Abstract
An exact solution of the Magnetohydrodynamic pipe flow equations is found in terms of elementary functions. As the Hartmann number increases from zero reverse motion in the pipe occurs and eventually separates from the boundary. With further increase in the Hartmann number the vorticity on the boundary continuously changes sign and the flow is analogous to laminar separation in field free hydrodynamics.
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References
Hunt, J. C. R. and J. A. Shercliff, Annual Review of Fluid Mech. 3 (1971) 37.
Todd, L., J. of Fluid Mech. 31 (1968) 321.
Van Dyke, M., Pertubation Methods in Fluid Mechanics, Academic Press, N.Y. 1964, p. 159–161.
Ranger, K. B., Math. Res. Center, Univ. of Wisconsin-Madison, Technical Summary Rep. No 1237, 1972.
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Sponsored by the United States Army under Contract No. DA-31-124-ARO-D-462.
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Ranger, K.B. Magnetohydrodynamic pipe flow with reverse motion. Appl. Sci. Res. 30, 81–92 (1974). https://doi.org/10.1007/BF00386062
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DOI: https://doi.org/10.1007/BF00386062