An electromagnet with Hall excitation

In 1911 Corbino showed that if a disk with a current flowing to the axis is placed in a magnetic field parallel to the axis of the disk, then due to the Hall emf the initially straight line of electric current is turned into a spiral. This leads to an increase in the length of the current line and thus to an increase in the disk resistance. The change in the disk resistance in a magnetic field was used in [1] to switch the current in the circuit of an inductive energy store. If the electric current carriers move from the edge of the disk to the axis, the azimuthal Hall current is accompanied by an increase in the magnetic field inside the disk compared with that outside it [2]. The same processes occur in a hydromagnet [3–5], in which the radial flow of a conducting liquid in an axial magnetic field is used to amplify a magnetic field. In the papers mentioned earlier the transients which occur when the steady magnetic field is established were not considered. To produce a magnetic field, and particularly for switching, the switch-on time of the device is of considerable importance. Hence, in this paper we consider the nonstationary problem of the amplification of a magnetic field. The amplification of the field is obtained and the time taken for the stationary state to build up is found. Both quantities depend exponentially on the magnetic Reynolds number. For a hydromagnet it is shown that the steady-state magnetic field differs considerably from that obtained in [4, 5]. The disagreement between the results is due to the fact that the boundary conditions in [4, 5] were arbitrarily chosen.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 44–48, May–June, 1979.The author thanks E. I. Bichenkov and R. L. Rabinovich for useful discussions and advice.     

Hall effect on MHD free convection boundary layer flow past a vertical flat plate

Effects of Hall current on MHD free convection boundary layer flow of a viscous incompressible electrically conducting fluid past a heated vertical flat plate of finite dimension in the presence of a uniform transverse magnetic field have been studied. An exact solution of the governing equations describing the flow has been obtained. The velocity field, induced magnetic field and bulk temperature distributions in the boundary layer flow have been discussed. It is found that the velocity components increase with an increase in Hall parameter. It is noticed that the induced magnetic field components are radically influenced by the Hall parameter. It is also found that the magnitude of bulk temperature in the x-direction decreases with an increase in either Hall parameter or magnetic parameter. On the other hand, the magnitude of the bulk temperature in the z-direction increases with an increase in Hall parameter whereas it decreases with an increase in magnetic parameter.     

Magnetoelastic fracture of soft ferromagnetic materials

Effects of magnetic field on fracture toughness of soft ferromagnetic materials were studied using experimental techniques and theoretical models. The manganese–zinc ferrite with a single-edge-notch-beam (SENB) were chosen to be the specimen and the Vickers’ indentation specimen subjected to a magnetic field were chosen to be the specimens. Results indicate that there is no significant variations of the measured fracture toughness of the manganese–zinc ferrite ceramic in the presence of the magnetic field. The theoretical model involves an anti-plane shear crack with finite length in an infinite magnetostrictive body where an in-plane magnetic field prevails at infinity. Magnetoelasticity is used. The crack-tip elastic field is different from that of the classical mode III fracture problem. Furthermore, the magnetoelastic fracture of the soft ferromagnetic material was studied by solving the stress field for a soft ferromagnetic plane with a center-through elliptical crack. The stress field at the tip of a slender elliptical crack is obtained for which only external magnetic field normal to the major axis of the ellipse is applied at infinity. The results indicate that the near field stresses are governed by the magnetostriction and permeability of the soft ferromagnetic material. The induction magnetostrictive modulus is a key parameter for finding whether magnetostriction or magnetic-force-induced deformation is dominant near the front an elliptically-shaped crack. The influence of the magnetic field on the apparent toughness of a soft ferromagnetic material with a crack-like flaw can be regarded approximately in two ways: one possesses a large induction magnetostrictive modulus and the other has a small modulus. Finally, a small-scale magnetic-yielding model was developed on the basis of linear magnetization to interpret the experimental results related to the fracture of the manganese–zinc ferrite ceramics under magnetic field. Studied also is the fracture test of the soft ferromagnetic steel with compact tension specimens published in the existing literature.     

A Magnetoelastic Field in a Ferromagnetic with an Elliptic Inclusion

A stress–strain problem is solved for an infinite isotropic magnetically soft body containing an elliptic inclusion. It is assumed that the body is in an external magnetic field. The basic characteristics of the stress–strain state and the induced magnetic field are determined and their features at the inclusion are analyzed. Graphs are drawn for the total magnetoelastic and Maxwell stresses versus the ratio of the ellipse axes and the angle of dip, and tabular maximum stresses versus the magnetic induction and the magnetic properties of the material.     

