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Stagnation-point viscous flow of an incompressible fluid between porous plates with uniform blowing

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Abstract

The axially-symmetric laminar flow of an incompressible viscous fluid resulting from uniform injection through two parallel porous plates is analyzed. An exact numerical solution as well as asymptotic solutions for high and low Reynolds numbers are obtained. It is found that the velocity component normal to the porous plates is everywhere independent of radial position. This property of uniform accessibility may make this flow geometry a useful experimental tool analogous to the rotating disc. The analysis of high Peclet number mass transfer across the center plane of this geometry is presented as an example.

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Abbreviations

c :

Constant of integration

C :

Dimensionless concentration

c A :

Concentration of solute A, gm-moles/cm3

c 1 :

Concentration at upper plate

c 2 :

Concentration at lower plate

c 0 :

Concentration at center plane

d :

Dimensionless pressure gradient perturbation function

d 1,d 2, ...:

Coefficients in expansion ofd

D p :

Dimensionless pressure gradient

D 0,D 1, ...:

Coefficients in expansion ofD p

D AB :

Diffusivity, cm2/sec

f :

Dimensionless velocity gradient,θ′

g :

Dimensionless velocity profile perturbation function

g :

Inner representation ofg

g :

Outer representation ofg

g 1,g 2, ...:

Coefficients in expansion ofg

g 1,g 2, ...:

Coefficients in expansion ofg

L :

Half-width between plates, cm

Nu AB :

Nusselt number for mass transfer

p :

pressure, gm/cm-sec2

P :

Head, defined as (p + ρgz), gm/cm sec2

Q :

Volumetric flow rate, cm3/sec

r :

Radial position coordinate, cm

Re :

Reynolds number, defined asLV ρ/μ

Sc :

Schmidt number

V :

Injection velocity, cm/sec

v r :

Radial velocity component, cm/sec

v z :

Axial velocity component, cm/sec

Y :

Stretched dimensionless axial position in inner region

z :

Axial position coordinate, cm

ɛ :

Perturbation parameter, 1/Re

φ :

z-dependent factor inv r , sec−1

μ :

Viscosity, gm/cm sec

ρ :

Density, gm/cm3

θ :

Dimensionless axial velocity,v z /V

θ 0,θ 1, ...:

Coefficients in smallRe expansion ofθ

ζ :

Dimensionless axial position,z/L

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Authors and Affiliations

  1. Dep. of Chem. Eng., Univ. of Wisconsin, 53706, Madison, Winconsin, U.S.A.

    Thomas W. Chapman & Gerald L. Bauer

Authors
  1. Thomas W. Chapman
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  2. Gerald L. Bauer
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Chapman, T.W., Bauer, G.L. Stagnation-point viscous flow of an incompressible fluid between porous plates with uniform blowing. Appl. Sci. Res. 31, 223–239 (1975). https://doi.org/10.1007/BF02116160

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  • DOI: https://doi.org/10.1007/BF02116160

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