Shape of the free surface of a magnetic fluid containing a cylindrical concentrator of the magnetic field

The shape of the surface of a magnetic fluid containing a cylindrical body made of a well-magnetizable material (magnetic field concentrator) in a uniform applied magnetic field is studied experimentally and theoretically. Various static shapes of the surface are calculated numerically taking into account the gravity forces, the surface tension, and the dependence of the magnetic fluid magnetization on the magnetic field strength. It is found that there exists several equilibrium shapes of the magnetic fluid surface. Abrupt changes in the magnetic fluid surface and its hysteresis are predicted theoretically and observed experimentally. The theoretical and experimental results are compared.     

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.     

Locally nonuniform cooling in magnetic fluid quenching

The process of quenching cylindrical steel specimens in a magnetic fluid in the presence of a magnetic field is investigated. It is shown that depending on the strength of the magnetic field and its orientation with respect to the surface of the cylinder, local vapor formations that result in nonuniform cooling may appear on the surface and that the boiling of the fluid on the surface may take place in different regimes. The processes of formation of local vapor films were experimentally modeled by observing the shape of the surface of the magnetic fluid surrounding a cylinder placed between the poles of an electromagnet. An equation describing the shape of the free surface of the magnetic fluid and the evolution of the air pockets with variation of the volume of magnetic fluid and the strength of the magnetic field is derived. The surface shape of the magnetic fluid calculated from the theory proposed is shown to be in good agreement with the experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 3–11, March–April, 1989.     

Instability of the magnetic fluid shape in the field of a line conductor with current

The static shape of the surface of a finite magnetic fluid volume between horizontal plates is investigated theoretically. The nonuniform magnetic field is generated by a horizontal line conductor with current, which is placed above the upper plate. The variational problem of minimum energy relative to plane surface perturbations is considered for a simply connected magnetic fluid volume. The problem is solved for arbitrary magnetic fields in the noninductive approximation with account for the gravity force and surface tension. Unstable solutions are found. The possibility of stepwise behavior in response to quasi-static changes of the current in the conductor is investigated for the surface shape of a finite magnetic fluid volume.     

Experiments and mechanism analysis of pool boiling heat transfer enhancement with water-based magnetic fluid

A pool boiling heat transfer comparison among water-based magnetic fluids in the absence and presence of a magnetic field with its carrier liquid water was made. The experimental results show that the boiling heat transfer of magnetic fluid increased much in the absence of a magnetic field, and the applied magnetic field made the boiling heat transfer of magnetic fluid enhance further. The effect of a magnetic field on bubbles was analyzed. It was clarified that the nonuniform magnetic field changed the bubble departure diameter and shape during boiling.     

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.     

Experiments on the magnetic damping of an inductively stirred liquid metal flow

This work is concerned with the stabilisation of both bulk liquid metal flow and free surface shape in inductively heated melts. Static magnetic fields in different orientation were used to damp the fluctuations generated by the alternating magnetic field of an induction heater. This superposition of a driving alternating with a braking static magnetic field was investigated experimentally in a low temperature isothermal model utilising a rectangular fluid volume in an induction-furnace-like setup fed by a current of intermediate frequency. Local velocity measurements in the liquid metal showed different damping characteristics for static fields aligned either normal or parallel to the melt surface.     

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.     

Analysis of relationships between residual magnetic field and residual stress

The impact of stress on changes in magnetisation is one of the most complex issues of magnetism. Magnetic methods make use of the impact of stress on permeability, hysteresis and magnetic Barkhausen noise, which are examined with fields with a high strength and a small frequency. The paper presents an analysis of the impact of residual stress resulting from inhomogeneous plastic deformations in the notch area of the examined samples on the changes in the strength of the residual magnetic field (RMF). The RMF on the surface of the component is the superposition of the simultaneous effect of the shape, the anisotropic magnetic properties of the material, as well as of the values of the components of a weak external magnetic field (most commonly—the magnetic field of the Earth). Distributions of the RMF components were measured on the surface of samples with a various degree of plastic strain. The finite element method was used to model residual stress in the samples. The impact of residual stress on changes in the residual magnetic field was shown. A qualitative correlation was found between places with residual stress and areas with increased values of the gradients of the RMF components. Further research is now in progress in order to develop the quantitative relationships.     

