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On hydromagnetic fluctuating flow past an infinite porous plate in slip flow regime

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Abstract

The effect of a uniform external magnetic field on the laminar, incompressible rarefied gas flow along an infinite porous flat plate is studied under the following conditions: 1) there is uniform suction, 2) the external flow velocity varies periodically with time in magnitude but not in direction, 3) the magnetic Reynolds number is small and 4) the current occurs under slip flow boundary conditions. Expressions for the velocity and temperature fields in the boundary layer are obtained. The response of skin friction, and heat transfer to the fluctuating stream is studied for variations in the rarefaction parameter h 1, the magnetic field parameter M, and the frequency of the fluctuating stream.

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Abbreviations

c p :

specific heat of the gas

f 1 :

Maxwells reflection coefficient

f 2 :

thermal accommodation coefficient

G :

as defined in (36)

h 1 :

rarefaction parameter (L 1 v 0/ν)

h 2 :

nondimensional temperature jump coefficient (L 2 v 0/ν)

H :

amplitude of the skin friction

k :

thermal conductivity

K n :

Knudsen number

L :

mean free path

L 1 :

(2−f 1/f 1) L

L 2 :

\(\frac{{2 - f_2 }}{{f_2 }} \cdot \frac{{2_\gamma }}{{\gamma + 1}} \cdot \frac{L}{\sigma }\)

M :

magnetic field parameter (σ 0 νB 20 /ρv 20 )

m :

1/2[1+(1+4M+4iλ)1/2], m r+im i

n 1 :

1/2[1+(1+4M)1/2]

q :

heat flux

R :

suction Reynolds number

T :

temperature

x, y :

coordinates along and perpendicular to the plates

u, v :

velocity components along x, y-directions

ρ :

density

ν :

kinematic viscosity

σ 0 :

electrical conductivity

σ :

Prandtl number

ω :

frequency of the fluctuating stream

λ :

nondimensional frequency parameter (ων/v 20 )

η :

nondimensional distance from wall (v 0 y/ν)

α :

phase lead

U 0 ξ 0 :

mean velocity in the boundary layer

εU 0 ξ 1, εU 0 ξ 2 :

amplitude of the velocity fluctuation in the boundary layer

γ :

specific heat ratio

References

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  4. Reddy, K. C., Quart. J. Mech. Appl. Math. 17 (1964) 381.

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  5. Street, R. E., A study of boundary conditions in slip flow aerodynamics in Rarefied gas dynamics, Pergamon, London 1960.

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Authors and Affiliations

  1. Dept. of Mathematics, I.I.T., Bombay (76), India

    V. M. Soundalgekar

Authors
  1. V. M. Soundalgekar
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Soundalgekar, V.M. On hydromagnetic fluctuating flow past an infinite porous plate in slip flow regime. Appl. Sci. Res. 23, 301–314 (1971). https://doi.org/10.1007/BF00413206

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  • DOI: https://doi.org/10.1007/BF00413206

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