Levitation of Magnets and Paramagnetic Bodies in Vessels Filled with Magnetic Fluid

Formulas are obtained for the forces and moments acting on a spherical body made of a paramagnetic material in an uniform applied magnetic field and a magnet in a spherical vessel filled with magnetic fluid. An approximate formula is found for the force acting on bodies in ellipsoidal and cylindrical vessels or in a plane channel with a magnetic fluid in an uniform magnetic field. An analogy between the forces acting on a magnet and a paramagnetic body is demonstrated. The possibility of levitation of magnets and paramagnetic bodies in a vessel with a magnetic fluid is investigated.     

Second order effects in fluidmagnetic buoyancy

A non-magnetic solid object placed in a magnetically responsive fluid in the presence of a magnetic field gradient experiences a net buoyancy force of magnetic origin. A procedure is developed to account for the effects of magnetic field distortion due to the difference of magnetic permeability between the fluid and the solid and non-zero dependence of fluid magnetization on magnetic field strength. This procedure gives an expression for the magnetic buoyancy force correct to first order in the dimensionless magnetization of the fluid and in the dimensionless variation of fluid magnetization across the object. Calculations are performed for a sphere, cylinder and plate in an applied magnetic field where the field and field gradient are either aligned or at right angles in order to give an indication of the range of force variation due to a change of shape and due to a change of applied field geometry. Variations on the order of 10% can be expected in typical applications.     

磁性流体密封磁场的解耦计算

分析了磁性流体密封中的磁场与力场的耦合问题,采用边界逼近的迭代方法准确计算了磁场分布,进而求出了密封压差,分析了解耦计算与线性计算的差别.结果表明,随着磁性流体磁化强度的提高,解耦计算与线性计算的差别增大.     

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.     

基于永磁环阵列的磁流体支撑及润滑特性研究

在本文中初步探讨了一种永磁环阵列的磁流体支撑及润滑特性,以期获得一种对固定目标区域精准支撑与润滑的方法,并实现低摩擦. 以3D打印树脂材料为基底,在其表面嵌入正方形点阵排布的永磁环阵列,分别在各磁体表面注入特定体积的磁流体,使其在各永磁环表面形成封闭的液体结构. 采用自行设计的支撑力测试系统及往复式摩擦磨损试验机分别对该液体结构支撑及润滑性能进行测试. 结果表明:在磁场作用下的磁流体,除自身磁化和内聚产生液体支撑力外,被磁流体密封于其液体结构内的气体将进一步提升支撑能力;而对于该磁环阵列结构而言,被吸附于其表面的磁流体支撑能力随着磁铁间距的增加而减小,并逐渐趋于稳定,同时磁极排布方式对支撑力也会有所影响;当磁流体密封结构的支撑能力大于外载荷时,即摩擦对偶完全被磁流体支撑,此时可获得0.005的低摩擦系数. 可见该磁流体液环密封结构所形成的液-气混合支撑力显著高于单一液体支撑,而磁环阵列结构可进一步提升总体支撑能力,当该支撑力高于负载时可避免摩擦副间的直接接触,在静止或低速状态下实现低摩擦. 该研究结果对于解决精密低速滑动机构中常出现的“冷焊”及“爬行”现象具有一定应用价值.      

Experimental and numerical analysis of thermo-magnetic convection in a vertical annular enclosure

In the present paper an experimental and numerical analysis of a thermo-magnetic convective flow of paramagnetic fluid in an annular enclosure with a round rod core and a cylindrical outer wall is presented. It is complemented by an experimental analysis of natural convection depending on the inclination angle to show the stability of the present configuration. Convection in an annulus between two vertical co-axial cylinders resulting from gravitational and magnetic environments has been investigated. A strong magnetic field can be an alternative to heat transfer enhancement. The effect of the magnetic field on the convection of the paramagnetic fluid in the annular vessel in various positions was compared. The numerical analysis was done based on the continuity, momentum and energy equations. A term related to the magnetic buoyancy force was added to the momentum equation. The distributions of Nusselt number present minima in two positions of the enclosure, which depends on the reciprocal relationship between the gravitational and magnetising forces.     

Viscous lifting of a conducting fluid in the presence of a magnetic field

Summary This paper describes the effect of a magnetic field upon the viscous lifting of a conducting fluid for two types of lifting surfaces; conducting and non-conducting. It is shown that the magnetic field produces very small effects on the film thickness and mass flow rate for the case of the dielectric plate. For the conducting plate, the effects are more pronounced and increase with larger values of the ratio of plate conductivity to fluid conductivity. The analysis employed here is simplified to the extent that the effects of surface tension are not included.     

The experimental study on flat plate heat pipe of magnetic working fluid

An effective thermal spreader can achieve uniform heat flux distribution and thus enhance heat dissipation of heat sinks. Flat plate heat pipe is one of the highly effective thermal spreaders. Magnetic fluid is liquid and can be moved by the force of magnetic field. Therefore, the magnetic fluid is suitable to be used as the working fluid of flat plate heat pipes which have a very small gap between evaporation and condensation surfaces. We prepared a disk-shaped wickless flat plate heat pipe, and the distance between evaporation and condensation surfaces is only 1 mm. From experimental study, the effect of heat flux and working fluid ratio on the performance of flat plate heat pipe is presented. Also we compared the experimental results between the performance of water and magnetic fluid as working fluids.     

