The transient Stokes flow induced by a point source of electric current

Meccanica ◽  
1985 ◽  
Vol 20 (1) ◽  
pp. 12-17 ◽  
Author(s):  
O. O. Ajayi
Keyword(s):  
Point Source ◽  
Electric Current ◽  
Stokes Flow ◽  
Transient Stokes Flow

ELECTRIC POTENTIAL NEAR A SPHERICAL BODY IN A CONDUCTING HALF‐SPACE

Geophysics ◽  
1971 ◽  
Vol 36 (4) ◽  
pp. 763-767 ◽  
Author(s):  
David B. Large
Keyword(s):  
Point Source ◽  
Electric Current ◽  
Half Space ◽  
Electric Potential ◽  
Spherical Body ◽  
Classical Potential

An extensive summary of classical potential solutions has been given recently by Van Nostrand and Cook (1966). This note presents a solution for the potential due to a point source of electric current placed on the earth’s surface in the vicinity of a buried spherical body of arbitrary resistivity. The analysis follows the procedure suggested by Van Nostrand and Cook and is similar to that used recently by Merkel (1969, 1971).

Magnetohydrodynamic flow in a container due to the discharge of an electric current from a finite size electrode

1978 ◽  
Vol 362 (1711) ◽  
pp. 509-523 ◽  
Keyword(s):  
Free Surface ◽  
Flow Field ◽  
Electric Current ◽  
Stokes Flow ◽  
Equatorial Plane ◽  
Finite Size ◽  
Magnetohydrodynamic Flow ◽  
Point Electrode ◽  
Equatorial Radius ◽  
Constant Potential

In this paper we consider the Stokes flow field generated in a hemispheroidal container by the axisymmetric discharge of an electric current. The current is discharged from a circular electrode which is at the centre of the equatorial plane of the spheroid. The electrode is assumed to be at a constant potential. The equatorial radius of the spheroid is a and that of the electrode is k , the annulus k ≼ r ≼ a being a free surface. For a given container depth it is shown that as k increases the intensity of the flow field decreases and when the depth of the container is comparable to k the intensity of the flow field is only a small fraction of that associated with the point electrode case. As one might expect, the vorticity has a singularity at the rim of the electrode. When the width of the annulus forming the free surface is small, relative to the radius of the electrode, an eddy is formed about the rim of the electrode. As the annulus increases the eddy decreases in size until it eventually disappears.

Submerged Jet of a Conducting Fluid in the Presence of the Magnetic Field

2012 ◽  
Vol 7 (2) ◽  
pp. 25-38
Author(s):  
Rustam Mullyadzhanov ◽  
Nikolay Yavorsky
Keyword(s):  
Magnetic Field ◽  
Exact Solution ◽  
Point Source ◽  
Electric Current ◽  
Stokes Equations ◽  
Conducting Fluid ◽  
Mhd Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Submerged Jet

We consider a steady flow of a viscous incompressible conducting fluid. New exact solution of the magnetohydrodynamic (MHD) equations is obtained, when the flow is induced by the point source of hydrodynamic momentum located at the end of a semi-infinite linear conductor with a set value of the electric current. The effects of the confinement of the current density and the loss of existence of the solution with the finite values of electric current and various values of the Reynolds number and the Batchelor number (magnetic Prandtl number) are found. The non-self-similar problem is considered, when the flow is induced by the point source of momentum, angular momentum, flow rate and electric current that are set at the origin. In this case, the first term of the asymptotic expansion of the velocity at the infinity is described by the exact solution of the Navier – Stokes equations of the submerged jet (Slezkin – Landau – Squire solution). We analyze the conservation laws. It is shown that the induced magnetic field reduces the intensity of the jet flow

EFFECT OF ION SHEATH ON RADIATION IN A MAGNETOIONIC MEDIUM: I. SOURCE CURRENT PARALLEL TO THE MAGNETOSTATIC FIELD

1966 ◽  
Vol 44 (7) ◽  
pp. 1401-1418
Author(s):  
S. R. Seshadri ◽  
K. L. Bhatnagar
Keyword(s):  
Point Source ◽  
Electric Current ◽  
Finite Length ◽  
Current Distribution ◽  
Radiation Resistance ◽  
Free Space ◽  
Sheath Thickness ◽  
Radiation Characteristics ◽  
Magnetostatic Field ◽  
Source Current

The radiation characteristics of an axially oriented point source of electric current and a filament of finite length with a triangular current distribution are treated for the case in which these sources are situated at the center of an infinite cylindrical column of free space and surrounded by a homogeneous, loss-free magnetoionic medium. The direction of the magnetostatic field is assumed to be parallel to the axis of the free-space column which is an idealization for the geometry of the ion sheath formed around the antenna in the ionosphere. The dependence of the radiation resistance of these sources on the frequency and the ion-sheath thickness is examined. It is found that, within the framework of the classical magnetoionic theory, the radiation resistance of even a point source of electric current remains finite for all frequencies, provided the ion-sheath effects are included. Also the radiation resistance of a finite-length filament with a triangular current distribution is found to be insensitive to the changes in the thickness of the ion sheath. This result is in conformity with the experimental observations, which indicate no data variations correlated with the changes in the thickness of the ion sheath.

APPARENT RESISTIVITY FOR DIPPING BEDS

Geophysics ◽  
1955 ◽  
Vol 20 (1) ◽  
pp. 123-139 ◽  
Author(s):  
Katsuro Maeda
Keyword(s):  
Differential Equation ◽  
Reflection Coefficient ◽  
Point Source ◽  
Electric Current ◽  
Potential Field ◽  
Apparent Resistivity ◽  
Computing Methods ◽  
Image Theory ◽  
The Earth ◽  
Dip Angle

The potential field of a point source of electric current, located on the surface of the earth above a dipping bed, is determined exactly by solving the appropriate differential equation. It is concluded that image theory is useful only in the two cases in which the reflection coefficient is plus one and the angle of dip is [Formula: see text] and in which the reflection coefficient is minus one and the dip angle is [Formula: see text] m being an integer. Computing methods are also developed for the cases in which the image theory is not applicable. Some numerical tables necessary for computation and several apparent resistivity curves are presented.

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