The force on a sphere moving through a conducting fluid in the presence of a magnetic field

1961 ◽  
Vol 11 (1) ◽  
pp. 133-142 ◽  
Author(s):  
J. R. Reitz ◽  
L. L. Foldy
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Pressure Distribution ◽  
Magnetic Field Line ◽  
Potential Flow ◽  
Uniform Magnetic Field ◽  
Magnetic Reynolds Number ◽  
Conducting Fluid ◽  
Joule Dissipation ◽  
Hydrodynamic Motion

The force on a sphere moving through an inviscid, conducting fluid in the presence of a uniform magnetic field B0 is calculated for the low-conductivity case where the hydrodynamic motion deviates only slightly from potential flow. The magnetic Reynolds number is assumed small. The force on the sphere is found to consist of both a drag and a deflective component which tends to orient its motion parallel to a magnetic field line; if the sphere's velocity is V, the force may be written $\bf {R} = -AB^2_0\bf {V} + \bf C(V.B_0)B_0$ where the coefficients A and C depend on the conductivities of both sphere and fluid. The coefficients are evaluated by calculating the Joule dissipation for particular orientations of V relative to B0. In one case the force is also calculated directly from the perturbed pressure distribution in the fluid. In an analogous way, a spinning sphere in a conducting fluid experiences both resistive and gyroscopic torques.

Fluid flow generated by switching a magnetic field on or off

1973 ◽  
Vol 61 (2) ◽  
pp. 209-217 ◽  
Author(s):  
Alfred Sneyd
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Uniform Magnetic Field ◽  
Magnetic Reynolds Number ◽  
Simple Expression ◽  
Conducting Fluid ◽  
Uniform Field ◽  
Vorticity Distribution ◽  
Magnetic Prandtl Number ◽  
Initial Vorticity

A uniform magnetic field is switched on at time t = 0 outside a body of conducting fluid. It is assumed that the field strength increases in time in proportion to 1 -e−αt, where α is a constant of the circuit generating the field. Under the assumption of small magnetic Reynolds number and small magnetic Prandtl number the equations governing the diffusion of the field into the fluid are derived and a simple expression is given for the initial vorticity distribution produced in the fluid. The situation in which an initially uniform field is switched off is also considered. It is shown that, for sufficiently symmetrically shaped bodies of fluid, the vorticity generated by the switching-on of the field is the same as that generated by the switching-off. The particular case of an infinitely long circular cylinder of conducting fluid is considered in detail and an explicit expression is derived for the vorticity distribution.

MHD flow in a rectangular duct with pairs of conducting and non-conducting walls in the presence of a non-uniform magnetic field

1980 ◽  
Vol 96 (2) ◽  
pp. 335-353 ◽  
Author(s):  
Richard J. Holroyd
Keyword(s):  
Magnetic Field ◽  
Experimental Study ◽  
Reynolds Number ◽  
Uniform Magnetic Field ◽  
Hartmann Number ◽  
Mhd Flow ◽  
Magnetic Reynolds Number ◽  
Rectangular Duct ◽  
Mean Velocity ◽  
Side Walls

A theoretical and experimental study has been carried out on the flow of a liquid metal along a straight rectangular duct, whose pairs of opposite walls are highly conducting and insulating, situated in a planar non-uniform magnetic field parallel to the conducting walls. Magnitudes of the flux density and mean velocity are taken to be such that the Hartmann numberMand interaction parameterNhave very large values and the magnetic Reynolds number is extremely small.The theory qualitatively predicts the integral features of the flow, namely the distributions along the duct of the potential difference between the conducting walls and the pressure. The experimental results indicate that the velocity profile is severely distorted by regions of non-uniform magnetic field with fluid moving towards the conducting walls; even though these walls are very good conductors the flow behaves more like that in a non-conducting duct than that predicted for a duct with perfectly conducting side walls.

scholarly journals Nonlinear Dynamo in Obliquely Rotating Stratified Electroconductive Fluid in an Uniformly Magnetic Field

