigh number

(R D ) C :

Critical Thermal Darcy-Rayleigh number

Rm:

Basic-density Rayleigh number

Rn:

Concentration Rayleigh number

Rs:

Solutal Rayleigh number

t:

Time (s)

T:

Temperature (K)

(u,v,w):

Darcy velocity components

(x,y,z):

Space co-ordinates (m)

α T :

Solute volumetric coefficient

α C :

Thermal volumetric coefficient (1/K)

φ:

Nanoparticles volume fraction

κ:

Thermal diffusivity

\({{\kappa }_{m}}\) :

Effective thermal diffusivity of porous medium (m/s2)

μ:

Viscosity of the fluid(Ns/m2)

μ’:

Viscoelasticity

ν:

Kinematic viscosity

\({{\nu }^{'}}\) :

Kinematic viscoelasticity

ρ:

Density of fluid (kg/m3)

\({{\rho }_{p}}\) :

Nanoparticle mass density (kg/m3)

ω:

Growth rate of disturbances

’:

Non-dimensional variables

’ ’:

Perturbed quantity

p:

Particle

f:

Fluid

b:

Basic state

0:

Lower boundary

1:

Upper boundary

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Acknowledgments

Authors would like to thank the learned referee for their valuable comments and suggestions for the improvement of quality of the paper.

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Authors and Affiliations

  1. Department of Mathematics, Sidharth Government College, Nadaun, District Hamirpur, Himachal Pradesh, India

    G. C. Rana

  2. Department of Mathematics, Government College, Nurpur, District Kangra, Himachal Pradesh, INDIA

    R. Chand

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  1. G. C. Rana
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  2. R. Chand
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Correspondence to G. C. Rana.

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Rana, G., Chand, R. Stability analysis of double-diffusive convection of Rivlin-Ericksen elastico-viscous nanofluid saturating a porous medium: a revised model. Forsch Ingenieurwes 79, 87–95 (2015). https://doi.org/10.1007/s10010-015-0190-5

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  • DOI: https://doi.org/10.1007/s10010-015-0190-5

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