A nonisothermal phase‐field model for the ferromagnetic transition

We propose a model for nonisothermal ferromagnetic phase transition based on a phase field approach, in which the phase parameter is related but not identified with the magnetization. The magnetization is split in a paramagnetic and in a ferromagnetic contribution, dependent on a scalar phase parameter and identically null above the Curie temperature. The dynamics of the magnetization below the Curie temperature is governed by the order parameter evolution equation and by a Landau–Lifshitz type equation for the magnetization vector. In the simple situation of a uniaxial magnet, it is shown how the order parameter dynamics reproduces the hysteresis effect of the magnetization. Copyright © 2012 John Wiley & Sons, Ltd.     

Effect of rotation on plane waves of generalized electro-magneto-thermoviscoelasticity with two relaxation times

A new model of the equations of generalized thermovisco-elasticity for a thermally, isotropic and electrically conducting half-space solid whose surface is subjected to a thermal shock is given. The formulation is applied to the generalized thermoelasticity based on the Green and Lindsay (GL) theory under the effect of rotation, where there is an initial magnetic field parallel to the plane boundary of the half-space. The medium is deformed because of thermal shock and due to the application of the magnetic field, it results an induced magnetic and electric fields in the medium. The normal mode analysis is used to obtain the expressions for the variables considered. The distributions of temperature, displacement, stress, induced magnetic and electric fields are represented graphically. Comparisons are made with the results predicted by the coupled theory (CD) in the presence and absence of rotation.     

The Rotation of a Gravitating Sphere in a Monatomic Gas,I

The flow resulting from the steady rotation of a gravitating sphere in a monatomic gas is studied in two special cases. If the rotation is slow, then the motion consists of a swirling flow whose streamlines are concentric circles around the rotation axis, and a slower meridional flow whose structure depends on the strength of the gravitational field. This meridional flow is investigated in detail for small and large field strength. In the latter case, the scale height is small compared to the sphere radius, and most of the fluid is in a thin recirculating layer on the surface. However, the mathematics imposes a severe restriction on the rotation speed if the field is large, which leads to a more general investigation of the flow for very large field strength, i.e. for a thin “atmosphere”. Compressibility effects can be quite sizeable in this final solution. Though a thin recirculating surface layer still exists in only slightly modified form, the fluid outside this layer is much less tenuous than for the case when the rotation is slow. The flow in the region outside the boundary layer involves solution of two quasilinear elliptic equations.     

On the motion of a solid in a magnetic field

The problem of the motion of a magnetic solid in a constant uniform magnetic field, taking gyromagnetic effects into account, is considered. The equations of motion are derived, the Hamiltonian structure is studied, and the cases of integrability indicated. Certain classes of stationary motions are studied and their stability examined.

The gyromagnetic effects arise because the electrons have magnetic and mechanical spin moments /1/. The rotation of the body causes it to become magnetized (the Barnett effect) and when a freely suspended body is magnetized, it begins to rotate (the Einsteinde Haas effect). It is found that gyromagnetic phenomena must be taken into account when analysing the motion of gyroscopic precision systems.     

Finite element analysis of thermoelastic field in a rotating FGM circular disk

This study focuses on the finite element analysis of thermoelastic field in a thin circular functionally graded material (FGM) disk subjected to a thermal load and an inertia force due to rotation of the disk. Due to symmetry, the FGM disk is assumed to have exponential variation of material properties in radial direction only. As a result of nonuniform coefficient of thermal expansion (CTE) and nonuniform temperature distribution, the disk experiences an incompatible eigenstrain which is taken into account. Based on the two dimensional thermoelastic theories, the axisymmetric problem is formulated in terms of a second order ordinary differential equation which is solved by finite element method. Some numerical results of thermoelastic field are presented and discussed for an Al₂O₃/Al FGM disk. The analysis of the numerical results reveals that the thermoelastic field in an FGM disk is significantly influenced by temperature distribution profile, radial thickness of the disk, angular speed of the disk, and the inner and outer surface temperature difference, and can be controlled by controlling these parameters.     

