Flow induced in a cylindrical column by a uniformly rotating magnetic field

1967 ◽  
Vol 297 (1451) ◽  
pp. 558-563
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Reynolds Number ◽  
High Frequency ◽  
Fourier Transforms ◽  
Reynolds Numbers ◽  
Magnetic Reynolds Number ◽  
Rotating Magnetic Field ◽  
Cylindrical Column ◽  
Field Lines

Under laboratory conditions, the magnetic Reynolds number is quite small in a conductor, but can be made appreciable if a high frequency rotating field is applied. Moffatt investigated this problem for high magnetic Reynolds numbers and concluded that there existed a magnetic boundary layer due to spiralling of field lines. Applying Fourier transforms and solving the corrected equations, we find that at low magnetic Reynolds numbers the field lines uniformly penetrate the cylindrical column and do not exhibit any appreciable spiralling. The rotation opposes the drift due to conductivity which is evened out as one proceeds from the centre to the surface. This uniform behaviour persists for small magnetic Reynolds number inside and outside. When the magnetic Reynolds number becomes large, of the order of 100 (say), the field lines passing through the axis of the cylinder exhibit spiralling as suggested by Moffatt since the diffusion is unable to counterbalance the rotational effects.

A physical description of magnetic helicity evolution in the presence of reconnection lines

1991 ◽  
Vol 46 (1) ◽  
pp. 179-199 ◽  
Author(s):  
Andrew N. Wright ◽  
Mitchell A. Berger
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Magnetic Reynolds Number ◽  
Magnetic Helicity ◽  
Two Dimensional ◽  
Flux Tubes ◽  
Physical Description ◽  
Reconnection Region ◽  
Field Geometry ◽  
Field Lines

The dissipation of relative magnetic helicity due to the presence of a resistive reconnection region is considered. We show that when the reconnection region has a vanishing cross-section, helicity is conserved, in agreement with previous studies. It is also shown that in two-dimensional systems reconnection can produce highly twisted reconnected flux tubes. Reconnection at a high magnetic Reynolds number generally conserves helicity to a good approximation. However, reconnection with a small Reynolds number can produce significant dissipation of helicity. We prove that helicity dissipation in two-dimensional configurations is associated with the retention of some of the inflowing magnetic flux by the reconnection region, vr. When the reconnection site is a simple Ohmic conductor, all of the magnetic field parallel to the reconnection line that is swept into vr is retained. (In contrast, the inflowing magnetic field perpendicular to the line is annihilated.) We are able to relate the amount of helicity dissipation to the retained flux. A physical interpretation of helicity dissipation is developed by considering the diffusion of magnetic field lines through vr. When compared with helicity-conserving reconnection, the two halves of a reconnected flux sheet appear to have slipped relative to each other parallel to the reconnection line. This provides a useful method by which the reconnected field geometry can be constructed: the incoming flux sheets are ‘cut’ where they encounter vr, allowed to slip relative to each other, and then ‘pasted’ together to form the reconnected flux sheets. This simple model yields estimates for helicity dissipation and the flux retained by vr in terms of the amount of slippage. These estimates are in agreement with those expected from the governing laws.

The magneto-hydrodynamic boundary layer in the two-dimensional steady flow past a semi-infinite flat plate. I. Uniform conditions at infinity

1963 ◽  
Vol 273 (1355) ◽  
pp. 496-508 ◽  
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Reynolds Number ◽  
Drag Coefficient ◽  
Flat Plate ◽  
Magnetic Reynolds Number ◽  
Linear Ordinary Differential Equations ◽  
Electrically Conducting ◽  
The Magnetic Field ◽  
Conditions At Infinity

The problem investigated is the flow of a viscous, electrically conducting liquid past a fixed, semi-infinite, unmagnetized but conducting flat plate. The liquid flow U and also the magnetic field H 0 at a distance from the plate are both assumed to be uniform and parallel to the plate. It is assumed that the Reynolds number R and magnetic Reynolds number R m are large enough for momentum and magnetic boundary layers to have developed. The standard boundary-layer techniques as used in the Blasius solution then apply and the problem reduces to the solution of two simultaneous non-linear ordinary differential equations. These are examined by the use of an iteration method suggested in the non ­ magnetic problem by Weyl and a solution of reasonable accuracy has been obtained for the drag coefficient. This confirms a similar result obtained in a different way by Carrier & Greenspan. The principal result of the paper is that the boundary layer thickens and drag coefficient diminishes steadily as the parameter S = µH 2 0 / 4πρU 2 increases. When S attains the finite value of unity the drag coefficient obtained here actually vanishes with the flow having been reduced to rest by the action of the magnetic field. This result might be inferred qualitatively since a finite amount of work has to be done in conveying liquid particles across the lines of magnetic force.

