Wave motions in a stratified electrically conducting rotating fluid

The 3D dynamics equations for the stratified superconducting rotating fluid are studied. These equations are reduced to a scalar equation by representing the magnetic and density fields by a superposition of the unperturbed fields corresponding to the steady state of the fluid and the induced fields appearing due to the wave motion; the reduction also uses two auxiliary functions. The analysis of the scalar equation enables us to prove the solvability of the initial-boundary value problems of the wave theory for electrically conducting rotating fluids with nonhomogeneous density.     

Dynamics of a rotating layer of an ideal electrically conducting incompressible fluid

A system of nonlinear partial differential equations is considered that models perturbations in a layer of an ideal electrically conducting rotating fluid bounded by spatially and temporally varying surfaces with allowance for inertial forces. The system is reduced to a scalar equation. The solvability of initial boundary value problems arising in the theory of waves in conducting rotating fluids can be established by analyzing this equation. Solutions to the scalar equation are constructed that describe small-amplitude wave propagation in an infinite horizontal layer and a long narrow channel.     

On the motion of visco-elastic electrically conducting liquid in the presence of a magnetic field

Zusammenfassung Es wird die Strömung einer viskoelastischen, elektrisch leitenden Flüssigkeit untersucht auf Grund der elektromagnetischen Grundgleichung und der für solche Flüssigkeiten geltenden Bewegungsgleichungen. Im besonderen wird die Strömung zwischen parallelen Platten erörtert. Sie ist charakterisiert durch zwei dimensionslose Kennzahlen, die Hartmannsche Zahl und die Elastizitätszahl. Das elastische Verhalten bewirkt eine Verflachung des Geschwindigkeitsprofils und verändert auch den Druck und die Schubspannungen.

---

Notations x ₁,x ₂,x ₃ space coordinates - B magnetic induction vector - E electric intensity - H magnetic field - D displacement vector - J current density vector - _e E electrostatic force - V×B current density due to the motion of the fluid - _e V convection current - _e excess charge density - electrical conductivity - magnetic permeability - dielectric constant - =1/ magnetic diffusivity - V=v ¹ i+v ² j+v ³ k velocity vector - v ₁= ₁/ kinematic viscosity - ₁ coefficient of viscosity - _c coefficient of cross-viscosity - v _c = _c / kinematic cross-viscosity - density of the fluid - relaxation time - S _j ⁱ stress-tensor - d _j ⁱ strain-tensor - x, y, z dimensionless coordinates - L spacing between the planes, taken as the characteristic length - U ₀ characteristic velocity - f non-dimensional velocity - H non-dimensionalx-component of the magnetic field.     

Propagation of nonlinear capillaary waves in an electrically conducting liquid

The article deals with the propagation of periodic capillary waves with finite amplitude on the surface of an electrically conducting liquid subjected to the effect of a magnetic field. It is shown that the evolution of wave packets is described by perturbed nonlinear Schrödinger equations. Its asymptotic solution is obtained, and it is established that the influence of MHD effects manifests itself in reduced frequency and amplitude of the propagating waves.Kiev. Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 21, pp. 97–99, 1990.     

Dynamics of a rotating layer of an ideal electrically conducting incompressible inhomogeneous fluid in an equatorial region

The equations describing the three-dimensional equatorial dynamics of an ideal electrically conducting inhomogeneous rotating fluid are studied. The magnetic and velocity fields are represented as superpositions of unperturbed steady-state fields and those induced by wave motion. As a result, after introducing two auxiliary functions, the equations are reduced to a special scalar one. Based on the study of this equation, the solvability of initial-boundary value problems arising in the theory of waves propagating in a spherical layer of an electrically conducting density-inhomogeneous rotating fluid in an equatorial zone is analyzed. Particular solutions of the scalar equation are constructed that describe small-amplitude wave propagation.     

Surface tension and buoyancy effects in the cellular convection of an electrically conducting liquid in a magnetic field

Zusammenfassung Eine frühere Analyse des Konvektionsanfangs in einer horizontalen Flüssigkeitsschicht, ausgelöst durch die gleichzeitige Einwirkung der Auftriebs- und Oberflächenspannungseffekte, wird auf eine elektrisch leitfähige Flüssigkeit in einem magnetischen Feld ausgedehnt. Zahlenresultate werden für den Fall gewonnen, wo die untere Fläche ein starrer Leiter ist und die obere freie Fläche für Temperaturstörungen entweder «leitet» oder «isoliert». Für die Wirkungen eines vertikalen magnetischen Felds ergibt sich folgendes: (1) Konvektion wird unter allen betrachteten Umständen gehemmt, (2) die horizontalen Dimensionen einer Konvektionszelle werden vermindert, und (3) die Kopplung zwischen den Oberflächenspannungs- und Auftriebswirkungen wird abgeschwächt. Die Wirkung (3) ist erstaunlich plötzlich, wenn die obere Fläche ein guter Leiter für Temperaturstörungen ist.     

Asymptotic model for free surface flow of an electrically conducting fluid in a high-frequency magnetic field

We study the behaviour of a layer of an electrically conducting inviscid incompressible fluid in a high-frequency alternating magnetic field. We derive nonlinear asymptotic equations governing the evolution of the fluid layer in the high-frequency limit. As a test for the model, we consider the linearised stability problem for an infinite planar free surface of a layer of finite depth.     

Temperature fields and stresses in an electrically conducting plate under surface heating by a ring-shaped conductor

We study the thermostressed state of a round nonferromagnetic plate subject to the action of a steady electromagnetic field produced by a system of external ring-shaped currents. It is determined that a decrease in the winding radius of a single-loop inductor leads to a decrease in the level of stress.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 36, 1992, pp. 43–47.     

