MHD flow of a second grade fluid in an orthogonal rheometer

The magnetohydrodynamics (MHD) flow of a conducting, homogeneous incompressible Rivlin-Ericksen fluid of second grade contained between two infinite, parallel, insulated disks rotating with the same angular velocity about two noncoincident axes, under the application of a uniform transverse magnetic field, is investigated. This model represents the MHD flow of the fluid in the instrument called an orthogonal rheometer, except for the fact that in the rheometer the rotating plates are necessarily finite. An exact solution of the governing equations of motion is presented. The force components in the x and y directions on the disks are calculated. The effects of magnetic field and the viscoelastic parameter on the forces are discussed in detail.     

Electro-magneto-thermo-elastic plane waves in rotating media with thermal relaxation

A study is made of the propagation of plane electro-magneto-thermo-elastic harmonic waves in an unbounded isotropic conducting medium permeated by a primary uniform magnetic field when the entire medium rotates with a uniform angular velocity. The thermal relaxation time of heat conduction, the electric displacement current, the coupling between heat flow density and current density and that between the temperature gradient and the electric current are included in the analysis. A more general dispersion relation is obtained to determine the effects of rotation, relaxation time and the external magnetic field on the phase velocity of the waves. Perturbation techniques are used to study the influence of small magneto-elastic and thermo-elastic couplings on the phase velocity of the waves. Cases of low and high frequencies are also studied to determine the effect of rotation, thermoelastic and magneto-elastic couplings on the waves.     

Angular distribution of rotational hysteresis losses in Fe-3.25%si single crystals with orientations

Measurements have been made of the difference torqueDeltaM(for the same angle φ) acting on a ferromagnetic material during the rotation of the magnetic field through 360° in opposite directions, depending on the angle φ of the magnetic field rotation and on magnetization ratio(I/I_{s}). The dependenceDeltaMon the angle φ is known as the angular distribution of losses. Experiments have been carried out on Fe-3.25%Si single crystals in the form of disks with surfaces parallel to the     

Heat transfer and thermal behaviour of a rotating disk passed by a planar air stream

The aerodynamics of a thin, but finite, free rotating disk in an outer forced flow field with constant mean velocity parallel to the disk plane are investigated numerically. The heat transfer coefficients and their distributions on the isothermal disk surface are calculated for several velocities in case of air. Appropriate correlations are derived for the Nusselt number as function of the involved similarity numbers. The idealised model is faced also with the heat transfer problem of an actual motorbike disk brake. The transient heat conduction within rotating disks are treated analytically using the integral-transform technique. This enables even for heat sources which are very short in space a certain estimation of the azimuthal variations of the temperature field due to the rotation.     

MHD Flow of an Oldroyd-B fluid between eccentric rotating disks

An exact solution is obtained for the magnetohydrodynamics (MHD) flow of a conducting, incompressible Oldroyd-B fluid between two infinite, parallel, insulated disks rotating about non-coincident axes normal to the disks in the presence of a uniform transverse magnetic field. The effects of the Hartmann number M, the Deborah number D, the Reynolds number R and the elastic number on the velocity field and the force are discussed. It is found that the value of the torque exerted by the fluid on one of the disks is zero.     

Electro-magneto-thermo-visco-elastic Plane Waves in Rotating Media with Thermal Relaxation

A study is made of the propagation of plane electro-magneto-thermo-visco-elastic harmonic waves in an unbounded isotropic conducting visco-elastic medium of Kelvin–Voigt type permeated by a primary uniform magnetic field when the entire medium rotates with a uniform angular velocity. The thermal relaxation time of heat conduction, the electric displacement current, the coupling between heat flow density and current density, and that between the temperature gradient and the electric current are included in the analysis. A more general dispersion relation is obtained to determine the effects of rotation, thermal relaxation time, visco-elastic parameters, and the external magnetic field on the phase velocity of the waves. Perturbation techniques are used to study the influence of small magneto-elastic and thermo-elastic couplings on the phase velocity of the waves. Cases of low and high frequencies are also analyzed to determine the effect of rotation, visco-elastic parameters, thermo elastic and magneto-elastic coupling, as well as thermal relaxation time of heat conduction on the waves.     