A re-examination of the role of magnetic field lines in electromagnetic induction

1988 ◽  
Vol 66 (3) ◽  
pp. 245-248
Author(s):  
D. H. Boteler
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Field Line ◽  
Electric Fields ◽  
Electromagnetic Induction ◽  
Magnetic Reynolds Number ◽  
Unified View ◽  
Field Lines ◽  
The Magnetic Field

By adopting a view of magnetic fields, originally proposed by Faraday, in which the magnetic field changes by a movement of field lines, it is shown that a changing magnetic field can be described by the relation [Formula: see text] where v is the velocity of the magnetic field lines. These field-line velocities are shown to be the same as material velocities in conditions of infinite magnetic Reynolds number. The "moving field-line" view provides a phenomenological model of a changing magnetic field that is useful in electromagnetic induction studies. It also allows for a unified view of electromagnetic induction in which all induced electric fields can be explained by the v × B force alone.

On the stability of plane flow of a conducting fluid in the presence of a coplanar magnetic field

1970 ◽  
Vol 43 (3) ◽  
pp. 591-596 ◽  
Author(s):  
C. Sozou
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Reynolds Numbers ◽  
Magnetic Reynolds Number ◽  
Conducting Fluid ◽  
Unstable Flow ◽  
Plane Flow ◽  
The Stability ◽  
Two Parameters ◽  
The Relationship

The equations governing the propagation of small perturbations to plane flow of a viscous incompressible conducting fluid are re-examined with special reference to the case when the constant unperturbed magnetic field and flow velocity are parallel. We use the relationship between two parameters in one equation and, without computations, show the following: If for a non-zero value of the Alfvén number the flow is unstable when the Reynolds and magnetic Reynolds numbers take particular finite values, then, for that value of the Alfvén number, the flow cannot be completely stabilized for all finite Reynolds numbers, when the magnetic Reynolds number is finite. Since for a finite Alfvén number one expects that unstable flow cannot be stabilized for all finite Reynolds numbers, unless the magnetic Reynolds number exceeds some value, we deduce the following: An unstable parallel flow of a finitely conducting fluid cannot be completely stabilized for all finite Reynolds numbers by a constant magnetic field, which is coplanar with the flow.

Fluid flow induced by a rapidly alternating or rotating magnetic field

1979 ◽  
Vol 92 (1) ◽  
pp. 35-51 ◽  
Author(s):  
A. D. Sneyd
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Magnetic Reynolds Number ◽  
Rotating Magnetic Field ◽  
Complex Flows ◽  
Rotating Magnetic Fields ◽  
Constant Rate ◽  
Axis Parallel ◽  
Uniform Cross Section ◽  
Vorticity Generation

This paper studies the effect of alternating or rotating magnetic fields on containers of conducting fluid. The magnetic Reynolds number is assumed small. The frequency of alternation or rotation is rapid so the magnetic field is confined to a thin layer on the surface of the container. A boundary-layer analysis is used to find the rate of vorticity generation due to the Lorentz force. When the container is an infinitely long cylinder of uniform cross-section, alternating fields normal to the generators or fields rotating about an axis parallel to the generators generate vorticity at a constant rate. For containers of any other shape the rate of vorticity generation includes both constant and oscillatory terms. A perturbation analysis is used to study the flow induced in a slightly distorted circular cylinder by a rotating field. Complex flows develop in the viscous-magnetic boundary layer which may be unstable.

Analysis of an Electromagnetic Boundary Layer Probe for Low Magnetic Reynolds Number Flows

1993 ◽  
Vol 115 (4) ◽  
pp. 726-731 ◽  
Author(s):  
L. S. Langston ◽  
R. G. Kasper
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Reynolds Number ◽  
Boundary Layer Flow ◽  
Magnetic Reynolds Number ◽  
Field Size ◽  
Flow Meter ◽  
Displacement Thickness ◽  
Layer Flow ◽  
Reynolds Number Flows

Electromagnetic (EM) flow meters are used to measure volume flow rates of electrically conductive fluids (e.g., low magnetic Reynolds number flows of seawater, milk, etc.) in pipe flows. The possibility of using a modified form of EM flow meter to nonobtrusively measure boundary-layer flow characteristics is analytically investigated in this paper. The device, named an electromagnetic boundary layer (EBL) probe, would have a velocity integral-dependent voltage induced between parallel wall-mounted electrodes, as a conductive fluid flows over a dielectric wall and through the probe’s magnetic field. The Shercliff-Bevir integral equation, taken from EM flow meter theory and design, is used as the basis of the analytical model for predicting EBL probe voltage outputs, given a specified probe geometry and boundary layer flow conditions. Predictions are made of the effective range of the nonobtrusive EBL probe in terms of electrode dimensions, the magnetic field size and strength, and boundary layer velocity profile and thickness. The analysis gives expected voltage calibration curves and shows that an array of paired electrodes would be a beneficial feature for probe design. A key result is that the EBL probe becomes a displacement thickness meter, if operated under certain conditions. That is, the output voltage was found to be directly proportional to the boundary layer displacement thickness, δ1, for a given free stream velocity.

