On magneto-thermo-elastic plane waves

1962 ◽  
Vol 58 (3) ◽  
pp. 527-531 ◽  
Author(s):  
G. Paria
Keyword(s):  
Magnetic Field ◽  
Electrical Conductivity ◽  
Elastic Wave ◽  
Plane Waves ◽  
Low Frequency ◽  
Coupling Factor ◽  
Elastic Wave Velocity ◽  
Elastic Plane ◽  
Elastic Coupling ◽  
Finite Electrical Conductivity

ABSTRACTThe propagation of plane waves in a thermo-elastic body placed in a magnetic field has been investigated. It is shown that the problem can be reduced to one of pure thermo-elasticity, provided that the longitudinal elastic wave velocity is suitably increased in the case of infinite electrical conductivity. For finite electrical conductivity and low frequency, however, the thermo-elastic coupling factor is to be increased.

scholarly journals Elastic wave velocity and electrical conductivity in a brine-saturated rock and microstructure of pores

2019 ◽  
Vol 71 (1) ◽  
Author(s):  
Tohru Watanabe ◽  
Miho Makimura ◽  
Yohei Kaiwa ◽  
Guillaume Desbois ◽  
Kenta Yoshida ◽  
...  
Keyword(s):  
Electrical Conductivity ◽  
Elastic Wave ◽  
Wave Velocity ◽  
High Pressures ◽  
Seismic Velocity ◽  
Volume Fraction ◽  
Elastic Wave Velocity ◽  
Fluid Volume ◽  
Sem Observation ◽  
Wide Aperture

AbstractElastic wave velocity and electrical conductivity in a brine-saturated granitic rock were measured under confining pressures of up to 150 MPa and microstructure of pores was examined with SEM on ion-milled surfaces to understand the pores that govern electrical conduction at high pressures. The closure of cracks under pressure causes the increase in velocity and decrease in conductivity. Conductivity decreases steeply below 10 MPa and then gradually at higher pressures. Though cracks are mostly closed at the confining pressure of 150 MPa, brine must be still interconnected to show observed conductivity. SEM observation shows that some cracks have remarkable variation in aperture. The aperture varies from ~ 100 nm to ~ 3 μm along a crack. FIB–SEM observation suggests that wide aperture parts are interconnected in a crack. Both wide and narrow aperture parts work parallel as conduction paths at low pressures. At high pressures, narrow aperture parts are closed but wide aperture parts are still open to maintain conduction paths. The closure of narrow aperture parts leads to a steep decrease in conductivity, since narrow aperture parts dominate cracks. There should be cracks in various sizes in the crust: from grain boundaries to large faults. A crack must have a variation in aperture, and wide aperture parts must govern the conduction paths at depths. A simple tube model was employed to estimate the fluid volume fraction. The fluid volume fraction of 10−4–10−3 is estimated for the conductivity of 10−2 S/m. Conduction paths composed of wide aperture parts are consistent with observed moderate fluctuations (< 10%) in seismic velocity in the crust.

Magneto-thermo-elastic plane waves

1965 ◽  
Vol 61 (4) ◽  
pp. 939-944 ◽  
Author(s):  
C. M. Purushothama
Keyword(s):  
Magnetic Field ◽  
Wave Propagation ◽  
Shear Wave ◽  
Wave Velocity ◽  
Compression Wave ◽  
Thermal Field ◽  
Plane Waves ◽  
Elastic Plane ◽  
Magnetic Diffusivity ◽  
The Magnetic Field

AbstractThe combined effects of uniform thermal and magnetic fields on the propagation of plane waves in a homogeneous, initially unstressed, electrically conducting elastic medium have been investigated.When the magnetic field is parallel to the direction of wave propagation, the compression wave is purely thermo-elastic and the shear wave is purely magneto-elastic in nature. For a transverse magnetic field, the shear waves remain elastic whereas the compression wave assumes magneto-thermo-elastic character due to the coupling of all the three fields—mechanical, magnetic and thermal. In the general case, the waves polarized in the plane of the direction of wave propagation and the magnetic field are not only coupled but are also influenced by the thermal field, once again exhibiting the coupling of the three fields. The shear wave polarized transverse to the plane retains its magneto-elastic character.Notation.Hi = primary magnetic field components,ht = induced magnetic field components,To = initial thermal field,θ = induced thermal field,C = compression wave velocity.S = shear wave velocity,ui = displacement components,cv = specific heat at constant volume,k = thermal conductivity,η = magnetic diffusivity,μe = magnetic permeability,λ, μ = Lamé's constants,β = ratio of coefficient of volume expansion to isothermal compressibility.

