Abstract
An explicit solution in terms of the stream function is found for the streaming M.H.D. flow past a semi-infinite flat plate in the presence of a perpendicular uniform magnetic field. Asymptotic forms of the velocity field at large distances are obtained, and a related problem involving a semi-infinite needle is also discussed.
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Abbreviations
- H 0 :
-
uniform magnetic field
- î :
-
unit vector directed along the x-axis
- ĵ :
-
unit vector directed along the y-axis
- \(\mathop k\limits^\Delta \) :
-
unit vector directed along the z-axis
- q :
-
fluid velocity vector
- r :
-
polar radius vector in two dimensions
- u :
-
two-dimensional harmonic in the (z, ρ) plane even in ρ
- V :
-
solution of the two-dimensional Helmholtz equation
- W :
-
solution of the axially symmetric Helmholtz equation
- (x, y, z):
-
Cartesian coordinates
- β 2 :
-
hydromagnetic parameter, (σμ 2/ρ 0 v)H 20
- η :
-
parabolic coordinate
- μ :
-
magnetic permeability
- ν :
-
kinematic viscosity
- ξ :
-
parabolic coordinate
- ρ 0 :
-
fluid density
- ρ :
-
parameter of integration
- σ :
-
electrical conductivity
- χ :
-
flux function for the fluid velocity field in asymmetric three-dimensional flow
- Ψ :
-
physical stream function
- ψ :
-
nondimensional stream function
- ω :
-
cylindrical radius vector
References
Greenspan, H. P., J. of Fluid Mech. 9 (1960) 455.
Ranger, K. B., J. of Math. and Mech. 14 (1965) 383.
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Ranger, K.B. M.H.D. flow past a flat plate in the presence of a non aligned magnetic field. Appl. Sci. Res. 25, 355–360 (1972). https://doi.org/10.1007/BF00382308
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DOI: https://doi.org/10.1007/BF00382308