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.

Magnetohydrodynamic Flow Past a Finite Flat Plate in the Presence of a Nonaligned Magnetic Field

1974 ◽  
Vol 52 (12) ◽  
pp. 1104-1106 ◽  
Author(s):  
W. D. Lakin
Keyword(s):  
Magnetic Field ◽  
Flat Plate ◽  
Related Problem ◽  
Uniform Magnetic Field ◽  
Hartmann Number ◽  
Mhd Flow ◽  
Order Partial Differential Equation ◽  
Perturbation Problem ◽  
Flow Past ◽  
Streaming Motion

We consider the steady flow past a finite flat plate due to a uniform stream in the presence of a uniform magnetic field which is not aligned with the streaming motion at infinity. The Hartmann number is assumed large and positive. This leads to a singular perturbation problem involving a second-order partial differential equation. As a result, solutions of the governing equation must be obtained in three separate regions and then matched asymptotically. A related problem involving magnetohydrodynamic (MHD) flow across a finite needle is also discussed.

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 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.

scholarly journals MHD flow in an insulating rectangular duct under a non-uniform magnetic field

PMC Physics B ◽  
2010 ◽  
Vol 3 (1) ◽  
Author(s):  
René Moreau ◽  
Sergey Smolentsev ◽  
Sergio Cuevas
Keyword(s):  
Magnetic Field ◽  
Uniform Magnetic Field ◽  
Mhd Flow ◽  
Rectangular Duct

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 Effect of magnetic field on nanofluid free convection in Conical Partially Annular Space

2020 ◽  
Vol 330 ◽  
pp. 01005
Author(s):  
Abderrahmane AISSA ◽  
Mohamed Amine MEDEBBER ◽  
Khaled Al-Farhany ◽  
Mohammed SAHNOUN ◽  
Ali Khaleel Kareem ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Hartmann Number ◽  
Volume Fraction ◽  
Boussinesq Approximation ◽  
Simulation Software ◽  
Comsol Multiphysics ◽  
Governing Equations ◽  
Element Analysis ◽  
Vertical Side ◽  
Side Walls

Natural convection of a magneto hydrodynamic nanofluid in a porous cavity in the presence of a magnetic field is investigated. The two vertical side walls are held isothermally at temperatures Th and Tc, while the horizontal walls of the outer cone are adiabatic. The governing equations obtained with the Boussinesq approximation are solved using Comsol Multiphysics finite element analysis and simulation software. Impact of Rayleigh number (Ra), Hartmann number (Ha) and nanofluid volume fraction (ϕ) are depicted. Results indicated that temperature gradient increases considerably with enhance of Ra and ϕ but it reduces with increases of Ha.

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.

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.

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