Three-dimensional modelling of GeSi growth in presence of axial and rotating magnetic fields

A three-dimensional numerical simulation has been performed to study the growth of Ge_0.98Si_0.02 by the Traveling Solvent Method. We attempted to suppress the buoyancy convection, in the Ge_0.98Si_0.02 melt zone, by applying axial and rotating magnetic fields. The effects of the applied magnetic field intensity, on the transport structures in the melt (flow and concentration fields, heat and mass transfer), have been investigated in detail. The steady-state full Navier–Stokes equations, as well as energy, mass species transport and continuity equations are numerically solved using the finite element method. By applying an axial magnetic field of various intensities (2, 10, and 22 mT), we found that as the axial magnetic field increases, the silicon distribution nearby the growth interface becomes more uniform. In the case of a rotating magnetic field, with different applied rotational speeds (2, 7 and 10 rpm), we found that such kind of magnetic field has a marked effect on the silicon concentration, which changes its shape from a convex one to a nearly flat shape as the magnetic field intensity increases. An alternative method to reduce or suppress buoyancy convection, in the melt zone, is the growing of the sample in a microgravity environment, with a gravity level of at least 10^?4 the earth normal gravity level; in this case the results revealed smooth and almost perfect straight concentration contours, due to the buoyancy convection weakness.     

Two-layer flow of magnetic fluids

The plane two-layer flow of viscous incompressible fluids with differentmagnetic properties between two horizontal rigid planes in a nonuniform traveling magnetic field is investigated. An arbitrary nonuniform periodic traveling magnetic field generates wavelike changes in the interface between the media and fluid flows with nonzero flow rates. From the given magnetic field the interface shape and the velocities, pressures and mean flow rates of the fluids are calculated. The cases of a cosine magnetic force and of the magnetic field created by ferromagnetic cylinders moving in a uniform magnetic field are considered. The effect of various parameters on the mean flow rates of the fluids is investigated.     

An approximate method for magnetic boundary layers

An approximate method is derived for obtaining the flow in magnetic boundary layers with aligned fields which were discussed by Stewartson (1965). On comparing with exact, computed solutions the method is found to be accurate when applied to forward stagnation point flow for the whole, allowable range of the magnetic field strength parameter. It is then applied to the layer that develops from the forward stagnation point on a circular cylinder placed in a uniform stream and values obtained for the point at which it separates from the surface.     

Numerical simulation and experimental verification of silicone oil flow over magnetic fluid under applied magnetic field

Two-layer flow of magnetic fluid and non-magnetic silicone oil was simulated numerically. The continuity equation, momentum equations, kinematic equation, and magnetic potential equation were solved in two-dimensional Cartesian coordinate. PLIC （piecewise linear integration calculation） VOF （volume of fluid） scheme was employed to track the free interface. Surface tension was treated via a continuous surface force （CSF） model that ensures robustness and accuracy. The influences of applied magnetic field, inlet velocity profile, initial surface disturbance of interface and surface tension were analyzed. The computed interface shapes at different conditions were compared with experimental observation.     

The influence of a magnetic field on the mechanical behavior of a fluid interface

This work focuses on a theoretical investigation of the shape and equilibrium height of a magnetic liquid–liquid interface formed between two vertical flat plates in response to vertical magnetic fields. The formulation is based on an extension of the so called Young–Laplace equation for an incompressible magnetic fluid forming a two-dimensional free interface. A first order dependence of the fluid susceptibility with respect to the magnetic field is considered. The formulation results in a hydrodynamic-magnetic coupled problem governed by a nonlinear second order differential equation that describes the liquid–liquid meniscus shape. According to this formulation, five relevant physical parameters are revealed in this fluid static problem. The standard gravitational Bond number, the contact angle and three new parameters related to magnetic effects in the present study: the magnetic Bond number, the magnetic susceptibility and its derivative with respect to the field. The nonlinear governing equation is integrated numerically using a fourth order Runge-Kutta method with a Newton–Raphson scheme, in order to accelerate the convergence of the solution. The influence of the relevant parameters on the rise and shape of the liquid–liquid interface is examined. The interface shape response in the presence of a magnetic field varying with characteristic wavenumbers is also explored. The numerical results are compared with asymptotic predictions also derived here for small values of the magnetic Bond number and constant susceptibility. A very good agreement is observed. In addition, all the parameters are varied in order to understand how the scales influence the meniscus shape. Finally, we discuss how to control the shape of the meniscus by applying a magnetic field.     

Effect of magnetic field on 3D flow and heat transfer during solidification from a melt

We present the effect of a magnetic field on three-dimensional fluid flow and heat transfer during solidification from a melt in a cubic enclosure. The walls of the enclosure are considered perfectly electrically conducting and the magnetic field is applied separately in three directions. The finite-volume method with enthalpy formulation is used to solve the mathematical model in the solid and liquid phases. The results obtained by our computer code are compared with the numerical and experimental data found in the literature. For Gr = 5 × 10⁵ and Ha = 0, 25, 50, 75, and 100 (where Gr and Ha are the Grashof and Hartmann numbers, respectively), the effects of magnetic field on flow and thermal fields, and on solid/liquid interface shape are presented and discussed. The interface is localized with and without magnetic field. The results show a strong dependence between the interface shape and the intensity and orientation of magnetic field. When the magnetic field is applied along the X-direction, the magnetic stability diagrams (V_max–Ha) and (Nu_avg–Ha) show the strongest stabilization of the flow field and heat transfer.     