Stability of flow of a thin layer of viscous magnetic liquid

The laminar flow of a thin layer of heavy viscous magnetic liquid down an inclined wall is examined. The stability and control of the flow of an ordinary liquid are affected only by alteration of the angle of inclination of the solid wall and the velocity of the adjacent gas flow. When magnetic liquids are used [1, 2], an effective method of flow control may be control of the magnetic field. By using magnetic fields of various configurations it is possible to control the flow of a thin film of viscous liquid, modify the stability of laminar film flow, and change the shape of the free surface of the laminarly flowing thin film, a factor which plays a role in mass transfer, whose rate depends on the phase contact surface area. The magnetic field significantly affects the shape of the free surface of a magnetic liquid [3, 4]. In this paper the velocity profile of a layer of viscous magnetic liquid adjoining a gas flow and flowing down an inclined solid wall in a uniform magnetic field is found. It is shown that the flow can be controlled by the magnetic field. The problem of stability of the flow is solved in a linear formulation in which perturbations of the magnetic field are taken into account. The stability condition is found. The flow stability is affected by the nonuniform nature of the field and also by its direction.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 59–65, September–October, 1977.     

The Stress State of a Ferromagnetic with an Elliptic Crack in a Homogeneous Magnetic Field

The problem on the stress–strain state of an infinite isotropic body made of a magnetically soft material and containing an elliptic crack is considered. It is assumed that the body is under an external magnetic field perpendicular to the crack plane. The basic characteristics of the stress–strain state and the magnetic field induced are determined and their singularities near the elliptic crack are studied. Formulas are given for the stress intensity factors for the force and magnetic fields near the crack tip     

Surface shape of a magnetic liquid drop near the edge of a magnetic wedge

The two-dimensional problem of the shape of the free surface of a magnetic fluid in a gravity field, a uniform external magnetic field and the nonuniform field of a magnetized metal wedge is considered. The results of numerically calculating the shape of the free surface of a magnetic liquid drop retained on an inclined plane by the field of a magnetizing wedge are presented. The changes in the shape of the free surface of an infinite volume of magnetic liquid near the edge of a wedge with increase in the external field are investigated. It is shown that for a certain critical field some of the magnetic liquid separates and adheres to the edge of the wedge. Experimental data on the determination of the maximum cross-sectional area of a drop retained by the magnetic field of a wedge and the critical rise of the magnetic liquid relative to the level outside the field are presented. The experimental and theoretical results are in agreement.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.4, pp. 113–119, July–August, 1992.The authors wish to thank V. V. Gogosov for useful discussions and his interest in the work.     

Experimental investigation on heat transfer characteristics of magnetic fluid flow around a fine wire under the influence of an external magnetic field

Experimental investigation is conducted to get insight into convective heat transfer features of the aqueous magnetic fluid flow over a fine wire under the influence of an external magnetic field. The convective heat transfer coefficient of the aqueous magnetic fluid flow around the heated wire is measured in both the uniform magnetic field and the magnetic field gradient. The effects of the external magnetic field strength and its orientation on the thermal behaviors of the magnetic fluids are analyzed. The experimental results show that the external magnetic field is a vital factor that affects the convective heat transfer performances of the magnetic fluids and the control of heat transfer processes of a magnetic fluid flow can be possible by applying an external magnetic field.     

A Magnetoelastic Field in a Ferromagnetic Medium with a Spherical Cavity

The problem on the stress–strain state of an infinite isotropic body made of a magnetically soft material and containing a spherical cavity is considered. It is assumed that the body is under an external magnetic field. The basic characteristics of the stress–strain state and the magnetic field induced are determined and their singularities near the cavity are studied. Graphs are presented for the total magnitoelastic and Maxwell stresses as functions of the magnetic induction, the angle of dip, and the mechanical and magnetic properties of the material     

MHD laminar wall jet over a curved surface in a variable normal magnetic field

The effects of a magnetic field on jets of an electrically conducting fluid flowing over a curved surface, in the presence of a variable normal magnetic field, are studied. It is noted that the convex surface curvature h and the magnetic interaction parameter m, in small perturbation similarity solution have qualitatively similar effects. They increase the mass flux, decrease the momentum flux, decrease the wall shear and cause an adverse pressure gradient in the flow field.     

