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Smith, Peter

Some extremum principles for pipe flow in magnetohydrodynamics. (English) Zbl 0248.76048

Z. Angew. Math. Phys. 23, 753-764 (1972).
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Cited in 5 Documents

MSC:

76W05 Magnetohydrodynamics and electrohydrodynamics
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References:

[1] J.A. Shercliff,Steady Motion of Conducting Fluids in Pipes under Transverse Magnetic Fields, Proc. Camb. Phil. Soc.49, 136–144 (1953). · Zbl 0050.19404 · doi:10.1017/S0305004100028139
[2] C.C. Chang andT.S. Lundgren,Duct Flow in Magnetohydrodynamics, Z. angew. Math. Phys.12, 100–114 (1961). · Zbl 0115.21904 · doi:10.1007/BF01601011
[3] R.R. Gold,Magnetohydrodynamic Pipe Flow. Part 1, J. Fluid Mech.13, 505–512 (1962). · Zbl 0117.43301 · doi:10.1017/S0022112062000889
[4] J.A. Shercliff,The Flow of Conducting Fluids in Circular Pipes under Transverse Magnetic Fields, J. Fluid Mech.1, 644–666 (1956). · Zbl 0074.21106 · doi:10.1017/S0022112056000421
[5] P.H. Roberts,Singularities of Hartmann Layers, Proc. R. Soc. [A]300, 94–107 (1967). · Zbl 0166.22704 · doi:10.1098/rspa.1967.0159
[6] P. Smith,Some Asymptotic Extremum Principles for Magnetohydrodynamic Pipe Flow, Appl. Sci. Res.24, 452–466 (1971). · Zbl 0235.76053
[7] T.M. Apostol,Mathematical Analysis (Addison-Wesley, Reading, Mass., 1957), p. 289. · Zbl 0077.05501
[8] W.E. Williams,Magnetohydrodynamic Flow in a Rectangular Tube at High Hartmann Number, J. Fluid Mech.16, 262–268 (1963). · Zbl 0226.76038 · doi:10.1017/S0022112063000732
[9] G.E. Roberts andH. Kaufman,Table of Laplace Transforms (Saunders, Philadelphia 1966). · Zbl 0137.08901
[10] M. Abramowitz andIrene A. Stegun,Handbook of Mathematical Functions (Dover, New York 1965). · Zbl 0171.38503
[11] J.A. Shercliff,Magnetohydrodynamic Pipe Flow. Part 2. High Hartmann Number, J. Fluid Mech.13, 513–518 (1962). · Zbl 0117.43302 · doi:10.1017/S0022112062000890
[12] E.T. Copson,Asymptotic Expansions (Cambridge University Press, 1965). · Zbl 0123.26001
[13] N.C. Wenger,A Variational Principle for Magnetohydrodynamic Channel Flow, J. Fluid Mech.43, 211–224 (1970). · Zbl 0212.59802 · doi:10.1017/S002211207000232X
[14] P. Smith,Some Extremum Principles for Magnetohydrodynamic Flow in Conducting Pipes, Proc. Camb. Phil. Soc.72, 303–313 (1972). · Zbl 0249.76065 · doi:10.1017/S0305004100047113
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