Nonlinear forced vibrations of an initially-deformed electrically-conducting layer in a magnetic field

1989 ◽  
Vol 25 (4) ◽  
pp. 393-399
Author(s):  
Ya. I. Burak ◽  
V. F. Kondrat ◽  
T. S. Nagirnyi
Keyword(s):  
Magnetic Field ◽  
Forced Vibrations ◽  
Conducting Layer ◽  
Electrically Conducting

On diffusive instabilities of a rapidly rotating electrically conducting layer of compressible fluid of varying depth

1980 ◽  
Vol 96 (3) ◽  
pp. 493-513 ◽  
Author(s):  
M. P. Gibbons
Keyword(s):  
Magnetic Field ◽  
Marginal Stability ◽  
Conducting Layer ◽  
Gravitational Acceleration ◽  
Depth Gradient ◽  
Azimuthal Magnetic Field ◽  
Electrically Conducting ◽  
Balance Of Forces ◽  
Boussinesq Fluid ◽  
Work Done

Compressibility is added to Busse's (1976) study of convection in a rotating, electrically conducting layer of fluid, of varying depth, which is permeated by an azimuthal magnetic field that is orthogonal to both the rotation vector Ω and the gravitational acceleration g. On the basis of a linear theory, we investigate the kinds of infinitesimal wave motion which the fluid can support when the dominant balance of forces is between pressure gradient and Coriolis force, so that the Proudman–Taylor theorem holds. Unlike Busse, however, we assume that the fluid is statically stable in the sense that the temperature gradient is sub-adiabatic.In the absence of diffusion, these waves are dynamically neutral and take the form of Rossby waves modified by compressibility and magnetic field. The waves are examined in two limits, the adiabatic and the isothermal, and we define two distinct frequencies at which a pure Rossby wave can oscillate. When diffusion is restored, the disparity between these frequencies makes the fluid susceptible to overstability. We prove that all such amplifying waves must propagate eastward, i.e. in the direction of g ∧ Ω, irrespective of the sign of the depth gradient or the magnitudes of the diffusivities. The theorem does not apply if the fluid is incompressible or convectively unstable at the outset, and therefore does not contradict Busse's result that the direction of azimuthal propagation can be altered by the diffusivities. Nevertheless, we suggest reasons why Busse's method of regarding the imaginary part of the marginal stability equation as a dispersion relation is not in general a reliable one.We examine the instabilities by subjecting the neutral waves to a weakly diffusive perturbation. We discover, in particular, a new kind of magnetic instability which is crucially dependent upon both compressibility and the depth gradient. In agreement with the general result described above, the instability takes the form of a slow, eastward propagating, amplifying wave.The principal source for all instabilities is elastic energy, which cannot be tapped in a Boussinesq fluid, since the work done by compression is neglected under that approximation.

scholarly journals 46. The störmertron

1958 ◽  
Vol 6 ◽  
pp. 446-447
Author(s):  
Willard H. Bennett
Keyword(s):  
Magnetic Field ◽  
Charged Particles ◽  
Mercury Vapor ◽  
Electron Gun ◽  
Conducting Film ◽  
New Developments ◽  
Electrically Conducting ◽  
The Earth ◽  
Magnetic Dipole Field ◽  
Glass Tubes

A tube has been developed in which the shapes of streams of charged particles moving in the earth's magnetic field can be produced accurately to scale. The tube has been named the Störmertron in honor of Carl Störmer who calculated many such orbits. New developments which have made this tube possible include a method for coating the inside of large glass tubes with a transparent electrically conducting film, and an electron gun producing gas-focused streams in less than ½ micron of mercury vapor, a nearly vapor-free grease joint, and a nearly vapor-free carbon black. The magnetic dipole field of the earth is simulated with an Alnico magnet capped with properly shaped soft iron caps. The stream is deflected using two pairs of yoke coils near the gun.

