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Free convection effects on the oscillatory flow of a couple stress fluid through a porous medium

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Summary

Effects of free convection currents on the oscillatory flow of a polar fluid through a porous medium, which is bounded by a vertical plane surface of constant temperature, have been studied. The surface absorbs the fluid with a constant suction and the free stream velocity oscillates about a constant mean value. Analytical expressions for the velocity and the angular velocity fields have been obtained, using the regular perturbation technique. The effects of Grashof numberG; material parameters α and β; Prandtl numberP; permeability parameterK and frequency parametern on the velocity and the angular velocity are discussed. The effects of cooling and heating of a polar fluid compared to a Newtonian fluid have also been discussed. The velocity of a polar fluid is found to decrease as compared to the Newtonian fluid.

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Abbreviations

C p :

specific heat at constant pressure

g :

acceleration due to gravity

G :

Grashof number

K + :

permeability of the porous medium

K :

dimensionless permeability

P :

Prandtl number

t + :

time

t :

dimensionless time

T w + :

mean temperature of the surface

T + :

temperature of the fluid

T +∞ :

temperature of the fluid away from the surface

ϱ:

density of the fluid

μ:

viscosity

μ r :

rotational viscosity

C a ,C d :

coefficients of couple stress viscosities

I :

a scalar constant of dimension equal to that of the moment of inertia of unit mass

x +,y + :

coordinate system

u +,v + :

velocity components in thex + andy + directions

u :

dimensionless velocity in thex +-direction

ω+ :

angular velocity component

ω:

dimensionless angular velocity

n + :

frequency of oscillations

n :

dimensionless frequency

ε:

perturbation parameter

U :

a constant velocity

u 0 :

mean velocity

u 1 :

fluctuating part of the velocity

ω0 :

mean angular velocity

ω1 :

fluctuating part of the angular velocity

T 0 :

mean temperature

T 1 :

fluctuating part of the temperature

β0 :

coefficient of the volume expansion

ν:

kinematic viscosity

νr :

rotational kinematic viscosity

α, β:

material parameters characterizing the polarity of the fluid

v 0 :

suction velocity

ϱ∞ :

density of the fluid far from the surface

y :

dimensionless coordinate normal to the surface

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Author notes

  1. P. S. Hiremath & P. M. Patil

    Present address: Department of Mathematics, Karnatak University, 580 003, Dharwad, India

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    1. P. S. Hiremath
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    2. P. M. Patil
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    Hiremath, P.S., Patil, P.M. Free convection effects on the oscillatory flow of a couple stress fluid through a porous medium. Acta Mechanica 98, 143–158 (1993). https://doi.org/10.1007/BF01174299

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    • DOI: https://doi.org/10.1007/BF01174299

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