2020 ◽  
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
External Magnetic Field ◽  
Uniform Magnetic Field ◽  
Large Scale ◽  
Conducting Fluid ◽  
Magnetic Vortex ◽  
Small Scale ◽  
Large Scale Vortex ◽  
External Uniform Magnetic Field

In this paper, we investigated a new large-scale instability that arises in an obliquely rotating convective electrically conducting fluid in an external uniform magnetic field with a small-scale external force with zero helicity. This force excites small-scale velocity oscillations with a small Reynolds number. Using the method of multiscale asymptotic expansions, we obtain the nonlinear equations for vortex and magnetic disturbances in the third order of the Reynolds number. It is shown that the combined effects of the Coriolis force and the small external forces in a rotating conducting fluid possible large-scale instability. The linear stage of the magneto-vortex dynamo arising as a result of instabilities of -effect type is investigated. The mechanism of amplification of large-scale vortex disturbances due to the development of the hydrodynamic - effect taking into account the temperature stratification of the medium is studied. It was shown that a «weak» external magnetic field contributes to the generation of large-scale vortex and magnetic perturbations, while a «strong» external magnetic field suppresses the generation of magnetic-vortex perturbations. Numerical methods have been used to find stationary solutions of the equations of a nonlinear magneto-vortex dynamo in the form of localized chaotic structures in two cases when there is no external uniform magnetic field and when it is present.

scholarly journals Oseen’s Flow Past Axially Symmetric Bodies in Magneto Hydrodynamics

2021 ◽  
Author(s):  
Deepak Kumar Srivastava
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Uniform Magnetic Field ◽  
Hartmann Number ◽  
Circular Disk ◽  
Matching Condition ◽  
Technical Note ◽  
Conducting Fluid ◽  
Slip Condition ◽  
Axially Symmetric

In the present technical note, drag on axially symmetric body for conducting fluid in the presence of a uniform magnetic field is considered under the no-slip condition along with the matching condition( ρ 2 U 2 = H 0 2 μ 3 σ ) involving Hartmans number and Reynolds number to define this drag as Oseen’s resistance or Oseen’s correction to Stokes drag is presented. Oseen’s resistance on sphere, spheroid, flat circular disk (broadside) are found as an application under the specified condition. These expressions of Oseen’s drag are seems to be new in magneto-hydrodynamics. Author claims that by this idea, the results of Oseen’s drag on axially symmetric bodies in low Reynolds number hydrodynamics can be utilized for finding the Oseen’s drag in magneto hydrodynamics just by replacing Reynolds number by Hartmann number under the proposed condition.

Magnetic field-line reconnexion by localized enhancement of resistivity. Part 4. Dependence on the magnitude of resistivity

1979 ◽  
Vol 22 (1) ◽  
pp. 1-14 ◽  
Author(s):  
Masayuki Ugai ◽  
Takao Tsuda
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Current Sheet ◽  
Field Line ◽  
Magnetic Field Line ◽  
Theoretical Work ◽  
Magnetic Reynolds Number ◽  
Diffusion Region ◽  
Anomalous Resistivity ◽  
Set Up

The present paper quantitatively examines how the process of fast reconnexion depends on the magnitude of the local resistivity enhanced in the vicinity of the magnetic neutral point. It is shown that quasi-steady Petschek-type configurations are set up, one for each of the variously imposed local resistivity enhancements. The fundamental structure of the quasi-steady configuration is largely controlled by the initially indented value of locally enhanced resistivity. It is especially remarked that the width of the diffusion region becomes smaller as the locally enhanced resistivity becomes smaller. We find that each of the quasi-steady configurations presents nothing other than the Petschek-type configuration that corresponds to the allowable maximum reconnexion rate for the relevant magnetic Reynolds number. We also see that the magnitude of fast reconnexion rate has a weak dependence on the local resistivity in the diffusion region. All our numerical results are very consistent with previous theoretical work on the fast reconnexion problem, once the problem is reconsidered from another angle. We hence suggest that the process of fast reconnexion should be viewed as a gross instability, inherent to the current sheet system itself, that can be triggered by some local onset of anomalous resistivity.

