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Unsteady convetion flow of micropolar fluids past a vertical porous plate embedded in a porous medium

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Summary

The unsteady two-dimensional laminar flow of a viscous incompressible micropolar fluid past a semi-infinite porous plate embebbed in a porous medium is studied. The free stream velocity follows an exponentially increasing or decreasing small perturbation law. The porous surface absorbs the micropolar fluid with a time varying suction velocity which has a small amplitude. The effects of material parameters on the velocity and temperature fields across the boundary layer are investigated. Numerical results of velocity distribution of micropolar fluids are compared with the corresponding flow problems for a Newtonian fluid. Results show that for the case of a surface cooling by natural convection the skin friction on the porous plate shows an increasing nature up to the critical value of ciscosity ratio. And the surface heat transfer tends to decrease slightly by increasing the magnitude of suction velocity with a given permeablity parameter, and given Prandtl number. However, for a surface heating case, the surface skin friction shows an opposite nature as compared with a surface cooling case.

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Abbreviations

A :

suction velocity parameter

C f :

skin-friction coefficient

C p :

specific heat at constant pressure

G :

Grashof number

g :

acceleration due to gravity

K :

permeability of the porous medium

k :

thermal conductivity

Nu :

Nusselt number

n :

dimensionless exponential index

Pr:

Prandtl number

T :

temperature

t :

dimensionless time

U o :

scale of free stream velocity

u, v :

components of velocities along and perpendicular to the plate, respectively

V o :

scale of suction velocity

x, y :

distances along and perpendicular to the plate, respectively

α:

fluid thermal diffusivity

β:

dimensionless viscosity ratio

β j :

coefficient of volumetric expansion of the working fluid

γ:

spin-gradient viscosity

ε:

scaler constant (≪1)

ρ:

fluid density

A :

coefficient of gyro-viscosity

μ:

fluid dynamic viscosity

v :

fluid kinematic viscosity

v r :

fluid kinematic rotational viscosity

θ:

dimensionless temperature

ω:

angular velocity vector

':

differentiation with respect toy

*:

dimensional properties

p :

plate

w :

wall condition

∞:

free stream condition

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  1. Y. J. Kim

    Present address: School of Mechanical Engineering, Sungkyunkwan University, 440-746, Suwon, Korea

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    Kim, Y.J. Unsteady convetion flow of micropolar fluids past a vertical porous plate embedded in a porous medium. Acta Mechanica 148, 105–116 (2001). https://doi.org/10.1007/BF01183672

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    • DOI: https://doi.org/10.1007/BF01183672

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