Magnetic Field Effects On Backward-facing Step Flow of Ferrofluids

2021 ◽  
Author(s):  
Wenming Yang ◽  
Boshi Fang ◽  
Beiying Liu
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Reynolds Numbers ◽  
Magnetic Reynolds Number ◽  
Magnetic Field Effects ◽  
Backward Facing Step ◽  
Number Range ◽  
Concave Corner ◽  
Small Reynolds Numbers ◽  
Recirculation Length

Abstract Backward-facing step (BFS) flow is a benchmark case study in fluid mechanics. Its control by means of electromagnetic actuation has attracted great interest in recent years. This paper focuses on the effects of a uniform stationary magnetic field on the laminar ferrofluid BFS flows for the Reynolds number range 0.1=Re=400 and different expansion ratios. The coupled ferrohydrodynamic equations, including the microscopically derived magnetization equation, for a two-dimensional domain are solved numerically by an Open FOAM solver after validation and a test of accuracy. The application of a magnetic field causes the corner vortices in the concave corner behind the step to be retracted compared with their positions in the absence of a magnetic field. The maximum percentage of the normalized decrease in length of these eddies reaches 41.23% in our simulations. For small Reynolds numbers (<10), the flow separation points on the convex corner are lowered in the presence of a magnetic field. Furthermore, the dimensionless total pressure drop between the channel inlet and outlet decreases almost linearly with Reynolds number Re, but the drop is greater when a magnetic field is applied. On the whole, the normalized recirculation length of the corner vortex increases nonlinearly with increasing magnetic Reynolds number Rem and Brownian Péclet number Pe, but it tends to constant values in the limits Re ≪ 1 and Re ≫ 1.

Numerical studies of magnetic field annihilation

1972 ◽  
Vol 7 (2) ◽  
pp. 293-311 ◽  
Author(s):  
J. C. Stevenson
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Solar Flare ◽  
Electrical Resistance ◽  
Numerical Solutions ◽  
Magnetic Reynolds Number ◽  
Numerical Studies ◽  
Order Of Magnitude ◽  
Field Lines ◽  
Magnitude Estimates

The behaviour of a plasma permeated by a magnetic field, where the field possessess a hyperbolic neutural point, is considered. Results from numerical solutions of the magnetohydrodynamic formulation for such flows are reported. Problems are posed with the solar flare models of Dungey, Sweet & Petschek in mind. No evidence is found to support the idea that compression of the field lines near a hyperbolic null, in the presence of electrical resistance, can radically alter the geometry of those field lines (e.g. the formation of switch-off shocks). These computations do show that, for large values of the magnetic Reynolds number, a rate of annihilation, more rapid than that derived from order-of-magnitude estimates, is possible.

Stability of a Hartmann boundary layer under the influence of a parallel magnetic field

1968 ◽  
Vol 32 (4) ◽  
pp. 721-735 ◽  
Author(s):  
S. Abas
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Reynolds Number ◽  
Asymptotic Methods ◽  
Transverse Magnetic ◽  
Magnetic Reynolds Number ◽  
Power Series Solution ◽  
Neutral Stability ◽  
Two Dimensional ◽  
Parallel Magnetic Field

Stability to infinitesimal disturbances—when a parallel magnetic field is imposed—is investigated for the flow in the boundary layer set up by two-dimensional motion between parallel planes of a viscous, incompressible, electrically conducting fluid under the influence of a transverse magnetic field. The flow is assumed to take place at low magnetic Reynolds number. The usual asymptotic methods are employed for the solution, but, apart from the Tollmientype power series solution, an exact solution of the inviscid equation is obtained in terms of the hypergeometric function and its analytic continuation. Curves of neutral stability for two-dimensional disturbances are calculated and the results for critical Reynolds number modified to take into account three-dimensional disturbances. The parallel magnetic field is found to have a strong stabilizing influence.

The effect of a parallel magnetic field on the stability of free boundary-layer type flows of low magnetic Reynolds number

1969 ◽  
Vol 38 (2) ◽  
pp. 243-253 ◽  
Author(s):  
S. Abas
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Reynolds Number ◽  
Free Boundary ◽  
Magnetic Reynolds Number ◽  
Wave Number ◽  
Neutral Stability ◽  
Parallel Magnetic Field ◽  
Limiting Profile ◽  
Small Wave Number

Stability to infinitesimal disturbances, when a parallel magnetic field is imposed, is investigated for the free boundary-layer type flows, of low magnetic Reynolds number, between two unbounded parallel streams of a viscous, incompressible, electrically conducting fluid. Neutral stability curves are calculated for small wave-number making use of the limiting profile: previous results by another author are found to be incomplete. A qualitative neutral stability picture is conjectured for other values of the wave-number and, granted a certain part of this conjecture, the conclusion is that the critical Reynolds number remains zero until the parameter Q/R exceeds the value (Q/R)crit [eDot ] 0·0233. It is suggested that a sufficiently strong magnetic field can stabilize a flow of any finite Reynolds number.

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