A magneto-hydrodynamic Stokes flow

1961 ◽  
Vol 260 (1300) ◽  
pp. 79-90 ◽  
Keyword(s):  
Reynolds Number ◽  
Stokes Flow ◽  
Hartmann Number ◽  
Magnetic Reynolds Number ◽  
Conducting Fluid ◽  
Slow Flow ◽  
Magnetic Pole ◽  
Total Drag ◽  
Conducting Sphere ◽  
Stokes Drag

This paper considers the slow flow of a viscous, conducting fluid past a non-conducting sphere at whose centre is a magnetic pole. The magnetic Reynolds number is assumed to be small, and the modifications to the classical Stokes flow and the free magnetic pole field are obtained for an arbitrary Hartmann number. The total drag D on the sphere has been calculated, and the ratio D / D s determined as a function of the Hartmann number M , where D s is the Stokes drag. In particular ( D — D s )/ D s = 37/210 M 2 + O ( M 4 ) for small M and ( D — D s )/ Ds ~ 0·7205 M - 1 as M → ∞.

The effect of a magnetic field on Stokes flow in a conducting fluid

1957 ◽  
Vol 3 (3) ◽  
pp. 304-308 ◽  
Author(s):  
W. Chester
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Stokes Flow ◽  
Hartmann Number ◽  
Low Reynolds Number ◽  
Conducting Fluid ◽  
Low Reynolds Number Flow ◽  
Reynolds Number Flow ◽  
Stokes Drag ◽  
Number Flow

Low Reynolds number flow of a conducting fluid past a sphere is considered. The classical Stokes solution is modified by a magnetic field which, at infinity, is uniform and in the direction of flow of the fluid.The formula for the drag is found to be $D = D_S \{ 1+\frac{3}{8}M+\frac{7}{960}M^2-\frac{43}{7680}M^3+O(M^4) \},$ Where DS is the Stokes drag and M is the Hartmann number.

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.

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.

Solver Development for Three-Dimensional Magnetohydrodynamic Flow on a Collocated Structured Grid System Based on SIMPLE Method

2014 ◽  
Vol 525 ◽  
pp. 247-250
Author(s):  
Jie Mao ◽  
Ke Liu ◽  
Hua Chen Pan
Keyword(s):  
Reynolds Number ◽  
Steady State ◽  
Velocity Vector ◽  
Hartmann Number ◽  
Three Dimensional ◽  
Magnetic Reynolds Number ◽  
Grid System ◽  
Simple Method ◽  
Conservative Scheme ◽  
Structured Grid

A steady state magnetohydrodynamic laminar solver with low magnetic Reynolds number has been developed in OpenFOAM platform. SIMPLE method has been used to solve the velocity vector and pressure. The induced electric potential and induced electric current has been solved according to a consistent and conservative scheme on a collocated structure grid. The solver has been validated by simulating Shercliff's case with medium Hartmann number. The results show that the numerical solution results match the analytical solutions well.

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.

The effect of a magnetic field on the flow of a conducting fluid past a circular disk

1961 ◽  
Vol 10 (3) ◽  
pp. 466-472 ◽  
Author(s):  
W. Chester ◽  
D. W. Moore
Keyword(s):  
Magnetic Field ◽  
Flow Field ◽  
Asymptotic Solution ◽  
Hartmann Number ◽  
Circular Disk ◽  
The Body ◽  
Conducting Fluid ◽  
Axial Distance ◽  
Body Of Revolution ◽  
Stokes Drag

In the previous paper (Chester 1961) it was shown that, for large values of the Hartmann number, the asymptotic solution for the flow past a body of revolution has a discontinuity on the surface of a cylinder which circumscribes the body. The flow in the region of this discontinuity is now investigated in more detail when the body is a circular disk broadside-on to the flow. It will be shown that there is actually a region of transition whose thickness is O(|x|½/M½), where x is the axial distance from the disk and M is the Hartmann number. This region is thin near the disk, but gradually thickens until it merges into the over-all flow field for x = O(M).The leading terms in the expression for the drag are given by $\frac{D}{D_s} = \frac{M \pi }{8} \left( 1 + \frac{2}{M} \right) $, where Ds is the Stokes drag.

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.

scholarly journals The Effects of Electrical Conductivity on Fluid Flow between Two Parallel Plates in a Porous Medioum

2021 ◽  
pp. 4953-4963
Author(s):  
Alaa Hammodat ◽  
Ghanim Algwauish ◽  
Iman Al-Obaidi
Keyword(s):  
Reynolds Number ◽  
Hartmann Number ◽  
Method Of Lines ◽  
Magnetic Reynolds Number ◽  
Temperature Profiles ◽  
Parallel Plates ◽  
Brinkman Number ◽  
The Method Of Lines ◽  
Energy Equations ◽  
Physical Quantities

This paper deals with a mathematical model of a fluid flowing between two parallel plates in a porous medium under the influence of electromagnetic forces (EMF). The continuity, momentum, and energy equations were utilized to describe the flow. These equations were stated in their nondimensional forms and then processed numerically using the method of lines. Dimensionless velocity and temperature profiles were also investigated due to the impacts of assumed parameters in the relevant problem. Moreover, we investigated the effects of Reynolds number , Hartmann number M, magnetic Reynolds number , Prandtl number , Brinkman number , and Bouger number , beside those of new physical quantities (N , ). We solved this system by creating a computer program using MATLAB.                                                                               

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.

scholarly journals Azimuthal magnetorotational instability with super-rotation

2018 ◽  
Vol 84 (1) ◽  
Author(s):  
G. Rüdiger ◽  
M. Schultz ◽  
M. Gellert ◽  
F. Stefani
Keyword(s):  
Reynolds Number ◽  
Prandtl Number ◽  
Numerical Solutions ◽  
Hartmann Number ◽  
Outer Cylinder ◽  
Magnetic Reynolds Number ◽  
Neutral Stability ◽  
Magnetorotational Instability ◽  
Magnetic Prandtl Number ◽  
The Stability

It is demonstrated that the azimuthal magnetorotational instability (AMRI) also works with radially increasing rotation rates contrary to the standard magnetorotational instability for axial fields which requires negative shear. The stability against non-axisymmetric perturbations of a conducting Taylor–Couette flow with positive shear under the influence of a toroidal magnetic field is considered if the background field between the cylinders is current free. For small magnetic Prandtl number $Pm\rightarrow 0$ the curves of neutral stability converge in the (Hartmann number,Reynolds number) plane approximating the stability curve obtained in the inductionless limit $Pm=0$. The numerical solutions for $Pm=0$ indicate the existence of a lower limit of the shear rate. For large $Pm$ the curves scale with the magnetic Reynolds number of the outer cylinder but the flow is always stable for magnetic Prandtl number unity as is typical for double-diffusive instabilities. We are particularly interested to know the minimum Hartmann number for neutral stability. For models with resting or almost resting inner cylinder and with perfectly conducting cylinder material the minimum Hartmann number occurs for a radius ratio of $r_{\text{in}}=0.9$. The corresponding critical Reynolds numbers are smaller than $10^{4}$.

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