磁性液体管道流动的数值模拟

通过将磁性液体的磁化曲线用一个反正切函数来模拟，并且将磁场体积力写成Az的函数形式来模拟磁性液体在圆管申的流动。结果表明，圆管内的磁性液体有最大流量时，磁性液体流在靠近永磁附近呈紊流状态流动，在圆管的最右端，大致呈层流状态流动；圆管内的磁性液体净流量为零时，靠近永磁的磁性液体在原地呈激烈的涡旋流动状态．     

Influence of temperature dependent viscosity on the MHD-channel flow of dusty fluid with heat transfer

Summary This paper studies the effect of variable viscosity on the transient flow of dusty fluid with heat transfer. The fluid is acted upon by a constant pressure gradient, and an external uniform magnetic field is applied perpendieular to the plates. The governing nonlinear partial differential equations are solved numerically, and some important effects for the variable viscosity and the uniform magnetic field on the transient flow and heat transfer of both the fluid and dust particles are indicated.     

MHD stagnation-point flow of an electrically conducting fluid on the surface of another quiescent fluid

An analysis is made of the orthogonal stagnation-point flow of an incompressible viscous electrically conducting fluid on the surface of another incompressible viscous electrically conducting quiescent fluid in the presence of a uniform magnetic field normal to the interface between the fluids. It is found that for small magnetic Reynolds number, the velocity at a point in the upper fluid increases and that at a point in the lower fluid decreases with increase in the magnetic field. It is also observed from the temperature distributions in the two given fluids that the interface temperature increases with increase in the magnetic field.     

磁流变液的流体动力学理论

在外加磁场作用下,磁流变液从牛顿流体变成了Bingham体,超过屈服应力开始流动,其的流变性(弹性、塑性、粘性)、磁化性、导电性、传热性以及其它的机械性质和物理学性质皆发生显著的改变.研究磁流变液在外加磁场作用下,流场分布规律随磁场强度变化的动态特性,建立磁流变液的流体动力学理论,对开发和设计磁流变器械至关重要.本文运用物理学和流体力学的基本理论,结合本构方程,考虑磁场对磁流变液的流动的影响,建立了磁流变液力磁耦合的流体动力学模型,给出了描述磁流变液流动的基本方程组.     

MHD flow of a viscoelastic fluid past a stretching surface

Summary The flow of a viscoelastic fluid past a stretching sheet in the presence of a transverse magnetic field is considered. An exact analytical solution of the governing non-linear boundary layer equation is obtained, showing that an external magnetic field has the same effect on the flow as the viscoelasticity.     

Stability of magnetohydrodynamic stratified shear flows

Summary A study is made of the stability of a stratified shear flow in a perfectly conducting fluid in the presence of an external magnetic field aligned with the flow. A semi-circle theorem for the present hydromagnetic case is proved. The magnetic field is found to have a stabilizing effect on the flow. The Rayleigh-Taylor instability problem in a stratified conducting fluid is discussed. Finally, a study is made of the absorption of wave energy by the mean flow in the hydromagnetic case by considering a shear flow with an anti-symmetric velocity profile given byU=tanhz. Unlike the hydrodynamic case, it is found that, in the critical layer atU=0, the transfer of the wave energy to the mean flow occurs for any value of the Richardson number. This result implies again the stabilizing effect of the magnetic field on the shear flow.     

Magnetorheological rotational flow with viscous dissipation

Effects of a magnetic field and fluid nonlinearity are investigated for the rotational flow of the Carreau-type fluid while viscous dissipation is taken into account. The governing motion and energy balance equations are coupled, adding complexity to the already highly correlated set of differential equations. The numerical solution is obtained for the narrow-gap limit and steady-state base flow. Magnetic field effect on local entropy generation due to steady two-dimensional laminar forced convection flow was investigated. This study was focused on the entropy generation characteristics and its dependency on various dimensionless parameters. The effects of the Hartmann number, the Brinkman number, and the Deborah number on the stability of the flow were investigated. The introduction of the magnetic field induces a resistive force acting in the opposite direction of the flow, thus causing its deceleration. Moreover, the study shows that the presence of magnetic field tends to slow down the fluid motion. It, however, increases the fluid temperature. Moreover, the total entropy generation number decreases as the Hartmann number and fluid elasticity increase and increases with increasing Brinkman number.     

Convective and Absolute Instability in the Incompressible Boundary Layer on a Rotating Disk in the Presence of a Uniform Magnetic Field

The stability of a conducting fluid flow over a rotating disk with a uniform magnetic field applied normal to the disk, is investigated. It is assumed that the magnetic field is unaffected by the motion of the fluid. The mean flow and linear stability equations are solved for a range of magnetic field-strength parameters and the absolute/convective nature of the stability is investigated. It is found that increasing the magnetic field parameter is in general stabilizing.     

MHD compressible turbulent boundary-layer flow with adverse pressure gradient

Summary The effects of the magnetic field and localized suction on the steady turbulent compressible boundary-layer flow with adverse pressure gradient are numerically studied. The magnetic field is constant and applied transversely to the direction of the flow (global or local). The fluid flow is subjected to a constant velocity of localized suction, and there is no heat transfer between the fluid and the plate (adiabatic plate). The Reynolds-Averaged Boundary-Layer (RABL) equations and their boundary conditions are transformed using the compressible Falkner-Skan transformation. The resulting coupled and nonlinear system of PDEs is solved using the Keller’s box method. For the eddy-kinematic viscosity the turbulent models of Cebeci-Smith and Baldwin-Lomax are employed. For the turbulent Prandtl number the extended Kays-Crawford’s model is used. The flow is subjected to an adverse pressure gradient. The obtained results show that the flow field can be controlled by the applied magnetic field as well as by localized suction.     