The Effect of an Axial Magnetic Field at the Interface of a Crystal Grown by the Czochralski Method

A mathematical model has been developed which aims to give insightinto the transport phenomena in the vicinity of the interfaceof a crystal grown by the Czochralski method in the presenceof an axial magnetic field. The fluid flow, temperature andconcentration fields in this region have a strong effect onthe distribution of impurities and the occurrence of cracks,dislocations and other physical defects in the crystal and soknowledge and ultimately control of these factors is of greatpractical importance. The model incorporates rotation of both the crystal and crucibleby considering the crystal to be an infinite disc rotating ina semi-infinite fluid which may be rotating at infinity. Axialsymmetry is assumed and the magnetic Prandtl number is consideredto be very much less than unity. This means that induced currentscan be neglected and allows a similarity solution to be developed.The system of partial differential equations can then be replacedby an ordinary differential boundary-value problem which issolved numerically.     

Hall Effects on Hydromagnetic Flow and Heat Transfer in a Rotating Channel

An exact solution has been obtained for the fully developedflow of a conducting fluid within a rotating channel due toaconstant pressure gradient in the presence of a uniform transversemagnetic field, taking Hall currents into account. The effectsof Hall current and rotation on the velocity and the magneticfield have been discussed. The shear stress at theplate decreasesdue to an increase in either the Hall parameter for the rotationparameter. Hall effects on the heat transfer have also beenconsidered. For small values of rotation parameter, the rateof heat transfer at the upper plate decreases while for largevalues of rotation parameter the rate of heat transfer firstdecreases, reaches a minimum and then increases with the increasein the Hall parameter. This result is reversed for the lowerplate whose temperature is below that of the upper plate.     

Analysis of melting behavior of PCMs in a cavity subject to a non-uniform magnetic field using a moving grid technique

Melting flow and heat transfer of electrically conductive phase change materials subjecting to a non-uniform magnetic field are addressed in a square enclosure. The top and bottom walls of the cavity are adiabatic, and the sidewalls are isothermal at different temperatures. The temperature of the hot wall is higher than the fusion temperature of PCM (T_f), and the cold wall is at the fusion temperature or lower. At the initial time, the cavity is filled with a solid saturated PCM. In the vicinity to the hot wall, there is an external line-source magnet, inducing a magnetic field. The location of the magnetic source (Y₀) can be changed along the hot wall. The cavity domain is divided into two parts of the liquid domain and the solid domain. The moving grid method is utilized to track the phase change interface at the exact fusion temperature of T_f. The governing equations for continuity, flow and heat transfer associated with the Arbitrary Lagrangian–Eulerian (ALE) moving mesh technique are solved using the finite element method. The results are investigated for the melting behavior of PCM by the study of Hartmann number (0 ≤ Ha ≤ 50) and the location of the magnetic source (0 ≤ Y₀ ≤ 1). Outcomes show that the effect of the magnetic field on the melting behavior of PCM is negligible at the initial stages of the melting (Fo < 1.15). However, after the initial stages of the melting, the effect of the presence of a magnetic field becomes significant. Moreover, the location of the magnetic source induces a feeble effect on the melting front at the initial melting stages, but its effect on the shape of the melting front increases by the increase of the non-dimensional time. The location of the magnetic source also significantly affects the streamlines patterns. Changing the position of the magnetic source from the bottom of the cavity (Y₀ = 0.2) to the almost middle of the cavity (Y₀ = 0.6) would decrease the required non-dimensional time of full melting from Fo = 10.4 to Fo = 9.0.     

