Laminarization of a submerged jet of electrically conducting fluid by means of a longitudinal magnetic field

A method of laminarizing electrically conducting jet flows by means of the combined use of a longitudinal magnetic field and inlet devices which form an initial velocity profile with smooth variation at the edge of the jet and a low perturbation level is proposed. An experimental investigation of delayed transition in a circular submerged jet, which demonstrates the high efficiency of the method, has been carried out.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 35–40, November–December, 1989.The authors are grateful to V. N. Kolomeits and V. P. Fomenko for helping to prepare and carry out the experiments.     

The Hall effect in an electrically conducting fluid for variable magnetic field and high magnetic Reynolds numbers

Hall phenomena in an electrically conducting fluid with a variable magnetic field were considered in [1]. In that paper the basic characteristics of the above-mentioned phenomena are determined, with certain unimportant constraints, for the case of fluid motion along a channel of rectangular cross section in a traveling magnetic field. The magnetic Reynolds number was assumed to be small, and a solution was given for the induction field in the form of a series in powers of the indicated parameter. Quantitative estimates based on the data of [1] are impossible in the case of relatively high electrical conductivity of the fluid, although certain conclusions of a qualitative nature remain valid. There is thus reason to consider the case of high magnetic Reynolds numbers. This will also allow a fuller picture of the characteristic Hall effect phenomena to be constructed for a variable magnetic field.     

Internal waves in a two-layer electrically conducting fluid in the presence of a magnetic field

The propagation of linear and nonlinear internal waves along the interface between two weakly conducting media differing in density and electrical conductivity is investigated and the influence of MHD interaction effects on their characteristics is analyzed. It is shown that in this system the waves propagate with dispersion and dissipation, and for harmonic waves of infinitesimal amplitude there exists a range of wave numbers on which propagating modes do not exist. For waves of finite amplitude a nonlinear Schrödinger equation with a dissipative perturbation is obtained and its asymptotic solution is found. It is established that the presence of electrical conductivity and an applied magnetic field leads to a decrease in the amplitude and the frequency of the envelope of the wave train.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 104–108, September–October, 1990.     

Effect of magnetic field on the buoyancy and thermocapillary driven convection of an electrically conducting fluid in an annular enclosure

The main objective of this article is to study the effect of magnetic field on the combined buoyancy and surface tension driven convection in a cylindrical annular enclosure. In this study, the top surface of the annulus is assumed to be free, and the bottom wall is insulated, whereas the inner and the outer cylindrical walls are kept at hot and cold temperatures respectively. The governing equations of the flow system are numerically solved using an implicit finite difference technique. The numerical results for various governing parameters of the problem are discussed in terms of the streamlines, isotherms, Nusselt number and velocity profiles in the annuli. Our results reveal that, in tall cavities, the axial magnetic field suppresses the surface tension flow more effectively than the radial magnetic field, whereas, the radial magnetic field is found to be better for suppressing the buoyancy driven flow compared to axial magnetic field. However, the axial magnetic field is found to be effective in suppressing both the flows in shallow cavities. From the results, we also found that the surface tension effect is predominant in shallow cavities compared to the square and tall annulus. Further, the heat transfer rate increases with radii ratio, but decreases with the Hartmann number.     

Propagation of a laminar jet of electrically conducting fluid in a uniform magnetic field

Several papers [1–4] have considered the propagation of a plane laminar jet of incompressible conducting fluid in a uniform magnetic field for magnetic Reynolds numbers much less than unity. These papers have investigated the flow of a free jet in a transverse magnetic field for small values of the magnetic interaction parameter. Equations for the first approximations were obtained in [1, 2] by a series expansion in the small interaction parameter close to the ordinary solution (without magnetic field) for the jet. The equations for the zero-th and first approximations were integrated in [3]. The same author also found a similar solution for a turbulent jet, the turbulent transfer coefficient being chosen according to Prandtl's method. As regards the solution found in [4], it suffers from the defect that the constant of integration which connects the real velocity profiles with those found in the paper remains undetermined. The present paper gives an approximate solution of the same dynamic problem of the propagation of a free plane jet in a uniform field, no assumption being made as to the smallness of the interaction parameter. In order to do this the integral method of solution, common in ordinary hydrodynamics [5, 6] is employed. The solution of the problem is generalized to include the case of a finite value of the Hall parameter.     

