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On unsteady magnetic low-speed slip flow in the boundary layer

Zur instationären magnetischen Gleitströmung geringer Geschwindigkeit in der Grenzschicht

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Summary

The influence of an uniform transverse magnetic field on the unsteady laminar boundary layer low-speed slip flow of a rarefied electrically conducting gas is considered. By means of the successive approximation method two problems are studied in detail. The first is an oscillating cylindrical body in a rarefied gas at rest. In the second problem the magnetic slip flow in the boundary layer around cylindrical bodies is studied for the case where the external speed of flow is exponentially dependent on time.

Zusammenfassung

Der Einfluß eines gleichförmigen transversalen Magnetfeldes auf die instationäre Gleitströmung geringer Geschwindigkeit in der laminaren Grenzschicht eines verdünnten, elektrisch leitenden Gases wird betrachtet. Zwei Probleme werden mit Hilfe der Methode der sukzessiven Approximationen genauer untersucht. Das erste ist das eines schwingenden zylindrischen Körpers in einem ruhenden Gas. Im zweiten Problem wird die Gleitströmung in der Grenzschicht um zylindrische Körper für den Fall einer exponentiell von der Zeit abhängigen äußeren Geschwindigkeit der Strömung betrachtet.

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Abbreviations

x :

distance along the surface from the leading edge

y :

distance normal to the surface

t :

time

u, v :

velocity components alongx andy respectively

∂:

density

V (x, t) :

velocity of external flow in a direction parallel to wall at the edge of the boundary layer

ν:

kinematic viscosity

σ:

the electrical conductivity

B (x, t) :

the magnetic induction

λ:

molecular mean free path

V ∞ :

free stream velocity

V 1(x):

potential flow velocity about the body in the steady state

N *, γ,N :

magnetic parameters

Λ:

molecular mean free path parameter

t s :

time of separation

R :

radius of circular cylinder

n :

circular frequency

i :

\(\sqrt { - 1} \)

a, b :

constants given by (41)

a 0, ...,a 7,E 0, ...,E 10,A 0, ...,A 13,p, q, C 1 *,C 1 **,C 2 :

constants given by (49–51) and (53–58)

E :

dimensionless slip velocity amplitude

δ:

slip velocity phase lag

References

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  1. Department of Mechanics Mechanical Engineering Faculty, University of Novi Sad, Jovana Boskovica 16, 21000, Novi Sad, Yugoslavia

    Dj. S. Djukic

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Djukic, D.S. On unsteady magnetic low-speed slip flow in the boundary layer. Acta Mechanica 18, 35–48 (1973). https://doi.org/10.1007/BF01173456

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  • DOI: https://doi.org/10.1007/BF01173456

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