Abstract
The investigation deals with unsteady laminar flow of a viscous, incompressible, electrically conducting fluid between conducting or nonconducting flat plates. A constant magnetic field is suddenly applied perpendicular to the plates and the created electromagnetic effects modify the motion. An approximate solution is obtained using time scales t and t/ε, where ε is the small magnetic Prandtl number.
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Abbreviations
- a :
-
half distance between the two perfectly conducting or nonconducting plates
- B :
-
dimensionless variable, (ρν/σ)1/2 H x /ka 2
- b(η, τ; ε):
-
initial layer variable, eqs. (13) and (14)
- H x :
-
induced magnetic field
- H 0 :
-
applied transverse magnetic field
- k :
-
pressure gradient in x-direction
- M :
-
Hartmann number, μ 0 H 0 a(σ/ρν)1/2
- t :
-
time or time multiplied by ν/a 2
- V x :
-
fluid velocity
- W :
-
dimensionless variable, ρ vV x ka 2
- ε :
-
magnetic Prandtl number, σμν
- η :
-
dimensionless y-coordinate, y/a
- σ :
-
electrical conductivity
- μ :
-
magnetic permeability
- ν :
-
kinematic viscosity
- ρ :
-
density
- τ :
-
stretched variable, t/ε
- ω(η, τ; ε):
-
initial layer variable, eqs. (13) and (14)
References
Yen, J. T., and C. C. Chang, Phys. Fluids 4 (1961) 1355.
Sloan, D. M., Appl. Sci. Res. 25 (1971) 126.
Chang, C. C., and T. S. Lundgren, Z. Angew. Math. Phys. 12 (1961) 100.
Davis, J. L., and E. L. Reiss, Trans. Soc. Rheology 14 (1970) 239.
Cole, J. D., Perturbation methods in applied mathematics. Blaisdell (1968).
Copson, E. T., Theory of Functions of a complex variable. Oxford University Press (1962).
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Sloan, D.M. Two time scale solution for an unsteady MHD duct flow. Appl. Sci. Res. 28, 361–380 (1973). https://doi.org/10.1007/BF00413077
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DOI: https://doi.org/10.1007/BF00413077