Unsteady incompressible Couette flow in a uniform transverse magnetic field

1960 ◽  
Vol 9 (1) ◽  
pp. 275-284 ◽  
Author(s):  
C. C. Mei
Keyword(s):  
Magnetic Field ◽  
Couette Flow ◽  
Transverse Magnetic Field ◽  
Transverse Magnetic

Article

1998 ◽  
Vol 76 (12) ◽  
pp. 937-947
Author(s):  
M Takashima
Keyword(s):  
Magnetic Field ◽  
Couette Flow ◽  
Transverse Magnetic Field ◽  
Wave Speed ◽  
Critical Reynolds Number ◽  
Maximum Velocity ◽  
Transverse Magnetic ◽  
Wave Number ◽  
Magnetic Prandtl Number ◽  
The Stability

The stability of combined plane Poiseuille and Couette flow of an electricallyconducting fluid under a transverse magnetic field is investigated using linear stability theory.In deriving the equations governing the stability, the so-called magnetic Stokes approximationis made using the fact that the magnetic Prandtl number Prm for most electrically conductingfluids is extremely small. The Chebyshev collocation method is adopted to obtain theeigenvalue equation, which is then solved numerically. The critical Reynolds number Rec,the critical wave number αc, and the critical wave speed cc are obtained for wide ranges ofthe Hartmann number Ha and the parameter k = U0 / (U0 + nu0), where U0 is the maximumvelocity of pure Couette flow and nu0 is the maximum velocity of pure Poiseuille flow. It isfound that a transverse magnetic field has both stabilizing and destabilizing effects on theflow depending on the value of k.PACS Nos. 47.20

Stability of the compressible viscous fluid around the plane Couette flow in the presence of a transverse uniform magnetic field

2018 ◽  
Vol 17 (01) ◽  
pp. 57-84
Author(s):  
Xingwei Zhang ◽  
Guojing Zhang ◽  
Hai-Liang Li
Keyword(s):  
Magnetic Field ◽  
Viscous Fluid ◽  
Couette Flow ◽  
Transverse Magnetic Field ◽  
Initial Perturbation ◽  
Three Dimensional ◽  
Transverse Magnetic ◽  
Plane Couette Flow ◽  
Compressible Viscous Fluid ◽  
The Stability

In this paper, we consider the stability of three-dimensional compressible viscous fluid around the plane Couette flow in the presence of a uniform transverse magnetic field and show that the uniform transverse magnetic field has a stabilizing effect on the plane Couette flow. Namely, for a sufficiently large Hartmann number, the compressible viscous plane Couette flow is nonlinear stable for small Mach number and arbitrary Reynolds number so long as the initial perturbation is small enough.

scholarly journals Effects of an imposed axial flow on a Ferrofluidic Taylor-Couette flow

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Sebastian Altmeyer ◽  
Younghae Do
Keyword(s):  
Magnetic Field ◽  
Couette Flow ◽  
Transverse Magnetic Field ◽  
Vortex Flow ◽  
Transverse Magnetic ◽  
Vortex Flows ◽  
Through Flow ◽  
Axial Pressure Gradient ◽  
Taylor Couette ◽  
Taylor Couette Flow

Abstract In this paper we investigate the effects of an externally imposed axial mass flux (axial pressure gradient, axial through flow) on ferrofluidic Taylor-Couette flow under the influence of either an axial or a transverse magnetic field. Without an imposed axial through flow, due to the symmetry-conserving axial field and the symmetry-breaking transverse field, it gives rise to various vortex flows in ferrofluidic Taylor-Couette flow such as wavy Taylor vortex flow (wTVF), wavy spiral vortex flow (wSPI) and wavy vortex flows ($${\boldsymbol{wTV}}{{\boldsymbol{F}}}_{{{\boldsymbol{H}}}_{{\boldsymbol{x}}}}$$ wTV F H x and $${\boldsymbol{wSP}}{{\boldsymbol{I}}}_{{{\boldsymbol{H}}}_{{\boldsymbol{x}}}}$$ wSP I H x ), which are typically produced by a nonlinear interaction of rotational, shear and magnetic instabilities. In addition, when an axial through flow is imposed to a ferrofluidic Taylor-Couette flow in the presence of either an axial or a transverse magnetic field, previously unknown new helical vortex structures are observed. In particular, we uncover ‘modulated Mixed-Cross-Spirals’ with a combination of at least three different dominant azimuthal wavenumbers. Emergence of such new flow states indicates richer but potentially more controllable dynamics in ferrofluidic flows, i.e., an imposed axial through flow will be a new controllable factor/parameter in applications of a ferrofluidic and magnetic flows flow.

Liquid‐metal Couette flow with a two‐dimensional periodic static surface and a transverse magnetic field

1992 ◽  
Vol 72 (2) ◽  
pp. 367-373 ◽  
Author(s):  
David J. Beatty ◽  
John S. Walker ◽  
Samuel H. Brown ◽  
Neal A. Sondergaard
Keyword(s):  
Magnetic Field ◽  
Liquid Metal ◽  
Couette Flow ◽  
Transverse Magnetic Field ◽  
Transverse Magnetic ◽  
Two Dimensional
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