MHD natural convection flow and heat transfer in a laterally heated partitioned enclosure

This study looks at MHD natural convection flow and heat transfer in a laterally heated enclosure with an off-centred partition. Governing equations in the form of vorticity–stream function formulation are solved using the polynomial differential quadrature (PDQ) method. Numerical results are obtained for various values of the partition location, Rayleigh, Prandtl and Hartmann numbers. The results indicate that magnetic field significantly suppresses flow, and thus heat transfer, especially for high Rayleigh number values. The results also show that the x-directional magnetic field is more effective in damping convection than the y-directional magnetic field, and the average heat transfer rate decreases with an increase in the distance of the partition from the hot wall. The average heat transfer rate decreases up to 80% if the partition is placed at the midpoint and an x-directional magnetic field is applied. The results also show that flow and heat transfer have little dependence on the Prandtl number.     

Numerical simulation of the continuous biomagnetic separation in a two-dimensional channel

Numerical simulation of magnetically mediated separation of labeled biospecies from a native fluid flowing through a two dimensional channel is presented. The transport of the magnetic biospecies is modeled by coupling the fluid flow with an Eulerian advection–convection concentration equation. A magnetic field is imposed in the separator that causes an accumulation of the magnetic labeled species in the vicinity of the higher magnetic field region. The accumulation of the magnetically labeled species in the highest magnetic field zone presents a scheme for the collection of these species from the heterogeneous samples under the simulation conditions. The axial magnetic forces, as resulted from a dipole-like magnetic field, is found to play a major role in the vortex formation and it complement the downward vertical force in confining the particles to a small region near the point with the highest magnetic strength. The interplay between the particle transfer mediated by magnetophoresis forces and that by normal diffusion is analyzed for high and low inertia flows. The present study predicts that the generated viscous shear stress levels in the interior region of the channel provide a safe transport mechanism for biological cells from the solution.     

带圆孔无限大受拉板的变形扰动磁场

利用磁弹性耦合问题的线性化理论,采用分离变量方法对带圆孔的无限大板在受拉应力和横向磁场共同作用下的变形扰动磁场进行了求解,得到了变形引致的扰动磁场的解析解,并对其强度量级和分布情况进行了讨论.结果表明,变形扰动磁场场强与外力成正比;与无变形磁场强度相比,变形扰动磁场小3个量级,但波峰波谷数目增加,且在圆孔边界径向扰动磁场强度迅速衰减.     

Stress State of a Transversely Isotropic Ferromagnetic with an Elliptic Crack in a Homogeneous Magnetic Field

The magnetoelastic stress-strain problem for a transversely isotropic ferromagnetic body with an elliptical crack in the isotropy plane is solved explicitly. The body is in an external magnetic field perpendicular to the isotropy plane. The magnetic field induces elastic strains and an internal magnetic field in the body. The main characteristics of stress-strain state and induced magnetic field are determined and their features in the neighborhood of the crack are analyzed. Formulas for the stress intensity factors of the mechanical and magnetic fields near the crack tip are presented__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 1, pp. 48–59, January 2005.     

Biomagnetic fluid flow in a 3D rectangular duct

The laminar, incompressible, three‐dimensional, fully developed viscous flow of a non‐conducting biomagnetic fluid in a impermeable rectangular duct is numerically studied in the presence of an applied magnetic field. It is assumed that the magnetic field strength is sufficiently strong to saturate the biofluid and the magnetization is given as a function of the magnetic field intensity. The system of the partial differential equations, resulting after the introduction of appropriate non‐dimensional variables, is solved applying an efficient numerical technique based on a pressure‐linked pseudotransient method on a common grid. Results concerning the existence and the uniqueness of the solution, are also given. The obtained results, for different values for the parameters entering into the problem under consideration, show that the flow is appreciably influenced by the presence of the magnetic field. Copyright © 2004 John Wiley & Sons, Ltd.     

Influence of a homogeneous axial magnetic field on Taylor–Couette flow of ferrofluids with low particle–particle interaction

Experimental results concerning the stability of Couette flow of ferrofluids under magnetic field influence are presented. The fluid cell of the Taylor–Couette system is subject to a homogeneous axial magnetic field and the axial flow profiles are measured by ultrasound Doppler velocimetry. It has been found that an axial magnetic field stabilizes the Couette flow. This effect decreases with a rotating outer cylinder. Moreover, it could be observed that lower axial wave numbers are more stable at a higher axial magnetic field strength. Since the used ferrofluid shows a negligible particle–particle interaction, the observed effects are considered to be solely based on the hindrance of free particle rotation.     