Transverse surface waves in magneto-elasticity

1966 ◽  
Vol 62 (3) ◽  
pp. 541-545 ◽  
Author(s):  
C. M. Purushothama
Keyword(s):  
Magnetic Field ◽  
Wave Propagation ◽  
Surface Waves ◽  
Elastic Medium ◽  
Uniform Magnetic Field ◽  
Shear Waves ◽  
Plane Shear ◽  
Electrically Conducting ◽  
Velocity Of Propagation

AbstractIt has been shown that uncoupled surface waves of SH type can be propagated without any dispersion in an electrically conducting semi-infinite elastic medium provided a uniform magnetic field acts non-aligned to the direction of wave propagation. In general, the velocity of propagation will be slightly greater than that of plane shear waves in the medium.

scholarly journals Homotopy Analysis Solution of Hydromagnetic Mixed Convection Flow Past an Exponentially Stretching Sheet with Hall Current

2012 ◽  
Vol 2012 ◽  
pp. 1-26 ◽  
Author(s):  
Mohamed Abd El-Aziz ◽  
Tamer Nabil
Keyword(s):  
Magnetic Field ◽  
Mixed Convection ◽  
Convection Flow ◽  
Mixed Convection Flow ◽  
Electrically Conducting ◽  
Hall Parameter ◽  
Homotopy Analysis ◽  
Continuous Sheet ◽  
Exponentially Stretching ◽  
The Magnetic Field

The effect of thermal radiation on steady hydromagnetic heat transfer by mixed convection flow of a viscous incompressible and electrically conducting fluid past an exponentially stretching continuous sheet is examined. Wall temperature and stretching velocity are assumed to vary according to specific exponential forms. An external strong uniform magnetic field is applied perpendicular to the sheet and the Hall effect is taken into consideration. The resulting governing equations are transformed into a system of nonlinear ordinary differential equations using appropriate transformations and then solved analytically by the homotopy analysis method (HAM). The solution is found to be dependent on six governing parameters including the magnetic field parameterM, Hall parameterm, the buoyancy parameterξ, the radiation parameterR, the parameter of temperature distributiona, and Prandtl number Pr. A systematic study is carried out to illustrate the effects of these major parameters on the velocity and temperature distributions in the boundary layer, the skin-friction coefficients, and the local Nusselt number.

Gas-ionizing shocks in a magnetic field

1967 ◽  
Vol 1 (1) ◽  
pp. 37-54 ◽  
Author(s):  
M. D. Cowley
Keyword(s):  
Magnetic Field ◽  
Electric Field ◽  
Wave Speed ◽  
Normal Velocity ◽  
Electrically Conducting ◽  
Shock Stability ◽  
The Face ◽  
Arbitrary Velocity ◽  
Flow Plane ◽  
The Magnetic Field

Ionizing shocks for plane flows with the magnetic field lying in the flow plane are considered. The gas is assumed to be electrically conducting downstream, but non-conducting upstream. Shocks whose downstream state has a normal velocity component less than the slow magneto-acoustic-wave speed and whose upstream state is supersonic are found to be non-evolutionary in the face of plane magneto-acoustic disturbances, unless the upstream electric field in a frame of reference where the gas is at rest is arbitrary. Velocity conditions are also determined for shock stability with the electric field not arbitrary.Shock structures are found for the case of large ohmic diffusion, the initial temperature rise and ionization of the gas being caused by a thin transition having the properties of an ordinary gasdynamic shock. For the case where shocks are evolutionary when the upstream electric field is arbitrary, the shock structure requirements only restrict the electric field by limiting the range of possible values. When shocks are evolutionary with the electric field not arbitrary, they can only have a structure for a particular value of the electric field. Limits to the current carried by ionizing shocks and the effects of precursor ionization are discussed qualitatively.

Magnetohydrodynamic lubrication flow between parallel rotating disks

1962 ◽  
Vol 13 (1) ◽  
pp. 21-32 ◽  
Author(s):  
W. F. Hughes ◽  
R. A. Elco
Keyword(s):  
Magnetic Field ◽  
Axial Magnetic Field ◽  
Load Capacity ◽  
Electrical Energy ◽  
Axial Current ◽  
Frictional Torque ◽  
Rotating Disks ◽  
Radial Magnetic Field ◽  
Electrically Conducting ◽  
Parallel Disks

The motion of an electrically conducting, incompressible, viscous fluid in the presence of a magnetic field is analyzed for flow between two parallel disks, one of which rotates at a constant angular velocity. The specific application to liquid metal lubrication in thrust bearings is considered. The two field configurations discussed are: an axial magnetic field with a radial current and a radial magnetic field with an axial current. It is shown that the load capacity of the bearing is dependent on the MHD interactions in the fluid and that the frictional torque on the rotor can be made zero for both field configurations by supplying electrical energy through the electrodes to the fluid.

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.

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