Effects of Hall currents and Coriolis force on Hartmann flow under general wall conditions

Summary The influence of Hall currents and rotation on a generalized Hartmann flow and heat transfer is investigated. The channel is rotating with a constant angular velocity around an axis perpendicular to the walls in a uniform transverse magnetic field. The walls may have the same thickness, electrical and thermal conductivity as well as Hall parameter or different ones. The flow may be driven either by a pressure gradient or by motion of one of the walls. Exact solutions are derived for the velocity, magnetic field, viscous stress, current density, temperature distribution, yield components, electric current components, mean temperature as well as Nusselt numbers. Representative numerical results are presented in diagrams and effects of different parameters are discussed.     

On the flow between two rotating disks enclosed by a cylinder

Summary The flow field inside a cylindrical container caused by the impulsively started constant co-rotation or counter rotation of the top-bottom endwalls with fixed sidewall is described. After a transient phase from an initial state at rest a steady flow situation is reached. The unsteady axisymmetric Navier-Stokes equations describing the transient flow are expressed in vorticity-stream function form. For large values of Reynolds number (based on angular velocity on the lower endwall) an upwind differencing in the spatial derivatives for the convective terms is used. A fourth-order accurate compact difference scheme is applied to solve the Poisson equation. The results show that the slight co-rotation of the topbottom endwalls induces a breakdown bubble at a critical value of the Reynolds number which is much smaller than the value of the Reynolds number for the onset of vortex breakdown in a flow due to rotation either of the top or bottom end wall. On the other hand, a weak counter-rotation of top-bottom endwalls suppresses the vortex breakdown. The question of whether the similarity solutions are locally useful in describing the flow between finite disks is also addressed.     

Experimental Investigation of Rotating Menisci

In upper stages of spacecrafts, Propellant Management Devices (PMD’s) can be used to position liquid propellant over the outlet in the absence of gravity. Centrifugal forces due to spin of the upper stage can drive the liquid away from the desired location resulting in malfunction of the stage. In this study, a simplified model consisting of two parallel, segmented and unsegmented disks and a central tube assembled at the center of the upper disk is analyzed experimentally during rotation in microgravity. For each drop tower experiment, the angular speed caused by a centrifugal stage in the drop capsule is kept constant. Steady-states for the menisci between the disks are observed for moderate rotation. For larger angular speeds, a stable shape of the free surfaces fail to sustain and the liquid is driven away. Additionally, tests were performed without rotation to quantify two effects: the removal of a metallic cylinder around the model to establish the liquid column and the determination of the the settling time from terrestrial to microgravity conditions.     

Magnetohydrodynamic flow between torsionally oscillating eccentric disks

The unsteady MHD flow of an incompressible, viscous electrically conducting fluid contained between two torsionally oscillating eccentric disks has been investigated. The state of uniform rotation of the central region visualised in the steady flow is seen to be absent in the case of oscillatory flow.     

Magnetic field effects on mixed convection between rotating coaxial disks

This paper deals with a similarity analysis of axisymmetric mixed convection between two horizontal infinite rotating coaxial disks in the presence of a magnetic field. The governing Navier-Stokes equations and energy equation reduce to a set of nonlinear ordinary differential equations using similarity. The resulting set of ordinary differential equations has been solved numerically using a shooting method and is represented graphically. For Reynolds number, Re, up to 500 and buoyancy parameter, B=βΔT, of the range |B| ≤0.05, the flow and heat transfer characteristics with Prandtl numbers 7, 0.7, 0.1 and 0.01 and magnetic field parameters of m=0.5, 1, and 2 are examined. The heat transfer increases with the Prandtl number but decreases with the magnetic parameter. It is established that the rotation of the two disks has a very small effect on the temperature of the fluid and the heat-transfer process. Published in Inzhenerno-Fizicheskii Zhurnal, Vol. 73, No. 5, pp. 1109–1117, September–October, 2000.     

