Two-dimensional flow of a perfect conducting gas in crossed electric and magnetic fields

Reference [1, 2] give a solution of the problem of the two-dimen-, sional flow of an inviscid thermally-nonconducting gas with constant conductivity in a channel of constant cross section for particular forms of the given applied magnetic field. The present paper obtains a solution of the problem of the two-dimensional flow of a gas with variable conductivity in crossed electric and arbitrary magnetic fields by means of the small parameter method. The magnetic Reynolds number R_m and the magnetohydrodynamic interaction parameter S are chosen as parameters. The international system of units is employed.Notation V flow velocity - j electric current density - p pressure in the flow - E electric field strength - gas density - electrical conductivity of the gas - T gas temperature - ratio of specific heats at constant pressure and volume - L channel half-height - ] permeability (magnetic) - B magnetic induction vector - B₀ applied magnetic field     

Influence of the hall effect on development of rotational MHD flow in a flat channel

In an experimental study of the heat transfer from a partially ionized gas it was found that the heat flux to the wall for flow of an electrically conducting gas in a circular tube located in a magnetic field of a solenoid depends not only on the magnitude of the magnetic field but also on the field orientation [1]; with the magnetic field parallel to the velocity the heat transfer is reduced by 15%, with antiparallel orientation it is reduced by only 1% in comparison with the heat transfer without the magnetic field. No explanation for this was given either in [1] or in the subsequent discussion [2]; moreover, on the basis of the constructed equations [1] this effect cannot be obtained at all, since the solution of the equations clearly is not changed by a change of the field sign. In the following we attempt to explain this effect by the processes which take place during the development of rotational flow of an anisotropically conducting medium. The idea of the possibility of such an explanation for this effect was proposed in general form in the survey paper [3].The detailed calculation of the development of MHD flows has been made previously only for the case of a transverse magnetic field and very simple channel geometry (see, for example, the survey [3]).In all the considered problems the components of the electrical field which appeared in the motion equations were known with an accuracy to constants from symmetry considerations. Therefore, under the assumption of smallness of the induced magnetic field these problems reduced simply to the solution of the equation of motion with additional terms which are linear in the velocity. In the present paper we construct an approximate simultaneous solution of a system consisting of the motion equations and the equation for the electrical potential.     

Nonlinear longitudinal current in the Maxwellian plasma generated under the action of a transverse electromagnetic wave

The nonlinear interaction between an electromagnetic field and collisionless classic and quantum Maxwellian plasmas is analyzed. Formulas for calculating the electric current are derived. The nonlinearity turns out to lead to generation of a longitudinal electric current aligned with the wave vector. This current is orthogonal to the well-known transverse current obtained in the linear analysis. The current densities for the classic Maxwellian plasma and the plasma with an arbitrary degree of degeneration of the electron gas are graphically compared. The classic and quantum plasmas are also compared. The current density as a function of the dimensionlesswavenumber is investigated for various oscillation frequencies of the electromagnetic field.     

Flux losses during compression of a magnetic field by flat strips

The compression of a magnetic field by a moving conductor — magnetic cumulation — is used to obtain powerful magnetic fields and large pulsed currents [1, 2]. The potentialities of magnetic cumulation are determined mainly by the flux losses due to diffusion of the magnetic field into the conductor and its capture in short-circuited cavities formed upon the joining of uneven conductor surfaces. Experiments on the compression of a magnetic field by flat strips of copper and Durai are described in the report, and a comparison is made with the calculation of diffusional flux losses. The possible role of a gutter instability of the copper conductors is evaluated for the explanation of the increase in flux losses when a critical linear current density, whose value in the experiments presented was 180–210 kA/cm, is exceeded in the strips.     

Extended thermodynamics of a relativistic plasma with finite electric conductivity

A system of equations for relativistic m.h.d, with finite electric conductivity and no heat flux is proposed, starting from the properties of the systems of conservation laws compatible with a supplementary balance law (entropy balance) with convex density (symmetric-hyperbolic systems). The electric current density is treated as a new field variable which contributes to non equilibrium entropy density (extended thermodynamics). The result is a theory in which only one new constitutive function, representing entropy increment respect to equilibrium, is necessary to characterize the properties of the medium related to electric conductivity.G.N.F.M. of the C.N.R.     

