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.

Stokes flow of a conducting fluid past an axially symmetric body in the presence of a uniform magnetic field

1960 ◽  
Vol 9 (3) ◽  
pp. 473-477 ◽  
Author(s):  
I-Dee Chang
Keyword(s):  
Magnetic Field ◽  
Stokes Flow ◽  
Uniform Magnetic Field ◽  
Hartmann Number ◽  
Magnetic Effect ◽  
Symmetric Body ◽  
Axially Symmetric ◽  
Low Reynolds Number Flow ◽  
Reynolds Number Flow ◽  
Number Flow

Low Reynolds number flow of an incompressible fluid past an axially symmetric body in the presence of a uniform magnetic field is studied using a perturbation method. It is found that for small Hartmann number M an approximate drag formula is given by $ D^ \prime = D^\prime_0 \left(1 + \frac {D^\prime_0} {16\pi \rho vaU}M\right) + O(M^2),$ where D′0 is the Stokes drag for flow with no magnetic effect.

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.

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.

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.

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.

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 natural convection of Cu/H2O nanofluid in a horizontal semi-cylinder with a local triangular heater

2018 ◽  
Vol 28 (12) ◽  
pp. 2979-2996 ◽  
Author(s):  
A.S. Dogonchi ◽  
Mikhail A. Sheremet ◽  
Ioan Pop ◽  
D.D. Ganji
Keyword(s):  
Magnetic Field ◽  
Rayleigh Number ◽  
Free Convection ◽  
Shape Factor ◽  
Uniform Magnetic Field ◽  
Hartmann Number ◽  
Volume Fraction ◽  
Horizontal Cylinder ◽  
Content Type ◽  
Nanoparticles Volume Fraction

Purpose The purpose of this study is to investigate free convection of copper-water nanofluid in an upper half of circular horizontal cylinder with a local triangular heater under the effects of uniform magnetic field and cold cylinder shell using control volume finite element method (CVFEM). Design/methodology/approach Governing equations formulated in dimensionless stream function, vorticity and temperature variables using the single-phase nanofluid model with Brinkman correlation for the effective dynamic viscosity and Hamilton and Crosser model for the effective thermal conductivity have been solved numerically by CVFEM. Findings The impacts of control parameters such as the Rayleigh number, Hartmann number, nanoparticles volume fraction, local triangular heater size, shape factor on streamlines and isotherms as well as local and average Nusselt numbers have been examined. The outcomes indicate that the average Nusselt number is an increasing function of the Rayleigh number, shape factor and nanoparticles volume fraction, while it is a decreasing function of the Hartmann number. Originality/value A complete study of the free convection of copper-water nanofluid in an upper half of circular horizontal cylinder with a local triangular heater under the effects of uniform magnetic field and cold cylinder shell using CVFEM is addressed.

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.

Second Law Analysis of Magneto-Micropolar Fluid Flow Between Parallel Porous Plates

2018 ◽  
Vol 10 (4) ◽  
Author(s):  
Abbas Kosarineia ◽  
Sajad Sharhani
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Fluid Flow ◽  
Entropy Generation ◽  
Hartmann Number ◽  
Second Law ◽  
Brinkman Number ◽  
Viscosity Parameter ◽  
Micropolar Fluid Flow ◽  
Second Law Analysis

In this study, the influence of the applied magnetic field is investigated for magneto-micropolar fluid flow through an inclined channel of parallel porous plates with constant pressure gradient. The lower plate is maintained at constant temperature and the upper plate at a constant heat flux. The governing motion and energy equations are coupled while the effect of the applied magnetic field is taken into account, adding complexity to the already highly correlated set of differential equations. The governing equations are solved numerically by explicit Runge–Kutta. The velocity, microrotation, and temperature results are used to evaluate second law analysis. The effects of characteristic and dominate parameters such as Brinkman number, Hartmann Number, Reynolds number, and micropolar viscosity parameter are discussed on velocity, temperature, microrotation, entropy generation, and Bejan number in different diagrams. The results depicted that the entropy generation number rises with the increase in Brinkman number and decays with the increase in Hartmann Number, Reynolds number, and micropolar viscosity parameter. The application of the magnetic field induces resistive force acting in the opposite direction of the flow, thus causing its deceleration. Moreover, the presence of magnetic field tends to increase the contribution of fluid friction entropy generation to the overall entropy generation; in other words, the irreversibilities caused by heat transfer reduced. Therefore, to minimize entropy, Brinkman number and Hartmann Number need to be controlled.

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