Unsteady hydromagnetic couette flow in a rotating system

Unsteady hydromagnetic flow of an electrically conducting viscous incompressible fluid in a rotating system under the influence of a uniform transverse magnetic field is investigated when one of the plates is set into motion with the time dependent velocity $\text{U(t)}$ in its own plane. Two cases of interest, namely, impulsive start as well as accelerated start of the moving plate are discussed. The asymptotic behaviour of the solution is also analysed for both small and large time to highlight the transient approach to the final steady state and effects of rotation parameter as well as Hartmann number. The shear stresses at the moving plate due to the primary and secondary flows are derived in both cases. It is found that the shear stress components due to the primary flow decrease, whereas that due to the secondary flow increase with the increase in rotation parameter.     

Time dependent rotational flow of a viscous fluid over an infinite porous disk with a magnetic field

Both the semi-similar and self-similar flows due to a viscous fluid rotating with time dependent angular velocity over a porous disk of large radius at rest with or without a magnetic field are investigated. For the self-similar case the resulting equations for the suction and no mass transfer cases are solved numerically by quasilinearization method whereas for the semi-similar case and injection in the self-similar case an implicit finite difference method with Newton's linearization is employed. For rapid deceleration of fluid and for moderate suction in the case of self-similar flow there exists a layer of fluid, close to the disk surface where the sense of rotation is opposite to that of the fluid rotating far away. The velocity profiles in the absence of magnetic field are found to be oscillatory except for suction. For the accelerating freestream, (semi-similar flow) the effect of time is to reduce the amplitude of the oscillations of the velocity components. On the other hand the effect of time for the oscillating case is just the opposite.     

Rotating compressible flow between non torsionally oscillating disks

A viscous compressible gas between two disks is initially in a state of rigid rotation. The initial density distribution depends on the distance from the axis of rotation. A three dimensional flow is created relative to a rotating frame by imposing small amplitude non torsional oscillations on the disks. The solution is obtained using the Laplace transform. The structure of the boundary layers formed on the disks due to interaction of viscous force, Coriolis force and compressibility is analysed for various ranges of values of the forcing frequency. The theory reveals interesting features in comparison with the non oscillatory case or the case of an incompressible fluid.     

Magneto-thermo-elastic plane waves in rotating media

A study is made of the propagation of plane harmonic waves in an infinite conducting thermo-elastic solid permeated by a primary uniform magnetic field when the entire elastic medium is rotating with a uniform angular velocity. A more general dispersion relation is obtained to determine the effects of rotation, relaxation time and the external magnetic field on the phase velocity of the waves. This result indicates that if the primary magnetic field has a transverse component, then the longitudinal and transverse components of the displacement field are linked together. For the case of low frequency (Gc ? 1 where κ is the ratio of the wave frequency to the characteristic frequency), the rotation and the thermal relaxation time are found to have no influence on the phase velocity, and the attenuation factor for both finite and infinite electrical conductivity. In the case of high frequency (κ ? 1), no effect of rotation on the phase speed is observed to the first order of ($\text{1}\text{κ}$), while the relaxation time affects both the phase velocity and the specific energy loss. However, the effects of rotation on the phase speed, the attenuation factor, and the specific energy loss are found only to the second order of ($\text{1}\text{κ}$) in the case of high frequency. Several limiting cases of interest are discussed.     

Temperature-rate dependent electro-magneto-thermoelastic plane waves in a rotating solid

Plane waves in an electrically conducting, homogeneous and isotropic unbounded thermoelastic solid rotating with a uniform angular velocity are discussed in the context of the temperaturerate dependent electro-magneto-thermoelasticity. Assuming that the primary magnetic field is aligned with the direction of propagation, the effects of rotation of the solid on the phase speed, energy loss and the decay coefficient are studied in some detail. Results of earlier works are deduced as particular cases of the more general results obtained here.     

