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.

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 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.

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 → ∞.

On fluid motions induced by an electromagnetic field in a liquid drop immersed in a conducting fluid

1972 ◽  
Vol 51 (3) ◽  
pp. 585-591 ◽  
Author(s):  
C. Sozou
Keyword(s):  
Magnetic Field ◽  
Electromagnetic Field ◽  
Flow Field ◽  
Electric Field ◽  
Lorentz Force ◽  
Liquid Drop ◽  
Conducting Fluid ◽  
Uniform Electric Field ◽  
Tangential Electric Field ◽  
Set Up

The deformation of a liquid drop immersed in a conducting fluid by the imposition of a uniform electric field is investigated. The flow field set up is due to the surface charge and the tangential electric field stress over the surface of the drop, and the rotationality of the Lorentz force which is set up by the electric current and the associated magnetic field. It is shown that when the fluids are poor conductors and good dielectrics the effects of the Lorentz force are minimal and the flow field is due to the stresses of the electric field tangential to the surface of the drop, in agreement with other authors. When, however, the fluids are highly conducting and poor dielectrics the effects of the Lorentz force may be predominant, especially for larger drops.

The effect of a strong magnetic field on two-dimensional flows of a conducting fluid

1963 ◽  
Vol 15 (3) ◽  
pp. 429-441 ◽  
Author(s):  
Stephen Childress
Keyword(s):  
Magnetic Field ◽  
Perturbation Technique ◽  
The Body ◽  
Conducting Fluid ◽  
Order Effects ◽  
Two Dimensional ◽  
Axially Symmetric ◽  
Exterior Region ◽  
Electrically Conducting ◽  
Higher Order Effects

The motion of a viscous, electrically conducting fluid past a finite two-dimensional obstacle is investigated. The magnetic field is assumed to be uniform and parallel to the velocity at infinity. By means of a perturbation technique, approximations valid for large values of the Hartmann number M are derived. It is found that, over any finite region, the flow field is characterized by the presence of shear layers fore and aft of the body. The limit attained over the exterior region represents the two-dimensional counterpart of the axially symmetric solution given by Chester (1961). Attention is focused on a number of nominally ‘higher-order’ effects, including the presence of two distinct boundary layers. The results hold only when M [Gt ] Re; Re = Reynolds number. However, a generalization of the procedure, in which the last assumption is relaxed, is suggested.

scholarly journals Heat transfer augmentation of magnetohydrodynamics natural convection in L-shaped cavities utilizing nanofluids

2012 ◽  
Vol 16 (2) ◽  
pp. 489-501 ◽  
Author(s):  
Ehsan Sourtiji ◽  
Seyed Hosseinizadeh
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Flow Field ◽  
Hartmann Number ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
The Magnetic Field

A numerical study of natural convection heat transfer through an alumina-water nanofluid inside L-shaped cavities in the presence of an external magnetic field is performed. The study has been carried out for a wide range of important parame?ters such as Rayleigh number, Hartmann number, aspect ratio of the cavity and solid volume fraction of the nanofluid. The influence of the nanoparticle, buoyancy force and the magnetic field on the flow and temperature fields have been plotted and discussed. The results show that after a critical Rayleigh number depending on the aspect ratio, the heat transfer in the cavity rises abruptly due to some significant changes in flow field. It is also found that the heat transfer enhances in the presence of the nanoparticles and increases with solid volume fraction of the nanofluid. In addition, the performance of the nanofluid utilization is more effective at high Ray?leigh numbers. The influence of the magnetic field has been also studied and de?duced that it has a remarkable effect on the heat transfer and flow field in the cavity that as the Hartmann number increases the overall Nusselt number is significantly decreased specially at high Rayleigh numbers.

A study of a conductive laminar jet flow in an applied magnetic field

SIMULATION ◽  
2019 ◽  
Vol 95 (10) ◽  
pp. 995-1011
Author(s):  
Cheng-Hsing Hsu ◽  
Te-Hui Tsai ◽  
Ching-Chuan Chang ◽  
Yi Chen
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Flow Field ◽  
Applied Magnetic Field ◽  
Recirculation Zone ◽  
Hartmann Number ◽  
Control Volume ◽  
Jet Flow ◽  
Channel Width ◽  
Laminar Jet

This study investigates steady two-dimensional laminar confined jet flow in the presence of an applied magnetic field. The magnetohydrodynamic equations with the format of the stream function and vorticity formulation of the fluid flow are solved numerically. A numerical method was developed by using a first-order upwind scheme at the boundaries and a second-order finite control volume scheme in the flow field. The results show that the expansion region of the jet is moving downstream while the channel width and the Reynolds number are increasing. The vortex and the recirculation zone are stretched with increased Hartmann number, and the jet expansion region is moving upstream while the vortex and the recirculation zone are reduced. The channel width and the Reynolds number for the jet development are positive efforts and the Hartmann number has a suppressed effect in the present confined jet flow field.

Effect of Magnetic Field on Free Convection in Inclined Cylindrical Annulus Containing Molten Potassium

2015 ◽  
Vol 07 (04) ◽  
pp. 1550052 ◽  
Author(s):  
Masoud Afrand ◽  
Nima Sina ◽  
Hamid Teimouri ◽  
Ali Mazaheri ◽  
Mohammad Reza Safaei ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Nusselt Number ◽  
Average Nusselt Number ◽  
Hartmann Number ◽  
Conducting Fluid ◽  
Electrically Conducting ◽  
Cylindrical Annulus ◽  
Electrically Conducting Fluid ◽  
Wide Range ◽  
The Magnetic Field

Three-dimensional (3D) numerical simulation of natural convection of an electrically conducting fluid under the influence of a magnetic field in an inclined cylindrical annulus has been performed. The inner and outer cylinders are maintained at uniform temperatures and other walls are thermally insulated. The governing equations of this fluid system are solved by a finite volume (FV) code based on SIMPLER solution scheme. Detailed numerical results of heat transfer rate, Lorentz force, temperature and electric fields have been presented for a wide range of Hartmann number (0 ≤ Ha ≤ 60) and inclination angle (0 ≤ γ ≤ 90). The results indicate that a magnetic field can control the magnetic convection of an electrically conducting fluid. Depending on the direction and strength of the magnetic field, the suppression of convective motion was observed. For vertical cylindrical annulus, increasing the strength of the magnetic field causes the loss symmetry, and as the consequence, isotherms lose their circular shape. With increasing the Hartmann number the average Nusselt number approaches a constant value. For vertical annulus, the effect of Hartmann number on the average Nusselt number is not prominent compared to the case of horizontal annulus.

The effect of a magnetic field on the flow of a conducting fluid past a body of revolution

1961 ◽  
Vol 10 (3) ◽  
pp. 459-465 ◽  
Author(s):  
W. Chester
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Flow Pattern ◽  
Magnetic Reynolds Number ◽  
The Body ◽  
Body Of Revolution ◽  
Leading Term ◽  
Axis Of Symmetry ◽  
The Magnetic Field ◽  
Streaming Motion

The problem described by the title is investigated when both the magnetic field and the streaming motion of the fluid at infinity are uniform and parallel to the axis of symmetry of the body. The flow pattern depends on three parameters, the Reynolds number R, the magnetic Reynolds number Rm and the Hartmann number M. In this paper it is assumed that M [Gt ] 1, M [Gt ] R, M [Gt ] Rm (no other restrictions on the parameters are imposed, so that R and Rm need not be small). The flow pattern then consists of an undisturbed uniform stream outside a cylinder circumscribing the body with generators parallel to the stream. Inside this cylinder the fluid is at rest. The leading term in the expression for the drag on the body is obtained.

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