Deformation of an ellipsoidal ferrogel sample in a uniform magnetic field

The elongation of a ferroelastic material sample (whose initial shape is a sphere or an ellipsoid of revolution) under the action of an external magnetic field is studied in an in approximation of small strains. For a sphere, there is a classical estimate obtained under the assumption that elongating in the direction of the field, it becomes a spheroid and the stress and strain fields remain uniform. In the present calculation, it is assumed that the body is an ellipsoid (a sphere in a particular case) only in the absence of an external field; the shape of the sample in the presence of a field is not specified in advance but is found from the condition of balance of surface forces (elastic and magnetic). For the spherical case, the problem is solved exactly: it is shown, that the contour of the deformed body is described by a third-order algebraic equation. The case where the initial configuration is an ellipsoid of revolution is studied numerically. It is shown that in all versions, the refined solution leads to an appreciable increase in the elongation of the sample compared to the classical estimate. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 3, pp. 153–164, May–June, 2005.     

Determination of a magnetic field with rotational symmetry about a given line of magnetic force

In certain technical applications when a magnetic field with rotational symmetry has to be calculated, it is often a principal requirement that a given line should be a magnetic line of force (or more accurately, that a given surface of rotation should coincide with a surface of magnetic force).An exact particular solution of the problem is found in the case when the given line of force is straight. This solution is subsequently generalized to the case of an arbitrary smooth line, approximating it by a broken line. A method is also proposed for producing and calculating a magnetic field satisfying the above conditions.The solution of this problem may be used in questions of magneto-hydrodynamics and plasmadynamics as the first approximation for the magnetic field in the case of small magnetic Reynolds numbers, when it is required that a certain line of fluid flow should coincide with a magnetic line of force.The authors would like to mention that it was due to the constant interest of E. S. Kuznetsov and his valuable advice that the present paper was completed.     

Interaction of a magnetic liquid with a conductor containing current and a permanent magnet

The present study investigates the force exerted by a magnetic liquid on a conductor with a current or a permanent magnet located near its infinite free surface. It is shown that this force is equal to the weight of the liquid raised by the magnetic field above the original horizontal level. The force is found for the cases when the liquid is weakly magnetic and when the shape of its surface differs little from plane. Consideration is given to the equilibrium of a magnet suspended on a small spring near the surface of the magnetic liquid. The critical height is found at which the magnet ceases to be held by the spring and is torn off into the liquid. The experimentally obtained values of the magnitude of of the force acting on the magnet and the height of collapse of the magnet into the liquid are in good agreement with the theoretical results.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 176–181, March–April, 1988.The authors are grateful to V. V. Gogosov for valuable discussion of the study.     

Influence of uniaxial plastic deformation on surface magnetic field in steel

Under geomagnetic field, surface magnetization measurements were made on 1045 and a3 steels samples uniaxially deformed to differing magnitudes of plastic strain, to study the dependence of surface magnetic field and its distribution on plastic deformation. The results indicated initial increase in surface magnetic field with increasing plastic strain followed by a decrease at higher plastic deformation. At still higher plastic deformation, the surface magnetic field was found to be almost independent of plastic strain. In the middle part of the sample, the uneven plastic deformation interrupted the linear distribution of surface magnetic field. The behavior of surface magnetic field and its distribution with plastic deformation were largely controlled by the different mechanisms of interaction of domain walls with isolated dislocation, dislocation tangles and dislocation cellular structures.     

Changes in the natural frequency of a ferromagnetic rod in a magnetic field due to magnetoelastic interaction

Based on the magnetoelastic generalized variational principle and Hamilton＇s principle, a dynamic theoretical model characterizing the magnetoelastic interaction of a soft ferromagnetic medium in an applied magnetic field is developed in this paper. From the variational manipulation of magnetic scale potential and elastic displacement, all the fundamental equations for the magnetic field and mechanical deformation, as well as the magnetic body force and magnetic traction for describing magnetoelastic interaction are derived. The theoretical model is applied to a ferromagnetic rod vibrating in an applied magnetic field using a perturbation technique and the Galerkin method. The results show that the magnetic field will change the natural frequencies of the ferromagnetic rod by causing a decrease with the bending motion along the applied magnetic field where the magnetoelastic buckling will take place, and by causing an increase when the bending motion of the rod is perpendicular to the field. The prediction by the mode presented in this paper qualitatively agrees with the natural frequency changes of the ferromagnetic rod observed in the experiment.