Summary
Certain steady magnetohydrodynamic flows of a viscous incompressible fluid, in which the magnetic field is everywhere orthogonal to the velocity field, are related to viscous compressible flows having zero magnetic field. Examples are given to illustrate this relationship. Other linked magnetic and non-magnetic flows can be found using similar processes.
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References
Goldsworthy, F. A., J. Fluid Mech. 11 (1961) 519.
Power, G. and D. Walker, Z. angew. Math. Phys. 16 (1965) 803.
Illingworth, C. R., Proc. Cambridge Phil. Soc. 46 (1950) 469.
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Power, G., Walker, D. Reduction of viscous flows having orthogonal magnetic and velocity field distributions. Appl. Sci. Res. 17, 223–232 (1967). https://doi.org/10.1007/BF00386092
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DOI: https://doi.org/10.1007/BF00386092