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Certain yawed magnetogasdynamic flows

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Abstract

Certain steady yawed magnetogasdynamic flows, in which the magnetic field is everywhere parallel to the velocity field, are related to certain reduced three-dimensional compressible gas flows having zero magnetic field. Under a restriction, the reduced flows are linked, by certain reciprocal relations, to a four parameter class of plane gas flows. In the instance of constant entropy an approximation method is suggested for obtaining magnetogasdynamic flows from the corresponding plane, irrotational gasdynamic flows and examples are given.

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Abbreviations

H :

magnetic intensity

q :

fluid velocity

ρ :

fluid density

p :

pressure

s :

entropy

Q t, H t :

component of q, H in the x−y plane

w \(\begin{array}{*{20}c} \wedge \\ k \\ \end{array}\), h \(\begin{array}{*{20}c} \wedge \\ k \\ \end{array}\) :

component of q, H perpendicular to the x−y plane

λ :

factor of proportionality

q*:

fluid velocity

ρ*:

fluid density

p*:

pressure

Q *t =u*î+v*ĵ, w*\(\begin{array}{*{20}c} \wedge \\ k \\ \end{array}\) :

components of q*

l :

arbitrary constant

A v :

Alfvén speed

Q′ t, ρ′, p′ :

fluid velocity, density, pressure of the reciprocal gas dynamic flow

L, n, k, μ :

arbitrary constants

φ, ψ :

velocity potential, stream function

θ :

angle made by Q t, Q *t , and V′ with the x-axis

γ :

adiabatic gas constant

a 2=(γ−1)/2γ:

constant

M :

Mach number

W :

constant value of w*

E :

approximate constant value of g(p)

φ*:

modified potential function

ω :

modified velocity coordinate

σ :

ω+iθ

\(f(\bar \sigma )\) :

complex potential of the irrotational flow

B :

arbitrary constant

V′ :

incompressible flow velocity

V :

modified fluid velocity

X p, Y p :

points on the profile

References

  1. Thibault, R., Compt. Rend. 256 (1963) 2528.

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  2. Power, G. and P. Smith, J. Math. Mech. 10 (1961) 349.

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  3. Power, G. and P. Smith, J. Fluid Mech. 4 (1958) 600.

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  4. Power, G. and A. Tunbridge, Z. Angew. Math. Mech. 43 (1963) 191.

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Authors and Affiliations

  1. Dept. of Mathematics, The University, Nottingham, UK

    G. Power & D. Walker

  2. Dept. of Mathematics, Loughborough University of Technology, Loughborough, UK

    D. Walker

Authors
  1. G. Power
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  2. D. Walker
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Power, G., Walker, D. Certain yawed magnetogasdynamic flows. Appl. sci. Res. 21, 341–355 (1969). https://doi.org/10.1007/BF00411618

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  • DOI: https://doi.org/10.1007/BF00411618

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