Masaki Takashima 1996 Fluid Dyn. Res. 17 293 doi:10.1016/0169-5983(95)00038-0
The stability of the modified plane Poiseuille flow in the presence of a transverse magnetic field
Masaki Takashima
Show affiliationsThe stability against small disturbances of the pressure-driven plane laminar motion of an electrically conducting fluid under a transverse magnetic field is investigated. Assuming that the outer regions adjacent to the fluid layer are electrically non-conducting and not ferromagnetic, the appropriate boundary conditions on the magnetic field perturbations are presented. The Chebyshev collocation method is adopted to obtain the eigenvalue equation, which is then solved numerically. The critical Reynolds number Rc, the critical wave number αc, and the critical wave speed cc are obtained for wide ranges of the magnetic Prandtl number Pm and the Hartmann number M. It is found that except for the case when Pm is sufficiently small, the magnetic field has both stabilizing and destabilizing effects on the fluid flow, and that for a fixed value of M the fluid flow becomes more unstable as Pm increases.
- PACS
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47.15.Fe Stability of laminar flows
- Subjects
- Dates
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Issue 6 (May 1996)
Received 22 March 1995, revised 11 August 1995, accepted for publication 15 December 1995
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The stability of the modified plane Poiseuille flow in the presence of a transverse magnetic field
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