Non-equilibrium relativistic M.H.D. with finite electrical conductivity

A system of balance laws for relativistic m.h.d, with finite eIectrical conductivity, heat flux and viscosity is proposed, starting from the properties of the systems of conservation laws compatible with a supplementary balance law (entropy balance). Adopting a two-fluid scheme the plasma is treated as a mixture of a neutral fluid and a charged fluid. Following the approach ofextended thermodynamics heat flux, viscous stress and electric current density are considered as new field variables contributing to non equilibrium entropy density and flux.     

Heat conduction and thermal stress induced by an electric current in an infinite thin plate containing an elliptical hole with an edge crack

A uniform electric current at infinity was applied to a thin infinite conductor containing an elliptical hole with an edge crack. The electric current gives rise to two states, i.e., uniform and uneven Joule heat. These two states must be considered to analyze the heat conduction problem. The uneven Joule heat gives rise to uneven temperature and thus to heat flux, and to thermal stress.Using a rational mapping function, problems of the electric current, the Joule heat, the temperature, the heat flux, the thermal stress are analyzed, and each of their solutions is obtained as a closed form. The distributions of the electric current, the Joule heat, the temperature, the heat flux and the stress are shown in figures.The heat conduction problem is solved as a temperature boundary value problem. Solving the thermal stress problem, dislocation and rotation terms appear, which complicates this problem. The solutions of the Joule heat, the temperature, the heat flux and the thermal stress are nonlinear in the direction of the electric current. The crack problems are also analyzed, and the singular intensities at the crack tip of each problem are obtained. Mode II (sliding mode) stress intensity factor (SIF) is produced as well as Mode I (opening mode) SIF, for any direction of the electric current. The relations between the electric current density and the melting temperature and between the electric current density and SIF are investigated for some crack lengths in an aluminum plate.     

磁流体流动控制中的磁场配置效率研究

采用数值模拟方法研究了不同磁场空间构型对弹道式再入飞行器基准外形表面热流分布的影响. 计算模型为低磁雷诺数近似下的磁流体力学模型. 数值模拟结果表明两个大小相同、方向不同的磁偶极子对表面热流密度分布的影响存在较大差异,由此指出热流控制应用中磁场配置的效率问题. 随后的磁场详细作用机理分析表明上述差异的原因在于不同空间磁场分布对流动能量转化机制的影响不同. 以此为基础给出了在流动的不同区域,磁场空间分布应遵循的一般性原则.      

Effect of viscous dissipation on an MHD free convective flow past a semi-infinite vertical cone with a variable surface heat flux

An analysis is presented to investigate the influence of viscous dissipation on a free convection flow over a vertical cone with a variable surface heat flux under the action of a transverse magnetic field. The heat transfer characteristics of the free convection flow are investigated numerically. Numerical solutions for transformed governing equations with a variable surface heat flux are obtained. Velocity, temperature, local shear stress, and heat transfer coefficients are calculated for various values of the problem parameters and presented in the graphical form. The effects of the magnetic parameter, the dissipation number, the power-law index, the angle between the cone generatrix and the vertical line, and the Prandtl number on the flow are discussed. For validation of the present numerical results, they are compared with available experimental data and are found to agree well.     

A MAGNETO-MECHANICAL FULLY COUPLED MODEL FOR GIANT MAGNETOSTRICTION IN HIGH TEMPERATURE SUPERCONDUCTOR

This paper presents a fully coupled model to account for the flux pinning induced giant magnetostriction in type-II superconductors under alternating magnetic field The superconductor E-J constitutive law is characterized by power law where the critical current density is assumed to depend exponentially on the flux density. The governing equations of the two-field problem(i.e., the interactions of elastic and magnetic effects) are formulated in a two-dimensional model. The magnetostriction curves and magnetization loops are calculated over a wide range of parameters. The effects of applied magnetic field frequency f and amplitude B0 and critical current density on magnetostriction and magnetization are discussed. Results show that the critical current density of high temperature superconductor(HTS) YBCO has a significant effect on the magnetization and magnetostriction. The pinning-induced magnetostriction which has been observed in experiment can be qualitatively simulated by this model.     