Free convection flow of an electrically conducting fluid past a porous flat plate under transverse magnetic field

Summary An analysis is made of the laminar free convection of a viscous electrically conducting fluid from a hot infinite porous flat plate maintained at constant temperature under transverse magnetic field. Expressions have been obtained for the velocity, magnetic field, skin friction at the plate and the momentum thickness. The effect of the Grashof number and the Prandtl number on these quantities is discussed.     

The stability of a free rotating layer in an electrically conducting fluid in an axial field

The subject considered is a homogeneous electrically conducting incompressible medium with a current in a homogeneous external magnetic field and bounded by parallel insulating planes normal to the induction vector. When the current is fed by means of a system of coaxial electrodes located on one or both of the insulating planes, regions arise in which the medium is in rotational motion. If the lateral wall is at a sufficient distance from the electrodes, the rotating layer which forms as a result of the interaction of the axial magnetic field and the radial component of the electric current has free lateral boundaries. A study is made of the way in which the Reynolds number for the loss of stability in such a layer depends on the Hartmann number and on the geometric parameter for high values of the Hartmann number and low values of the magnetic Reynolds number.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 166–173, September–October, 1984.     

Steady and transient free convection of an electrically conducting fluid from a vertical plate in the presence of a magnetic field

Summary An analysis is made for the laminar free convection and heat transfer of a viscous electrically conducting fluid from a hot vertical plate in the case when the induced field is negligible compared to the imposed magnetic field. It is found that similar solutions for velocity and temperature exist when the imposed magnetic field (acting perpendicular to the plate) varies inversely as the fourth root of the distance from the lowest end of the plate. Explicit expressions for velocity, temperature, boundary layer thickness and Nusselt number are obtained and the effect of a magnetic field on them is studied. It is found that the effect of the magnetic field is to decrease the rate of heat transfer from the wall. In the second part, the method of characteristics is employed to obtain solutions of the time-dependent hydromagnetic free convection equations (hyperbolic) of momentum and energy put into integral form. The results yield the time required for the steady flow to be established, and the effect of the magnetic field on this time is studied.     

Stationary simple waves in an electrically conducting magnetizable fluid

A study is made of the analog of Prandt1—Meyer flow in an incompressible electrically conducting ideal fluid that is magnetizable in accordance with an arbitrary isotropic law. It is shown that inhomogeneity of the magnetization in a conducting fluid makes possible the existence of stationary simple waves with varying magnetic permeability. For a paramagnetic fluid magnetized to saturation, the equations of these waves are integrated completely in the case of a magnetic field parallel to the velocity. Some regions of such flows of magnetizable fluids are discussed in the present paper for the example of the problem of flow around a perfectly conducting profile.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 136–143, September–October, 1980.I thank I.E. Tarapov for his interest in the work and valuable comments made in a discussion.     

Motion of a sphere in an electrically conducting rotating fluid

The combined effect of rotation and magnetic field is investigated for the axisymmetric flow due to the motion of a sphere in an inviscid, incompressible electrically conducting fluid having uniform rotation far upstream. The steady-state linearized equations contain a single parameter α=1/2βR _m, β being the magnetic pressure number and R _m the magnetic Reynolds number. The complete solution for the flow field and magnetic field is obtained and the distribution of vorticity and current density is found. The induced vorticity is O(α⁴) and the current density is O(R _m) on the sphere.     

Quasi-geostrophic motions in a rotating layer of an electrically conducting fluid

Large-scale nonlinear oscillations of an electrically conducting ideal fluid of varying depth are considered with the magnetic, Archimedean, and Coriolis forces taken into account. The main equations are derived from an analysis of the scales of quasi-geostrophic motions. Under the assumptions that the Rossby numbers (a measure of the ratio of the local and advective accelerations to the Coriolis acceleration) are of the same order, the problem is reduced to a system of three nonlinear equations for hydromagnetic pressure and two functions describing the magnetic field. For an infinitely long horizontal layer of an electrically conducting rotating fluid, the exact solution of the corresponding nonlinear equations and the dispersion relation are obtained under the assumption of an approximately constant slope of the upper boundary surface of the layer at a distance of the order of the wavelength. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 1, pp. 30–41, January–February, 2009.     

