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Variable fluid properties and thermal radiation effects on flow and heat transfer in micropolar fluid film past moving permeable infinite flat plate with slip velocity

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Abstract

This work deals with the influence of thermal radiation on the problem of the mixed convection thin film flow and heat transfer of a micropolar fluid past a moving infinite vertical porous flat plate with a slip velocity. The fluid viscosity and the thermal conductivity are assumed to be the functions of temperature. The equations governing the flow are solved numerically by the Chebyshev spectral method for some representative value of various parameters. In comparison with the previously published work, the excellent agreement is shown. The effects of various parameters on the velocity, the microrotation velocity, and the temperature profiles, as well as the skin-friction coefficient and the Nusselt number, are plotted and discussed.

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Abbreviations

c p :

specific heat at constant pressures

C f :

skin-friction coefficient

\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{F}\) :

body force per unit mass

f w :

dimensionless suction or injection velocity

g :

gravitational acceleration acting in the downward direction

g(η):

dimensionless microrotation

J :

microinertia

k :

gyroviscosity

K :

material parameter

k*:

mean absorption coefficient

\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{l}\) :

body couple per unit mass

m 1 :

buoyancy parameter

n :

boundary parameter

N :

dimensional component of microrotation vector normal to the XY-plane

Nu :

Nusselt number

p :

pressure

Pr :

Prandtl number

Q :

internal heat generation density

q r :

radiation heat flux

q w :

heat transfer from the plate

R :

radiation parameter

Re :

Reynolds number

T :

fluid temperature

T 0 :

temperature on the free surface

T w :

surface temperature of the plate

U,V :

dimensional components of the velocities along and perpendicular to the plate, respectively

U w :

surface velocity

u :

dimensionless velocity along the plate

\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{U}\) :

translational vector

V w :

dimensional suction or injection velocity

X,Y :

dimensional distances along and perpendicular to the plate, respectively.

α*,β*,γ*:

material constants for micropolar fluids

β 1,β 2 :

viscosity and thermal conductivity parameters, respectively

µ0 :

fluid viscosity at the temperature T 0

κ 0 :

thermal conductivity at the temperature T 0

φ :

dissipation function

δ :

film thickness

ν 0 :

kinematic viscosity at the temperature T 0

α w :

dimensional slip coefficient

ρ 0 :

density of the fluid at the temperature T 0

η :

dimensionless distance normal to the plate

σ*:

Stefan-Boltzmann constant

κ f :

thermal conductivity

µ:

dynamic viscosity

ρ :

fluid density

α :

dimensionless slip parameter

τ w :

wall shear stress

β :

thermal expansion coefficient

\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\sigma }\) :

microrotation vector

θ :

dimensionless temperature

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Benha University, Benha, 13518, Egypt

    M. A. A. Mahmoud & S. E. Waheed

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  1. M. A. A. Mahmoud
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  2. S. E. Waheed
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Correspondence to M. A. A. Mahmoud.

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Mahmoud, M.A.A., Waheed, S.E. Variable fluid properties and thermal radiation effects on flow and heat transfer in micropolar fluid film past moving permeable infinite flat plate with slip velocity. Appl. Math. Mech.-Engl. Ed. 33, 663–678 (2012). https://doi.org/10.1007/s10483-012-1578-x

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