Calculations for a cylindrical electric arc with allowance for energy transfer by radiation with the hydrogen at a pressure of 100 atm

An approximate method is described for the consideration of energy transfer by radiation during the utilization of real properties of a gas (in particular, the frequency-dependent absorption coefficient under conditions of local thermal equilibrium). With increasing pressure, it becomes necessary to take self-absorption into account over almost the entire frequency spectrum.Calculations are carried out for a wall-stabilized cylindrical electric arc in hydrogen as an example for a pressure of 100 atm and channel radii of 0.3, 1, and 3 cm at values of current strength up to the order of 10 A. The strong effect of radiation on the current-voltage characteristic of the arc, the gas temperature, and the nature of its distribution over the arc radius is demonstrated.The process of energy transfer by radiation plays a significant and sometimes predominant role in the thermal balance of electric arcs with high current strengths [1–9]. Calculations have been performed for cylindrical arcs in atmospheres of argon and hydrogen [5, 7] with allowance for energy transfer by radiation and for atmospheric pressure in which case the gas is essentially transparent to radiation. Approximate estimates were obtained for the self-absorbed portion of the radiation.The role played by radiation increases with increasing current strength, arc radius, and pressure, while self-absorption in this process extends over an increasingly large region of the spectrum. Hence, calculations must be carried out for the arc if conditions are such that the gas in the arc does not transmit radiation.In [10–13], an approximate method was developed for taking into account energy transfer by radiation in the presence of intense selfabsorption as applied to heat transfer problems under conditions of local thermal equilibrium with allowance for the variation of the absorption coefficient as a function of the frequency. The conditions for local thermal equilibrium in an arc passing through an argon or hydrogen atmosphere are fulfilled for pressures greater than atmospheric pressure and for current strengths greater than 10 A [14–16], The results of [10–12] were used as the foundation for calculations based on an electric arc in argon at atmospheric pressure, under which conditions, self-absorption affects only the transitions to the ground state. The part played by radiation in the heat transfer process is smaller than the part played in the energy transfer by conduction. Calculations confirmed the results of [5, 7].The role of energy transfer by radiation in the energy balance of the arc increases with increasing pressure, while in turn, the role of the continuous spectrum increases for the radiation. The results of calculations performed for a wall-stabilized arc burning in an atmosphere of hydrogen at a pressure of 100 atm are given in the present paper. In this case, almost the entire energy supply is lost by radiation. The approximate method of accounting for energy transfer by radiation is demonstrated by an example.Notation and T gas density and temperature, respectively - u velocity - c_p heat capacity of the gas at constant pressure - coefficient of thermal conductivity - coefficient of electrical conductivity - x and r cylindrical coordinates - r₀ channel radius - I current strength - E electric field strength - u ° equilibrium value of radiation energy density - u value of radiation energy density - radiation frequency - divergence of energy flux density transported by radiation - k absorption coefficient - c speed of light - _i emissivity of the i-th region of the spectrum     

Transport phenomena in a knudsen molecular gas in a magnetic field

We consider the behavior of a strongly rarefied (Knudsen) polyatomic gas between two surfaces that have different temperatures in a magnetic field. We show that in the magnetic field H there can arise a flux of gas and a heat flux along the surfaces (odd functions in H), and also normal and tangential forces on the walls.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 124–130, January–February, 1979.     

Determination of current flow in a plasma by a simulation method

A method is proposed which, for specific assumptions, allows us to determine the density distribution of a constant current flowing between electrodes in a plasma for plane parallel or radially symmetric electric and magnetic fields, allowing for anisotropic conductivity.Notation e_r, e, e_z unit vectors in a cylindrical coordinate system - E, e_r, e_z electric field strength vector and its components - V electric field potential - H, H_r, H, H_z magnetic field strength and its components - j current density vector - e electron charge - m electron mass - c velocity of light - momentum transfer time - ₀ normal plasma conductivity - _e electron cyclotron frequency - h unit vector in the direction of the magnetic field     

Unsteady laminar mixed convection about a spinning sphere with a magnetic field

The unsteady laminar boundary-layer flow over an impulsively started translating and spinning isothermal body of revolution in the presence of buoyancy force and magnetic field applied normal to the surface are investigated. Velocity components and temperature are obtained as series of functions in powers of time. Leading and first order functions are obtained analytically and second order functions are determined numerically. The general results are applied to a sphere to investigate the effects of magnetic field and buoyancy force on the velocity and temperature fields and the onset of separation. The magnetic field and buoyancy force are more effective for small rotational speeds and the presence of magnetic field retards the onset of separation. The effect of magnetic field on the temperature field and surface heat flux is weak, indirect and through the velocity field. The magnetic field is observed to initially increase the surface heat flux on the upstream face of the sphere and decrease it on the downstream face.     