Convective stability of a rotating conducting fluid layer in an external magnetic field

The stability of the rest state of a conducting incompressible fluid forming a horizontal layer with rigid dielectric boundaries heated from below and rotating about a vertical axis, with a vertical magnetic field superimposed, is studied in the Boussinesq approximation. With increase in the Rayleigh number, depending on the relationship between the problem parameters (Taylor, Chandrasekhar and kinematic and magnetic Prandtl numbers), the eigenvalue of the critical mode of the linearization operator may be zero or imaginary, so that the instability of the rest state may be monotonic or oscillatory. The effect of the parameter values on the instability mode is investigated. In particular, the parameter ranges on which the critical eigenvalue is zero or imaginary are found.     

Effect of a longitudinal magnetic field on the flow of an electrically conducting fluid in a circular tube with a sharp narrowing at the entrance

The procedure described in [1] is used to study the effect of entry conditions to the test section on the nature of the flow of an electrically conducting fluid in a circular tube in a longitudinal magnetic field.

     

On the effect of magnetic field on viscous lifting and drainage of conducting fluid

This paper concerns with obtaining the solution of the problem of viscous lifting and drainage of a thin liquid film clinging to a vertical plane surface moving with a velocityf(t) in the presence of a transverse magnetic field. Specializing to the case when the surface moves with a constant acceleration, it has been found that the film thickness, for large magnetic fields, increases with the increase in magnetic field.Nomenclature a acceleration of the plate - A non-dimensional acceleration, =a/g - B magnetic induction vector - B ₀ applied magnetic field - f(t) any function oft - Laplace transform off(t) - g gravitational acceleration - h film thickness - H non-dimensional film thickness, =h(g/ ²)^1/3 - J current density vector - k (/)^1/2 B ₀ - M k( ²/g)^1/3 - n summation index - q mass flow rate - Q non-dimensional mass flow rate, =q/ - t time - T non-dimensional time, =t(g ²/)^1/3 - Laplace transform ofv(x, t) - V fluid velocity vector, =[0,v(x, t), 0] - (x, y, z) space coordinates - Y non-dimensionaly-coordinate, =y(g/ ²)^1/3 Greek symbols _n (n+1/2) - conductivity - density - kinematic viscosity     

Hall current effects on waves in an electrically conducting rotating fluid

The waves generated by an obstacle moving with constant velocity U along the axis of an inviscid, incompressible, infinitely conducting fluid with Hall current effects, rotating with an angular velocity are studied by Lighthill's technique. Three cases arise according as U>A ₁, U=A ₁ or U ₁, where A ₁ is the modified Alfven velocity due to Hall current term. In the cases U> and <A ₁ the wave-number surface consists of two distinct spheres and four coincident planes. The waves corresponding to the points on the outer sphere trail behind and those on the inner sphere travel ahead of the disturbance if U>A ₁ and vice-versa if U ₁. When U=A ₁ the wave-number surface consists of two coincident spheres and four coincident planes and the spherical waves are found both ahead and behind. By drawing appropriate normals to the four planes, it is seen that the formation of the Taylor column ahead of the disturbance is possible in all the cases.     

Laminar slip flow of an electrically conducting incompressible rarefied gas in a channel with a transverse magnetic field

Summary The effects of a constant external magnetic field on the laminar, fully developed flow of an electrically conducting incompressible rarefied gas in a nonconducting parallel-plate channel are studied. Consideration is given to the slip-flow regime, wherein a gas velocity discontinuity occurs at the channel walls. It is found that the magnitude of the slip velocity is unaffected by the magnetic-field strength for a given pressure drop, but that the mean gas velocity and wall friction coefficient are functions of both the velocity slip coefficient and the magnetic-field strength. The effect of a second-order slip-flow boundary condition is briefly discussed.