The effects of strong magnetic fields and rotation on soliton stars at finite temperature

We study the effects of strong magnetic fields and uniform rotation on the properties of soliton stars in Lee-Wick model when a temperature dependence is introduced into this model. We first recall the properties of the Lee-Wick model and study the properties of soliton solutions, in particular, the stability condition, in terms of the parameters of the model and in terms of the number of fermions N inside the soliton (for very large N) in the presence of strong magnetic fields and uniform rotation. We also calculate the effects of gravity on the stability properties of the soliton stars in the simple approximation of coupling the Newtonian gravitational field to the energy density inside the soliton, treating this as constant throughout. Following Cottingham and Vinh Mau, we also make an analysis at finite temperature and show the possibility of a phase transition which leads to a model with parameters similar to those considered by Lee and his colleagues but in the presence of magnetic fields and rotation. More specifically, the effects of magnetic fields and rotation on the soliton mass and transition temperature are computed explicitly. We finally study the evolution on these magnetized and rotating soliton stars with the temperature from the early universe to the present time.     

Magnetic properties and microstructure of HDDR isotropic Nd-Dy-Fe-Co-B bonded magnets with high coercivity

The effect of small amount of Co and Dy addition on the magnetic properties of HDDR isotropic Nd-Dy-Fe-Co-B bonded magnets was investigated. The experimental results show that the intrinsic coercivity H_cj and the reversible temperature coefficient of remanence of (Nd_0.65 Dy_0.35)_12.5-(Fe_0.9Co_0.1)₈₁B_6.5 magnet were 1.53 MA·m^-1(19.3 kOe) and -0.059%/°C (25–155°C), respectively. The high coercivity and low temperature coefficient of the magnet are due to the enhanced anisotropy field, increased Curie temperature and improved microstructure by Dy and Co addition.     

Secondary flow about a magnetized sphere rotating in viscous conducting fluid

The problem of secondary motion induced by the steady rotation of a magnetized sphere in an infinite incompressible viscous conducting fluid is considered. It is found that the secondary flow adds nothing to the couple required tomaintain the motion and the effect of the magnetic field is to damp the secondary velocity field.     

Electromagnetic forces in high field magnet coils

There has been considerable study in recent years of the mechanical effects of the electromagnetic forces in large high field magnet coils. The problem of supporting the electromagnetic forces acting on the windings has become a limiting factor in the design of such magnets. Caldwell has already obtained a mathematical model representing the stress distribution in magnet windings but a number of simplifying assumptions were made in deriving the equations. This paper checks the accuracy of this method by comparing it with homogeneous thick cylinder theory which involves the calculation of stresses by solving the Timoshenko stress equations. Thus values of the circumferential stress are compared for two different coil configurations and reasonable agreement is obtained.     

The Rotation of a Gravitating Sphere in a Monatomic Gas,II

The purpose of this work is to study the fluid motion caused by the high speed rotation of a gravitating sphere in a monatomic gas. It has been possible to find a stable steady solution only for very small Prandtl number, which can be interpreted to mean an optically thick gas. The flow is characterized by a flat radial jet in the equatorial plane and a viscous boundary layer on the spherical surface which, in some cases, lies beneath a thermal boundary layer. That the outer region must be hydrostatic puts very stringent constraints on the associated velocity field which necessitate still another boundary layer on the sphere. This last layer is shown to be unstable to small disturbances in certain temperature ranges. Finally, a similar solution that exists for order one Prandtl number must be disregarded because this last boundary layer is always unstable.     

矩形永磁体磁场分布的解析表达式

从分子环流模型出发,利用毕奥-萨伐尔定理,对于仅在一个方向均匀完全充磁的矩形永磁块体,导出了其外部空间磁场分布的解析表达式．该解析式能精确描述一块至多块按极性相反并列放置时矩形永磁体外部空间的磁场分布．针对单块永磁体,还分析了磁场分布与永磁体几何尺寸之间的依赖关系,以及磁场大小随外部空间点离开永磁体表面距离之间的关系;定量分析了横向磁场的强度均匀度和分布均匀度随永磁体几何尺寸和离开永磁体表面距离的变化规律．     