Hydromagnetic flow near an accelerated plate in the presence of a magnetic field

Summary Hydromagnetic flow of a viscous incompressible fluid due to uniformly accelerated motion of an infinite flat plate in the presence of a magnetic field fixed relative to the plate, is discussed. It is assumed that the induced magnetic field is negligible compared to the imposed magnetic field. It is observed under these conditions that the velocity at any point and at any instant decreases when the strength of the magnetic field is increased.     

Combined heat and mass transfer by mixed convection MHD flow along a porous plate with chemical reaction in presence of heat source

An exact and a numerical solutions to the problem of a steady mixed convective MHD flow of an incompressible viscous electrically conducting fluid past an infinite vertical porous plate with combined heat and mass transfer are presented.A uniform magnetic field is assumed to be applied transversely to the direction of the flow with the consideration of the induced magnetic field with viscous and magnetic dissipations of energy.The porous plate is subjected to a constant suction velocity as well as a uniform mixed stream velocity.The governing equations are solved by the perturbation technique and a numerical method.The analytical expressions for the velocity field,the temperature field,the induced magnetic field,the skin-friction,and the rate of heat transfer at the plate are obtained.The numerical results are demonstrated graphically for various values of the parameters involved in the problem.The effects of the Hartmann number,the chemical reaction parameter,the magnetic Prandtl number,and the other parameters involved in the velocity field,the temperature field,the concentration field,and the induced magnetic field from the plate to the fluid are discussed.An increase in the heat source/sink or the Eckert number is found to strongly enhance the fluid velocity values.The induced magnetic field along the x-direction increases with the increase in the Hartmann number,the magnetic Prandtl number,the heat source/sink,and the viscous dissipation.It is found that the flow velocity,the fluid temperature,and the induced magnetic field decrease with the increase in the destructive chemical reaction.Applications of the study arise in the thermal plasma reactor modelling,the electromagnetic induction,the magnetohydrodynamic transport phenomena in chromatographic systems,and the magnetic field control of materials processing.     

磁性靶向药物递送中铁磁流体的动力学建模

Among the proposed techniques for delivering drugs to specific locations within human body, magnetic drug targeting prevails due to its non-invasive character and its high targeting efficiency. Magnetic targeting drug delivery is a method of carrying drug-loaded magnetic nanoparticles to a target tissue target under the applied magnetic field. This method increases the drug concentration in the target while reducing the adverse side-effects. Although there have been some theoretical analyses for magnetic drug targeting, very few researchers have addressed the hydrodynamic models of magnetic fluids in the blood vessel. A mathematical model is presented to describe the hydrodynamics of ferrofiuids as drug carriers flowing in a blood vessel under the applied magnetic field. In this model, magnetic force and asymmetrical force are added, and an angular momentum equation of magnetic nanoparticles in the applied magnetic field is modeled. Engineering approximations are achieved by retaining the physically most significant items in the model due to the mathematical complexity of the motion equations. Numerical simulations are performed to obtain better insight into the theoretical model with computational fluid dynamics. Simulation results demonstrate the important parameters leading to adequate drug delivery to the target site depending on the magnetic field intensity, which coincident with those of animal experiments. Results of the analysis provide important information and suggest strategies for improving delivery in clinical application.     

Viscous lifting and drainage of a conducting fluid in the presence of a transverse magnetic field

A theoretical investigation of the effects of a transverse magnetic field on the combined problem of viscous lifting and drainage of a conducting fluid on a plate is presented. The effects of inertia and transverse magnetic field on the liquid film thickness is studied for two cases namely a plate withdrawn with a constant velocity and one withdrawn with a constant acceleration. The expressions for the flow rate and the free surface profiles are obtained for the above two cases. It is found that the free surface profiles are convex in nature as in the non-magnetic case thus showing that the inertia does not effect the general pattern of flow, and the effect of the magnetic field is to retard both the lifting and drainage of the fluid.     

Non-linear vibration analysis of an elastic plate subjected to heavy fluid loading in magnetic field

In the present study, the non-linear vibration of an elastic plate subjected to heavy fluid loading in an inclined magnetic field is investigated. The structural non-linearity, fluid non-linearity, and the effects of magnetic field are all incorporated in the formulations to derive the governing equation of the plate. The method of multiple scales is adopted to determine the eigenvalues and mode shapes of the linear vibration, and then the amplitude of the non-linear vibration response of the plate is calculated. Based on the assumptions of ordering and formulations of multiple scales, it can be concluded that the linear dynamic behavior of the plate under heavy fluid loading but weak near-resonant loading is influenced by the effects of the fluid loading, linear structural rigidity and linear magnetic field, furthermore, the non-linear dynamic behavior of the plate under heavy fluid loading but weak near-resonant loading is dominated and controlled by the effects of the fluid loading, non-linear structural rigidity and non-linear magnetic field. Both thick and thin plates are investigated; the contributions due to the structural non-linearity and acoustic linear radiation damping are of the same order for a rather thick plate. For a thin plate, the structural non-linearity completely controls the behavior of the plate, which implies that in this case the effect of fluid loading is considerably negligible. In general, it can be concluded that both the effects of magnetic field and structural non-linearity play important roles only on the first few modes of the plate.     

