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.

scholarly journals Hodograph method in MHD orthogonal fluid flows

1992 ◽  
Vol 15 (1) ◽  
pp. 149-159
Author(s):  
P. V. Nguyen ◽  
O. P. Chandna
Keyword(s):  
Electrical Conductivity ◽  
Incompressible Fluid ◽  
Viscous Incompressible Fluid ◽  
Fluid Flows ◽  
Legendre Transform ◽  
Hodograph Method ◽  
Hodograph Plane ◽  
Finite Electrical Conductivity ◽  
Steady Plane

Equations for steady plane MHD orthogonal flows of a viscous incompressible fluid of finite electrical conductivity are recast in the hodograph plane by using the Legendre transform function of the streamfunction. Three examples are studied to illustrate the developed theory. Solutions and geometries for these examples are determined.

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.

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.

The thermal and electrical resistance of tin in the intermediate state

1966 ◽  
Vol 289 (1418) ◽  
pp. 377-401 ◽  
Keyword(s):  
Magnetic Field ◽  
Electrical Conductivity ◽  
Intermediate State ◽  
Electrical Resistance ◽  
Critical Value ◽  
Transverse Magnetic ◽  
Thermal Resistivity ◽  
Measured Temperature ◽  
Domain Configuration ◽  
Unique Variation

The thermal and electrical conductivity of tin in its intermediate state has been measured over the temperature range 1·5 to 3·7 °K. The specimens were in the form of cylindrical single crystals with resistance ratios of from 300 to 50 000. Unlike earlier work, particular attention was directed to setting up a domain configuration of known form. It has been found that, provided the transverse magnetic field employed in establishing the intermediate state is suitably rotated as its strength is slowly increased, and provided a small electric current (of some few tenths per cent of the critical) simultaneously flows along the specimen, the thermal resistance is reproducible and stable with time. In addition, a unique variation of electrical resistance with field, which is linear up to the highest temperature examined, of 3·0 °K, is always obtained under these conditions. It is argued that the intermediate state established by this means consists of a stack of cylindrical superconducting and normal laminae. There is strong evidence to suggest that no domains are eliminated in an increasing field until the critical value is reached; when they suddenly disappear and the therm al resistance falls discontinuously to its normal state value. No corresponding discontinuities are observed when the field is reduced to half the critical temperature. Qualitative explanations are offered for these phenomena. The measured temperature variation of the thermal resistivity in the intermediate state is in satisfactory agreement with the theory of Andreev. Magnetothermal resistive effects have also been studied.

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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