Non-smooth dynamics of a magnetic track brake

During the first stages of braking with a magnetic track brake in low suspension impacts occur between the force transmitting components, giving rise to a non-smooth system behaviour. Initially, when the electric current is switched on, the magnet moves down until it impinges on the rail. Thereafter, it is decelerated by the friction force, and subsequently there occurs a first impact of the transmission link of the magnet on the transmission link of the bogie frame. Due to the elasticity of the components there follows a high-frequency series of impacts with decreasing intensity until the velocity of the magnet relative to the bogie frame vanishes. Of course, the occurring forces are multiples of the steady-state ones, and this must be taken into account at the design of the force transmitting components.     

On Rivlin-Erickson elastico-viscous fluid heated and soluted from below in the presence of compressibility, rotation and hall currents

A layer of compressible, rotating, elastico-viscous fluid heated & soluted from below is considered in the presence of vertical magnetic field to include the effect of Hall currents. Dispersion relation governing the effect of viscoelasticity, salinity gradient, rotation, magnetic field and Hall currents is derived. For the case of stationary convection, the Rivlin-Erickson fluid behaves like an ordinary Newtonian fluid. The compressibility, stable solute gradient, rotation and magnetic field postpone the onset of thermosolutal instability whereas Hall currents are found to hasten the onset of thermosolutal instability in the absence of rotation. In the presence of rotation, Hall currents postpone/hasten the onset of instability depending upon the value of wavenumbers. Again, the dispersion relation is analyzed numerically & the results depicted graphically. The stable solute gradient and magnetic field (and corresponding Hall currents) introduce oscillatory modes in the system which were non-existent in their absence. The case of overstability is discussed & sufficient conditions for non-existence of overstability are derived.     

Thermal instability in compressible fluids in the presence of rotation and magnetic field

The thermal instability of compressible fluids pervaded by a uniform rotation and a uniform magnetic field, separately, is considered. For $\text{(}\text{Cp}\text{g}\text{)β < 1}$, with Cp, g, and β denoting the specific heat at constant pressure, the acceleration due to gravity, and the uniform temperature gradient, respectively, the system is shown to be stable. The magnetic field as well as rotation introduces oscillatory modes in thermal instability of compressible fluids, which are completely missing for $\text{(}\text{Cp}\text{g}\text{)β > 1}$ in the absence of rotation or magnetic field. The sufficient conditions which do not allow overstable modes are obtained.     

On the Swimming of a "Pod "

A "pod" is a medical device consisting of a small hollow magnetattached to a plastic "tail". If it is placed in a blood vesselof a patient, and an alternating magnetic field applied, themagnet oscillates angularly and the plastic tail causes it toswim. The purpose of the device is to deliver medicaments, whichmay have been placed in the hollow magnet, or perform othertasks at any desired location in the main circulatory system.This paper seeks to analyse the swimming process and suggestdesign characteristics for efficient swimming. The analysis can also be regarded as a contribution to the generaltheory of swimming of elastic bodies excited by an externalforce.     

Sufficient Global Stability Condition for a Model of the Synchronous Electric Motor under Nonlinear Load Moment

We study a model of the synchronous electric motor, which is described by a system of ordinary differential equations, including equations for electric currents in the windings of the rotor. The load moment is assumed to be a nonlinear function of the angular velocity of the rotor, allowing a linear estimate. The system of differential equations under consideration has a countable number of stationary solutions corresponding to the operating mode of uniform rotation of the rotor with the angular velocity equal to the angular velocity of rotation of the magnetic field in the stator. An effective sufficient condition is derived under which any motion of the rotor of the synchronous electric motor tends with time to uniform rotation.     

Local conjugacy classes for analytic torus flows

If a real-analytic flow on the multidimensional torus close enough to linear has a unique rotation vector which satisfies an arithmetical condition Y, then it is analytically conjugate to linear. We show this by proving that the orbit under renormalization of a constant Y-vector field attracts all nearby orbits with the same rotation vector.