Flow of a Weakly Conducting Fluid in a Channel Filled with a Porous Medium

We investigate the fully developed flow in a fluid-saturated porous medium channel with an electrically conducting fluid under the action of a parallel Lorentz force. The Lorentz force varies exponentially in the vertical direction due to low fluid electrical conductivity and the special arrangement of the magnetic and electric fields at the lower plate. Exact analytical solutions are derived for fluid velocity and the results are presented in figures. All these flows are new and are presented for the first time in the literature.     

Heat and Mass Transfer in MHD Micropolar Flow Over a Vertical Moving Porous Plate in a Porous Medium

An analysis is presented for the problem of free convection with mass transfer flow for a micropolar fluid via a porous medium bounded by a semi-infinite vertical porous plate in the presence of a transverse magnetic field. The plate moves with constant velocity in the longitudinal direction, and the free stream velocity follows an exponentially small perturbation law. A uniform magnetic field acts perpendicularly to the porous surface in which absorbs the micropolar fluid with a suction velocity varying with time. Numerical results of velocity distribution of micropolar fluids are compared with the corresponding flow problems for a Newtonian fluid. Also, the results of the skin-friction coefficient, the couple stress coefficient, the rate of the heat and mass transfers at the wall are prepared with various values of fluid properties and flow conditions.     

Force acting on a body in a nonuniformly heated magnetizable fluid

The force acting on a spherical particle in a nonuniformly heated magnetizable fluid is calculated in the case in which the permeability of the particle material depends arbitrarily on temperature and the strength of the magnetic field, and the permeability of the fluid on temperature. In calculating the force the difference between the thermal conductivities of the particle material and the fluid and, as distinct from [6], the distortion of the applied magnetic field due to the presence of a temperature gradient are taken into account. Accordingly, the expression for the force differs from that obtained in [6]. It is shown that the expression obtained for the force is correct up to terms of the order of a certain power of a small parameter — the ratio of the particle size to the characteristic interval of variation of the parameters (temperature, strength of magnetic field, etc.). A condition determining the value of this power is derived.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 76–83, March–April, 1989.     

A numerical study of flows driven by a rotating magnetic field in a square container

The magnetically induced fluid flow in a square container is investigated by means of numerical simulations. Low frequency/ low induction conditions are assumed. The effect of the rotating magnetic field gives rise to a time-independent magnetic body force, computed via the electrical potential equation and Ohm's law and a time-dependent part that is neglected due to the low-interaction parameter. The magnetic body force calculation is verified successfully by comparison with the exact solution. The behavior of the fluid flow in the square container reveals similar features to the flow in the cylindrical container, for instance, in the dependence on the intensities of the magnetic field. However, we did find differences in the velocity field distribution. Particularly, in the finite as well as infinite geometry, the velocity field is influenced by the corner of the container and remains non-axisymmetric in a wide range of Taylor numbers.     

Effects of radiation in an optically thin gray gas flowing past a vertical infinite plate in the presence of a magnetic field

This paper studies the two dimensional flow of an electrically conducting fluid which is an optically thin gray gas past a stationary vertical infinite plate in the presence of radiation. It is assumed that the temperature of the plate and the suction at the plate are constant. The presence of the induced magnetic field is also taken into account. Numerical solutions for the velocity and the induced magnetic field are derived and the effects of the radiation parameter are discussed.     

Natural convection in unsteady MHD couette flow

 The combined effect of natural convection and uniform transverse magnetic field on the couette flow of an electrically conducting fluid between two parallel plates for impulsive motion of one of the plates in discussed. Under the assumption of negligible induced magnetic field and applied magnetic field being fixed relative to the fluid or plate, the governing equations have been solved exactly, and the expressions for velocity and temperature field have been presented for two different cases. A comparative study is made between the velocity field for magnetic field fixed with respect to plate and magnetic field fixed with respect to fluid. Received on 12 July 1999     

Stationary cylindrical vortex in a viscous electrically conducting fluid

An exact solution of the magnetohydrodynamic equations is constructed which describes steady vortex flow in a stationary cylinder on the axis of which a conductor carrying a known current is located. The solution is obtained under the assumption that the fluid is viscous and has finite electrical conductivity and that the magnetic field has only the axial and azimuthal components in a cylindrical coordinate system. It is found that the action of the Lorentz force is compensated by changing the pressure. Fluid flow occurs from the periphery to the axis of the cylinder under a pressure gradient, with flow rotation and swirling. The fluid flow causes a concentration of the magnetic lines near the axis of the cylinder, providing an exponential decrease in the magnetic field strength with distance from the axis. This flow can be considered as a model of a local increase in the magnetic field strength due to the transfer of its force lines by the flow of the electrically conducting fluid.