Unsteady hydromagnetic motion of a rotating conducting fluid

The combined effects of stratification and magnetic field on the unsteady motion of a viscous, electrically conducting fluid between two rotating disks are analysed. Solutions are obtained for the linearized equations under Boussinesq approximation and steady state solutions are deduced from them. The results are compared with those obtained by Loper and Benton and Balanet al. Graphs are presented for the steady state velocity, magnetic field and temperature distributions.     

An electrically conducting sphere in a three-dimensional, alternating magnetic field

The electrical vector and scalar potential as well as the underlyinginduced eddy current density of a conducting sphere exposedto an external, time-varying magnetic field are calculated.The external magnetic field is assumed to be generated by sinusoidallyalternating current density distributions. Admitting arbitrarythree-dimensional current density fields, this paper extendsprevious results on this subject. Among other things, thesecalculations prove that in a sphere there is no radial componentof the induced eddy current density field. As an applicationof these results the impedance and power absorption of the sphereare derived. The impedance is the key for the contactless, inductivemeasurement of the electrical conductivity of metallic melts.     

Unsteady hydromagnetic rotating flow of a conducting second grade fluid

The purpose of this work is to investigate the hydromagnetic oscillatory flow of a fluid bounded by a porous plate, when the entire system rotates about an axis normal to the plate. The fluid is assumed to be non-Newtonian (second grade), incompressible and electrically conducting. The magnetic field is applied transversely to the direction of the flow. Such a flow model has great significance not only of its theoretical interest, but also for applications to geophysics and engineering. The resulting initial value problem has been solved analytically for steady and unsteady cases. The analysis of the obtained results showed that the flow field is appreciably influenced by the material parameter of the second grade fluid, the applied magnetic field, the imposed frequency, rotation and suction and blowing parameters. It is observed in a second grade fluid that a steady asymptotic hydromagnetic solution exists for blowing and resonance which is different from the hydrodynamic situation.     

The flow of an electrically conducting fluid at a rear stagnation point

Summary We consider the impulsively generated magnetohydrodynamic flow at a rear stagnation point. The work of Leibovich is carried further by formulating the inner viscous problem and providing analytical solutions and complete numerical solutions for the entire range of the interaction parameter. It is shown that the present results are consistent with previously obtained numerical solutions to the steady equations of both similarity and non-similarity form.

---

Résumé Nous considérons l'écoulement magneto-hydrodynamique impulsivement engendré à un point de stagnation arrière. On porte plus loin l'étude de Leibovich par la formulation du problème visqueux intérieur et en fournissant des solutions analytiques et numériques complètes correspondantes au champ entier du paramètre d'interaction. On montre que les résultats actuels sont en accord avec les solutions numériques, et de similitude et de non-similitude, déjà connues des équations stationnaires.

     

Physical concepts and technological aspects of electrically conducting polymers

A review is given on the present physical concepts of understanding electrically conducting polymers. Experimental data on the electrical conductivity as a function of doping level, conjugation length, and temperature are presented and discussed in the framework of a modified model of variable range hopping. Experiments of the transient photoconductivity in the picosecond regime give information on local transport properties and on the anisotropy of motion parallel and perpendicular to the polymer chains.     

Secondary flow of a conducting fluid in a rotating straight annular pipe

A theoretical analysis is made of the flow of a conducting viscous and incompressible fluid through a straight annular pipe of circular cross-section flowing under a constant pressure gradient. The pipe is rotated about an axis perpendicular to it and also there is imposed a uniform magnetic field transverse to the motion. The secondary flow pattern has been studied in detail for small values of angular velocity and Hartman number.     

On oscillations of a semi-infinite rotating liquid with its free surface excited by moving sources

Propagation of small perturbations in a homogeneous inviscid liquid rotating with a constant angular velocity in the lower half-space is considered. The source of excitation is a plane wave traveling on the free surface of the liquid. The explicit analytical solution to the problem is constructed. Uniqueness and existence theorems are proved. The wave pattern in the liquid at large times is examined.     

Stretching a surface in a rotating fluid

Summary A surface is stretched in a rotating fluid. The solution to the governing set of nonlinear differential equations depends on a parameter which is the ratio of the rotation rate to the stretching rate. Perturbation solutions for small and large compare well with exact numerical integration.     

An approximate method of computing the magneto-acoustic heating of electrically conducting bodies

We discuss a method of approximate computation of the noncontact magneto-acoustic heating of nonmagnetic viscoelastic matter, based on the asymptotic separation of the initial equations of the theory of magnetoelasticity and the expansion of the solutions of the resulting sequence of problems in a series of eigenfunctions of the classical problems of electrodynamics and the dynamic theory of elasticity. The asymptotic parameter ε<1 for the problem was taken to be the criterion ε=Co. Rm forRm≤1 and ε=Co forRm≥1. We obtain expressions for the average power of the Joule losses and losses due to internal friction. Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, No. 37. 1994. pp. 70–73.     

Flow of an electrically conducting non-newtonian fluid between two rotating coaxial cones in the presence of external magnetic field due to an axial current

Bhatnagar and Rathna (Quar. Journ. Mech. Appl. Maths., 1963,16, 329) investigated the flows of Newtonian, Reiner-Rivlin and Rivlin-Ericksen fluids between two rotating coaxial cones. In case of the last two types of fluids, they predicted the breaking of secondary flow field in any meridian plane. We find that such breaking is avoided by the application of a sufficiently strong azimuthal magnetic field arising from a line current along the axis of the cones.