On the re-connexion of magnetic field lines in conducting fluids

1970 ◽  
Vol 4 (2) ◽  
pp. 207-229 ◽  
Author(s):  
Tyan Yeh ◽  
W. Ian Axford
Keyword(s):  
Magnetic Field ◽  
Electrical Conductivity ◽  
Two Dimensions ◽  
Neutral Point ◽  
Inviscid Fluid ◽  
Hydromagnetic Flow ◽  
Finite Electrical Conductivity ◽  
Field Lines ◽  
Two Sides ◽  
Special Case

The reconnexion of magnetic field lines is described for a special case of steady, incompressible hydromagnetic flow in two dimensions. A similarity solution is obtained which corresponds to the flow of a perfectly conducting, inviscid fluid such that magnetic field lines are carried from two sides toward, then on the other two sides away from, the centre of an X-configuration. The effects of viscosity are important in shocks which form in the vicinity of the X-lines of the configuration. The effects of finite electrical conductivity must be taken into account near the centre of the configuration which, in the symmetrical case discussed, is an X-type neutral point. From an approximate solution valid in this region it is found that the fluid must flow from the larger to the smaller wedges of the X-configuration. Hence, the reconnexion process is such that oppositely directed magnetic field lines move towards the neutral point in the larger wedges, become reconnected at the neutral point, and move away in the smaller wedges. Since the solution in the vicinity of the neutral point appears to be no more than a response to the external flow, which is in turn controlled by conditions far from the neutral point and is essentially unaffected by viscosity and finite electrical conductivity, it is tentatively concluded that the rate of re-connexion of magnetic field lines does not depend on these quantities, and that, in general, re-connexion can be expected to take place rapidly if circumstances are favourable.

The propagation of magneto-thermo-viscoelastic plane waves in a parallel union of the Kelvin and Maxwell bodies

1971 ◽  
Vol 70 (2) ◽  
pp. 343-350 ◽  
Author(s):  
D. S. Chandrasekhariah
Keyword(s):  
Magnetic Field ◽  
Electrical Conductivity ◽  
Electromagnetic Field ◽  
Wave Propagation ◽  
Thermal Field ◽  
Plane Waves ◽  
Viscoelastic Body ◽  
Longitudinal Component ◽  
Transverse Component ◽  
Wave Travel

AbstractThe propagation of plane waves in a viscoelastic body representing a parallel union of the Kelvin and Maxwell bodies placed in a magneto-thermal field is investigated. It is shown that the longitudinal component of the wave is in general coupled with a transverse component and the wave travels in two families. In particular if the primary magnetic field is either parallel or perpendicular to the direction of wave propagation, the three components of the wave travel unlinked, with either the longitudinal component or the transverse components unaffected by the presence of the electromagnetic field. If the electrical conductivity of the solid is infinite the effect of the primary magnetic field is to increase the values of the material constants. The effect of wave propagation on magnetic permeability is equivalent to an anisotropic rescaling of the primary magnetic field. Some of the results obtained in the earlier works are obtained as particular cases of the more general results derived here.

Stability of a stratified partially ionized plasma in a vertical magnetic field

1978 ◽  
Vol 19 (1) ◽  
pp. 183-191 ◽  
Author(s):  
S. L. Maheshwari ◽  
P. K. Bhatia
Keyword(s):  
Magnetic Field ◽  
Electrical Conductivity ◽  
Growth Rate ◽  
The Other ◽  
Conducting System ◽  
Vertical Magnetic Field ◽  
One Dimensional ◽  
Finite Electrical Conductivity ◽  
Partially Ionized ◽  
The Stability

The dynamic stability of a stratified layer of partially ionized compressible plasma is discussed to investigate the effects of finite electrical conductivity and ion viscosity. The prevailing magnetic field is assumed to be uniform and vertical. For a semi-infinite plasma having a one-dimensional exponential density gradient along the vertical, the dispersion relation has been obtained by variational methods. It is found that the ion viscosity and ion–neutral collisions, whether included jointly or separately, do not change the stability criterion of the perfectly conducting system. Their inclusion, however, has a tendency to reduce the growth rate of the unstable perturbations showing that they have a stabilizing influence. On the other hand the inclusion of the effects of finite resistivity and compressibility of the medium is found to be destabilizing as the wavenumber range over which the plasma would otherwise be stable, becomes unstable.