UDV measurements of single bubble rising in a liquid metal Galinstan with a transverse magnetic field

Liquid metal is an important type of energy transport carrier in nuclear reactors, such as in accelerator-driven sub-critical systems, fusion reactors and spallation neutron source devices. It is necessary to conduct research for bubbles rising in a liquid metal under different magnetic field intensities. The Perspex container is positioned concentrically inside a transverse magnetic field, which provides a homogeneous DC longitudinal magnetic field that passes through the fluid district. The coils are supplied with maximum field strength of 1.97 T. The equivalent diameter of the bubble is 3.1–5.6 mm. The Ultrasonic Doppler Velocimetry (UDV) method is used to evaluate the internal flow velocity of opaque liquid metals. Research shows that the influence of the Lorenz force on the bubble ascension velocity is not simply positive or negative. The magnetic field inhibits the ascension velocity of small bubbles with diameters of 3.1 mm and 3.4 mm. The terminal velocity for large bubbles with diameters of 4.57 mm, 5.15 mm and 5.6 mm is higher under a weak magnetic field than without a magnetic field. The positive effect happens under strong magnetic intensity. The target is to obtain the hydro-dynamical relationships between the terminal velocity, drag coefficient, the Eötvös number, Reynolds number, and Stuart number in a strong magnetic field using a multiple regression method to reveal that the mechanism of the induced current's restraining influence determines the ascension velocity of the bubble in viscous electric liquids with a strong magnetic field.     

Magneto elastic stress subjected to uniform magnetic field over a thin infinite plate containing an elliptical hole with an edge crack

Two dimensional solutions of the magnetic field and magneto elastic stress are presented for a magnetic material of a thin infinite plate containing an elliptical hole with an edge crack subjected to uniform magnetic field. Using a rational mapping function, each solution is obtained as a closed form. The linear constitutive equation is used for these analyses. According to the electro-magneto theory, only Maxwell stress is caused as a body force in a plate. In the present paper, it raises a plane stress state for a thin plate, the deformation of the plate thickness and the shear deflection. Therefore the magneto elastic stress is analyzed using Maxwell stress. No further assumption of the plane stress state that the plate is thin is made for the stress analysis, though Maxwell stress components are expressed by nonlinear terms. The rigorous boundary condition expressed by Maxwell stress components is completely satisfied without any linear assumptions on the boundary. First, magnetic field and stress analyses for soft ferromagnetic material are carried out and then those analyses for paramagnetic and diamagnetic materials are carried out. It is stated that those plane stress components are expressed by the same expressions for those materials and the difference is only the magnitude of the permeability, though the magnetic fields H_x, H_y are different each other in the plates. If the analysis of magnetic field of paramagnetic material is easier than that of soft ferromagnetic material, the stress analysis may be carried out using the magnetic field for paramagnetic material to analyze the stress field, and the results may be applied for a soft ferromagnetic material. It is stated that the stress state for the magnetic field H_x, H_y is the same as the pure shear stress state. Solutions of the magneto elastic stress are nonlinear for the direction of uniform magnetic field. Stresses in the direction of the plate thickness and shear deflection are caused and the solutions are also obtained. Figures of the magnetic field and stress distribution are shown. Stress intensity factors are also derived and investigated for the crack length.     

The effect of a magnetic field on the rheodynamic behavior of ferromagnetic suspensions

In this work a simplified analytical model and the results of an experimental investigation of the influence of an external magnetic field on the rheological characteristics of a suspension of iron particles in silicon oil is presented. The particles of iron were approximately of a circular shape, from 3 to 5 μm, with a maximum concentration of 10¹⁰ particles/cm³. The viscosity of the carrying fluid varied from 80 to 240 cP.The experimental channel was located in a closed circuit of forced circulation of the ferromagnetic suspension. The entire length of 750 mm was placed in an area of a homogeneous magnetic field, with the velocity vector of the suspension being perpendicular to the direction of the magnetic field. The strength of the magnetic field could be changed continually from 0 to 9000 G.The results obtained are shown in the form of parametrical dependencies of the rheological characteristics of the ferromagnetic suspension. With that, the concentration of the solid phase of the suspension is parametrically changed, along with the strength of the external magnetic field and the viscosity of the carrying fluid.In the range of parameters studied, the external magnetic field leads to a Bingham character of behavior of the ferromagnetic suspension.     

Interaction of quasiuniform magnetic field with ensemble of MHD oscillations

It is shown that inhomogeneous MHD turbulence in a cold plasma manifests itself as an inhomo-geneous diamagnet. An equation describing the evolution of the regular component of the magnetic field is derived and a formula obtained whereby the coefficient of turbulent magnetic field diffusion can be estimated. Estimates are made which indicate that this is an efficient mechanism for the decay of the magnetic field of a sunspot.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 16–22, March–April, 1976.In conclusion, the author wishes to thank S. I. Vainshtein for suggesting the problem and for his constant interest in the work.