Spontaneous rotation in the exact solution of magnetohydrodynamic equations for flow between two stationary impermeable disks

Magnetohydrodynamic (MHD) flow of a viscous electrically conducting incompressible fluid between two stationary impermeable disks is considered. A homogeneous electric current density vector normal to the surface is specified on the upper disk, and the lower disk is nonconducting. The exact von Karman solution of the complete system of MHD equations is studied in which the axial velocity and the magnetic field depend only on the axial coordinate. The problem contains two dimensionless parameters: the electric current density on the upper plate Y and the Batchelor number (magnetic Prandtl number). It is assumed that there is no external source that produces an axial magnetic field. The problem is solved for a Batchelor number of 0–2. Fluid flow is caused by the electric current. It is shown that for small values of Y, the fluid velocity vector has only axial and radial components. The velocity of motion increases with increasing Y, and at a critical value of Y, there is a bifurcation of the new steady flow regime with fluid rotation, while the flow without rotation becomes unstable. A feature of the obtained new exact solution is the absence of an axial magnetic field necessary for the occurrence of an azimuthal component of the ponderomotive force, as is the case in the MHD dynamo. A new mechanism for the bifurcation of rotation in MHD flow is found.     

On the frame dependence of constitutive equations. I. Heat transfer through a rarefied gas between two rotating cylinders

To verify the principle of material frame indifference a numerical calculation of the heat flux field in a rotating gas has been carried out based on the kinetic equation over wide ranges of gas rarefaction and angular velocity. It has been confirmed that a radial gradient of the temperature causes a tangential heat flux. Also, it has been found that the radial heat flux is affected by the rotation.On temporary leave from Department of Physics, Urals State University, 620083 Ekaterinburg, Russia     

Development of magnetohydrodynamic boundary layers associated with the sudden initiation or deceleration of a supersonic flow at the boundary of a half-space

The problem of nonstationary magnetohydrodynamic flow of a viscous fluid in a half-space resulting from the motion of an infinite plate has received much attention. In [1], for example, solutions are presented for the case of isotropic conductivity, while in [2] a solution of the Rayleigh problem is offered for the case of anisotropic conductivity. In these instances the fluid was assumed incompressible and uniform, and the system of equations was found to be linear. In problems involving nonstationary flow of a gas in a transverse magnetic field resulting from the deceleration of a high-velocity gas flow at the boundary of a half-space or the motion of an infinite plate at supersonic speed relative to a stationary gas it becomes necessary to take into account the compressibility of the gas and the temperature dependence of the conductivity. It is then possible to have flows in which the gas becomes electrically conducting and begins to interact with the magnetic field solely as a result of the increase in temperature due to viscous dissipation of energy. The magnetic field, interacting with the conducting gas, exerts an effect on the drag and heat transfer to the surface of the plate. At sufficiently low gas pressures and strong magnetic fields a Hall effect may be observed. The system of equations describing the motion of a compressible gas with variable conductivity is essentially nonlinear. The present article is devoted to a study of such motions.     

INTERFACE CRACK IN BIPIEZOTHERMOELASTIC MEDIA

By using the extended version of Eshelby-Stroh's formulation and the method of analyt-ical continuation,the problems of interface cracks are reduced to a Hilbert problem of vector form.Ageneral explicit closed form solution for the piezothermoelastic interface crack problem is then ob-tained,the whole field solutions of temperature,heat flux,displacements,electric field,stress andelectric induction are given,the explicit expressions for the crack opening displacements and electricpotential are also provided.     

Heat transfer in a hydromagnetic flow over a stretching sheet

Exact solutions are obtained for the heat transfer in an electrically conducting fluid past a stretching sheet subjected to the thermal boundary with either a prescribed temperature or a prescribed heat flux in the presence of a transverse magnetic field. The solutions for the heat transfer characteristics are evaluated numerically for different parameters, such as the magnetic parameterN, the Prandtl numberPr, the surface temperature indexs, and the surface heat flux indexd. It is observed that for the prescribed surface temperature case the fluid temperature increases due to the existance of the magnetic field, and decreases as the Prandtl number or the surface temperature index increases; for the prescribed surface heat flux case, the surface temperature decreases as the Prandtl number of the surface heat flux index increases, and the magnetic parameter decreases. In addition, varying the prescribed surface temperature indexs affects the mechanism of heat transfer.