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.

Turbulent dynamo action at low magnetic Reynolds number

1970 ◽  
Vol 41 (2) ◽  
pp. 435-452 ◽  
Author(s):  
H. K. Moffatt
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Large Scale ◽  
Isotropic Turbulence ◽  
Magnetic Energy ◽  
Magnetic Reynolds Number ◽  
Dynamo Action ◽  
Ohmic Dissipation ◽  
Magnetic Energy Density ◽  
Magnetic Diffusivity

The effect of turbulence on a magnetic field whose length-scale L is initially large compared with the scale l of the turbulence is considered. There are no external sources for the field, and in the absence of turbulence it decays by ohmic dissipation. It is assumed that the magnetic Reynolds number Rm = u0l/λ (where u0 is the root-mean-square velocity and λ the magnetic diffusivity) is small. It is shown that to lowest order in the small quantities l/L and Rm, isotropic turbulence has no effect on the large-scale field; but that turbulence that lacks reflexional symmetry is capable of amplifying Fourier components of the field on length scales of order Rm−2l and greater. In the case of turbulence whose statistical properties are invariant under rotation of the axes of reference, but not under reflexions in a point, it is shown that the magnetic energy density of a magnetic field which is initially a homogeneous random function of position with a particularly simple spectrum ultimately increases as t−½exp (α2t/2λ3) where α(= O(u02l)) is a certain linear functional of the spectrum tensor of the turbulence. An analogous result is obtained for an initially localized field.

scholarly journals Span-Wise Fluctuating MHD Convective Flow of a Viscoelastic Fluid through a Porous Medium in a Hot Vertical Channel with Thermal Radiation

2016 ◽  
Vol 21 (3) ◽  
pp. 667-681 ◽  
Author(s):  
K.D. Singh
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Vertical Channel ◽  
Magnetic Reynolds Number ◽  
Conducting Fluid ◽  
Temperature Fields ◽  
Convection Flow ◽  
Electrically Conducting ◽  
Unsteady Mixed Convection ◽  
Phase Angles

Abstract An unsteady mixed convection flow of a visco-elastic, incompressible and electrically conducting fluid in a hot vertical channel is analyzed. The vertical channel is filled with a porous medium. The temperature of one of the channel plates is considered to be fluctuating span-wise cosinusoidally, i.e., $T^* \left( {y^* ,z^* ,t^* } \right) = T_1 + \left( {T_2} - {T_ 1} \right)\cos \left( {{{\pi z^* } \over d} - \omega ^* t^* } \right)$ . A magnetic field of uniform strength is applied perpendicular to the planes of the plates. The magnetic Reynolds number is assumed very small so that the induced magnetic field is neglected. It is also assumed that the conducting fluid is gray, absorbing/emitting radiation and non-scattering. Governing equations are solved exactly for the velocity and the temperature fields. The effects of various flow parameters on the velocity, temperature and the skin friction and the Nusselt number in terms of their amplitudes and phase angles are discussed with the help of figures.

scholarly journals Deformation of a magnetic liquid drop in an applied non-stationary uniform magnetic field

2018 ◽  
Vol 185 ◽  
pp. 09006
Author(s):  
Alexander Tyatyushkin
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Steady State ◽  
Uniform Magnetic Field ◽  
Liquid Drop ◽  
Magnetic Liquid ◽  
Stationary Approximation ◽  
The Magnetic Field

Small steady-state deformational oscillations of a drop of magnetic liquid in a nonstationary uniform magnetic field are theoretically investigated. The drop is suspended in another magnetic liquid immiscible with the former. The Reynolds number is so small that the inertia can be neglected. The variation of the magnetic field is so slow that the quasi-stationary approximation for the magnetic field and the quasi-steady approximation for the flow may be used.

Sign in / Sign up

Export Citation Format

Share Document