Steady transverse MHD viscous flows

1976 ◽  
Vol 54 (3) ◽  
pp. 262-267
Author(s):  
O. P. Chandna ◽  
M. R. Garg
Keyword(s):  
Magnetic Field ◽  
Electrical Conductivity ◽  
Viscous Flows ◽  
Transverse Magnetic ◽  
Incompressible Fluids ◽  
Parallel Lines ◽  
Logarithmic Spirals ◽  
Finite Electrical Conductivity ◽  
Concentric Circles ◽  
Steady Plane

Steady plane flows of viscous incompressible fluids of finite electrical conductivity in the presence of a transverse magnetic field are studied. The only flows with straight streamline pattern are shown to be those with parallel or concurrent streamlines and if the streamlines are involutes of a curve, then they are concentric circles. It is also established that if the natural net is isometric, then the streamlines are restricted to parallel lines, concurrent lines, concentric circles, or logarithmic spirals.

Magnetoelastic Plane Waves in Infinite Rotating Media

1983 ◽  
Vol 50 (2) ◽  
pp. 283-287 ◽  
Author(s):  
S. K. Roy Choudhuri ◽  
L. Debnath
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Phase Velocity ◽  
Applied Magnetic Field ◽  
Plane Waves ◽  
Low Frequency ◽  
Phase Speed ◽  
Elastic Solid ◽  
Finite Conductivity ◽  
The Waves

A study is made of the propagation of magnetoelastic plane waves in an electrically conducting, infinite elastic solid permeated by a primary uniform magnetic field when the entire medium rotates with a constant angular velocity. A more general dispersion relation is obtained to investigate the effects of rotation and the external magnetic field on the phase velocity of the waves. This analysis reveals that when the applied magnetic field has both longitudinal and transverse components, the coupled magnetoelastic waves are dispersive and damped in an infinitely conducting medium in contrast to the nonrotating medium where the coupled waves are dispersive, but undamped. In the case of finite conductivity, the waves are dispersive and undamped in the absence of the applied magnetic field. At low frequency ω, the phase velocity of the waves varies as ω1/2 for finite conductivity, and is independent of the external magnetic field and rotation; while in the nonrotating case with low frequency (when the applied magnetic field has either longitudinal or transverse components) the phase speed is less than that in the rotating medium and is found to depend on the applied magnetic field. Also in both rotating and nonrotating cases, the phase velocity becomes very small for finitely conducting material with a very high magnetic permeability.

On plane flow of a gas with finite electrical conductivity in a strong magnetic field

1963 ◽  
Vol 15 (4) ◽  
pp. 577-596 ◽  
Author(s):  
M. D. Cowley
Keyword(s):  
Magnetic Field ◽  
Electrical Conductivity ◽  
Strong Magnetic Field ◽  
Shock Structure ◽  
Flow Behaviour ◽  
Structure Theory ◽  
Transition Curve ◽  
Plane Flow ◽  
Finite Electrical Conductivity ◽  
Object Of Study

The principal object of study is plane flow over bodies with a sharp apex at Mach numbers greater than unity. The magnetic field is assumed to be uniform, rectilinear, and parallel to the undisturbed stream. Flow behaviour near the apex of a wedge is investigated by the method of characteristics. It is found that for small wedge angles an attached shock attenuates initially with distance from the apex, but for larger wedge angles the shock grows stronger.The structure of a slow magneto-gasdynamic shock is investigated for the case of strong magnetic field and small electrical conductivity. The streamlines are displaced within the shock although the initial and final flow directions are the same. An ordinary gasdynamic shock may occur on the upstream side of the transition. The shock structure theory gives a solution for the flow near the apex of a certain class of bodies.For the study of slow shock structure, it is shown that the transition is described by a curve in the (F, H)-plane. F is the sum of pressure and momentum flux in the direction of variation; H is the sum of enthalpy and kinetic energy due to the velocity component in the direction of variation. General properties of the (F, H)-plane are found for a gas whose equation of state obeys the conditions of Weyl (1949). Flow behaviour on the transition curve is then determined. The theory of the (F, H)-plane can be used in the study of other one-dimensional processes in magneto-gasdynamics.

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