Hydromagnetic couette flow of an Oldroyd-B fluid in a rotating system

The motion of electrically conducting, Oldroyd-B and incompressible fluid between two infinitely extended non-conducting parallel plates under a uniform transverse magnetic field, fixed relative to the fluid has been considered. The lower plate is at rest and the upper plate is oscillating in its own plane. The governing partial differential equation of this problem, subject to boundary conditions are solved analytically. The expressions for the steady and unsteady velocity fields for the conducting Oldroyd-B fluid are obtained. The graphs are plotted for different values of dimensionless parameters of the problem and the analysis of the results showed that the flow field is appreciably influenced by the applied magnetic field, the rotation and the material parameters of the fluid.     

Shape effect of the matrix on the capture cross section of particles in high gradient magnetic separation

A high gradient magnetic separator consists of a region of a high and approximately uniform magnetic field and a ferromagnetic matrix of fine wires which distort the field and produce large local gradients. As a particle is carried through the separator by a carrying fluid, both magnetic forces and drag forces are exerted on it. In order to gain insight into the capture mechanism, the drag and magnetic forces on a spherical paramagnetic particle were examined. The equilibrium of these forces defines the path of the particle as it passes by a matrix element. It is shown that for any geometry the particle motion is a function of two dimensionless variables. A computer with a plotter was used to compute the particle paths. In order to provide for most flexibility the magnetic field is that of a magnetized elliptical cylinder with any orientation with respect to the background field and flow stream, while the flow velocities are those corresponding to another elliptical cylinder of different configuration and orientation which allows computation of the change of capture cross section as the matrix element collects material. Examples of particle orbits and changes of capture cross section are given inthe paper for various aspect ratios of the original matrix element.     

Magnetic flow of viscous gas between rotating surfaces of revolution

In this work the steady laminar magnetic flow of viscous gas is considered in a narrow space (slot) between two surfaces of revolution rotating with constant angular velocities around a common axis of symmetry. The linearised equations of magnetic motion of the viscous gas flow for axial symmetry in the intrinsic curvilinear orthogonal coordinate system $\text{x, φ, y}$ are used. The obtained solutions of the equations of motion have been illustrated by examples of gas flow through the slot of constant thickness between rotating and fixed conical surfaces, and between rotating and fixed spherical surfaces.     

不同形貌纳米Fe3O4颗粒磁流体的传动性能

选用无规则、正八面体和六方片状形貌的纳米Fe3O4磁性颗粒制备的磁流体,通过设计、组装磁流体传动性能测试仪,探讨了磁流体传动性能与传动盘间距、传动盘之间的转速差的关系,并研究了磁流体中纳米磁性颗粒的形貌对磁流体传动性能的影响。结果表明,在传动盘间隙一定时,磁流体传递扭矩的大小在磁性粒子未达到其饱和磁化强度时,传递扭矩大小随感应磁场强度增大而迅速增大,但随着磁感应强度的进一步加大,磁性粒子逐步达到其饱和磁化强度,磁流体传递扭矩大小的增长减缓,最后几乎不再增大;传动盘之间的间隙对磁流体传递扭矩的大小影响很大,间隙越大,传递的扭矩越小;传动盘之间的转速差对磁流体传递扭矩的大小影响较小,在低转速差下传递的扭矩随转速差的增加而有所增加,但超过一定的转速差后,由于磁流体的剪切稀化效应,传递的扭矩将有所减小。另外,磁流体中磁性粒子的形貌对磁流体传递扭矩的大小有一定的影响,正八面体形貌的磁性粒子相对于无规则和六方片状形貌的磁性粒子,其磁流体能够传递更大的扭矩。