A similarity solution for the flow and heat transfer over a moving permeable flat plate in a parallel free stream

Abstract

This paper presents both a numerical and analytical study in connection with the steady boundary layer flow and heat transfer induced by a moving permeable semi-infinite flat plate in a parallel free stream. Both the velocities of the flat plate and the free stream are proportional to x 1/3. The surface temperature is assumed to be constant. The governing partial differential equations are converted into ordinary differential equations by a new similarity transformation. Numerical results for the flow and heat transfer characteristics are obtained for various values of the moving parameter, transpiration parameter and the Prandtl number. Approximate analytical solutions are also obtained when the suction or injection parameter is very large. It is found that dual solutions exist for the case when the fluid and the plate move in the opposite directions.

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Abbreviations

f(η):

Dimensionless stream function

g(η):

Dimensionless temperature

k :

Thermal conductivity

L :

Characteristic length

Pr:

Prandtl number

q w :

Heat transfer from the stretching sheet

Re:

Reynolds number

s :

Dimensionless mass flux parameter

T :

Fluid temperature

T w :

Uniform temperature of the stretching sheet

T :

Ambient temperature

u, v :

Dimensionless velocity components along the x- and y- directions, respectively

u e (x):

Dimensionless velocity of the free stream or far from the plate

u w (x):

Dimensionless velocity of the moving plate

U e , U w :

Dimensionless constants

U :

Characteristic velocity

v w (x):

Dimensionless mass flux velocity

x, y :

Dimensionless Cartesian coordinates along the surface and normal to it, respectively

ΔT :

Characteristic temperature

η :

Similarity variable

λ :

Dimensionless moving parameter

μ :

Dynamic viscosity

ν :

Kinematic viscosity

θ :

Dimensionless temperature

τ w :

Wall skin friction or wall shear stress

ψ :

Dimensionless stream function

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Acknowledgments

The authors wish to express their very sincerely thanks to the reviewers for the very good and interesting comments.

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Correspondence to Ioan Pop.

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Bachok, N., Jaradat, M.A. & Pop, I. A similarity solution for the flow and heat transfer over a moving permeable flat plate in a parallel free stream. Heat Mass Transfer 47, 1643 (2011). https://doi.org/10.1007/s00231-011-0821-9

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Keywords

  • Flat Plate
  • Free Stream
  • Boundary Layer Flow
  • Free Stream Velocity
  • Dual Solution