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Oscillating Convection of Nanofluid in Porous Medium

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Abstract

In this paper, oscillatory convection in a horizontal layer of nanofluid in porous medium is studied. For porous medium, Darcy model is applied. A linear stability theory and normal mode analysis method is used to find the solution confined between two free boundaries. The onset criterion for oscillatory convection is derived analytically and graphically. Regimes of oscillatory and non-oscillatory convection for various parameters are derived. The effects of Lewis number, concentration Rayleigh number, Prandtl–Darcy number (Vadasz Number) and modified diffusivity ratio on the oscillatory convection are investigated graphically. We examine the validity of ‘PES’ and concluded that ‘PES’ is not valid for the problem.

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Abbreviations

a :

Wave number

D B :

Diffusion coefficient (m 2/s)

D T :

Thermophoretic diffusion coefficient

Da :

Darcy number

g :

Acceleration due to gravity (m/s 2)

j :

Mass flux (kg/m 2 s)

k 1 :

Medium permeability

k m :

Thermal conductivity (w/mK)

k B :

Boltzmann constant (j/K)

L e :

Lewis number

n :

Growth rate of disturbances

N A :

Modify diffusivity ratio

N B :

Modify particle-density increment

p :

Pressure (Pa)

p′:

Pressure

P r :

Prandtl number

q :

Darcy velocity vector (m/s)

R a :

Rayleigh–Darcy number

\({R_{a_{\rm c}}}\) :

Critical Rayleigh–Darcy number

R m :

Density Rayleigh number

R n :

Concentration Rayleigh number

t :

Time (s)

t′:

Time

T :

Temperature (K)

T′:

Temperature

Va :

Prandtl–Darcy number (Vadasz number)

u,v,w :

Velocity components

x, y, z :

Space co-ordinates (m)

x′, y′, z′:

Space co-ordinates

α :

Thermal expansion coefficient (1/K)

μ :

Viscosity

ε :

Porosity

ρ :

Density of the nanofluid(kg/m 3)

(ρc)m :

Heat capacity in porous medium

(ρc)p :

Heat capacity of nanoparticles

φ :

Volume fraction of the nanoparticles

ρ p :

Density of nanoparticles

ρ f :

Density of base fluid

κ :

Thermal diffusivity

ω :

Dimensional frequency

′:

Non dimensional variables

′′:

Perturbed quantity

p:

Particle

f:

Fluid

0:

Lower boundary

1:

Upper boundary

H:

Horizontal plane

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Authors and Affiliations

  1. Department of Mathematics, Government P. G. College, Dhaliara, 177103, Himachal Pradesh, India

    Ramesh Chand

  2. Department of Mathematics, NSCBM Government P. G. College, Hamirpur, 177005, Himachal Pradesh, India

    G. C. Rana

Authors
  1. Ramesh Chand
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  2. G. C. Rana
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Correspondence to Ramesh Chand.

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Chand, R., Rana, G.C. Oscillating Convection of Nanofluid in Porous Medium. Transp Porous Med 95, 269–284 (2012). https://doi.org/10.1007/s11242-012-0042-9

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