On the flow of an electrically conducting nonlocal viscous fluid between parallel plates in the presence of a transverse magnetic field in magnetohydrodynamics

A continuum theory is constructed for the flow of an electrically conducting nonlocal viscous fluid between two nonconducting parallel plates. The flow is subject to the influence of a transverse magnetic field. The effects of long range or nonlocal interactions at a material point in the fluid arising from all material points in the rest of the fluid are taken into account by means of a nonlocal influence function. Equations of motion governing the nonlocal viscous flow are derived from localized forms of global balance laws and constitutive equations appropriate for electromagnetically active media. These field equations are analytically solved for the nonlocal velocity and the nonlocal stress fields. The effects of varying the magnetic field strength on the shear stress are investigated. The effects of such variations on the shear stress exerted on the walls of microscopic channels are also determined. Numerical computations are provided for these results.     

基于磁流体动力学的电磁流量计数值模拟

通过计算流体力学和磁流体动力学的耦合计算,直接给出了一种电磁流量计二维模型里流动(层流)和外加磁场(均匀稳态)的相互作用结果,并得到信号输出即感应电动势与流量的基本关系以及其他变量如感应电场与感应电流的详细空间分布。模拟结果符合理论值,表明可利用磁流体动力学数值模拟来广泛研究不同流场和外加磁场分布下电磁流量计特性。     

Variable viscosity effect on hydromagnetic flow and heat transfer about a fluid underlying the axisymmetric spreading surface

Summary. The effect of variable viscosity on the flow and heat transfer about a fluid underlying the axisymmetric spreading surface in the presence of an axial magnetic field has been investigated. The viscosity of the fluid is assumed to vary as an inverse linear function of temperature and the magnetic field strength is inversely proportional to the radial coordinate. The partial differential equations, governing the present problem, have been transformed, by suitable similarity variables, into a system of ordinary differential equations. This system is solved numerically by the shooting technique. Numerical results are introduced in graphical form for different values of viscosity parameter, _r, and magnetic field parameter. In the presence of variable viscosity, an increase in Prandtl number leads to a rise in the velocity field. Generally, it leads to a fall in the temperature field. Both magnetic field and variable viscosity raise the heat transfer and suppress the fluid flow.     

MHD flow over a moving plate in a rotating fluid with magnetic field, Hall currents and free stream velocity

The non-similar boundary layer flow of a viscous incompressible electrically conducting fluid over a moving surface in a rotating fluid, in the presence of a magnetic field, Hall currents and the free stream velocity has been studied. The parabolic partial differential equations governing the flow are solved numerically using an implicit finite-difference scheme. The Coriolis force induces overshoot in the velocity profile of the primary flow and the magnetic field reduces/removes the velocity overshoot. The local skin friction coefficient for the primary flow increases with the magnetic field, but the skin friction coefficient for the secondary flow reduces it. Also the local skin friction coefficients for the primary and secondary flows are reduced due to the Hall currents. The effects of the magnetic field, Hall currents and the wall velocity, on the skin friction coefficients for the primary and secondary flows increase with the Coriolis force. The wall velocity strongly affects the flow field. When the wall velocity is equal to the free stream velocity, the skin friction coefficients for the primary and secondary flows vanish, but this does not imply separation.     

Biofluid flow in a channel under the action of a uniform localized magnetic field

In this work the fundamental problem of the biomagnetic (blood) fluid flow in a channel under the influence of a steady localized magnetic field is studied. For the mathematical formulation of the problem both magnetization and electrical conductivity of blood are taken into account and blood is considered as a homogeneous Newtonian fluid. For the numerical solution of the problem, which is described by a coupled, non linear system of PDEs, with appropriate boundary conditions, the stream function–vorticity formulation is adopted. The solution is obtained by the development of an efficient numerical technique based on finite differences. Results concerning the velocity and temperature field, skin friction and rate of heat transfer, indicate that the presence of the magnetic field influences considerably the flow field. It is also obtained that the electrical conductivity of blood should be taken into account at the area of the uniform magnetic field.     

Hydromagnetic flow and heat transfer of a second-grade viscoelastic fluid in a channel with oscillatory stretching walls: application to the dynamics of blood flow

The characteristics of flow and heat transfer of a fluid in a channel with oscillatory stretching walls in the presence of an externally applied magnetic field are investigated. The fluid considered is a second-grade viscoelastic electrically conducting fluid. The partial differential equations that govern the flow are solved by developing a suitable numerical technique. The computational results for the velocity, temperature and the wall shear stress are presented graphically. The study reveals that flow reversal takes place near the central line of the channel. This flow reversal can be reduced to a considerable extent by applying a strong external magnetic field. The results are found to be in good agreement with those of earlier investigations.     

Use of paired, bonded NdFeB magnets in redox magnetohydrodynamics

Bonded neodymium-iron-boron (NdFeB) permanent magnets in a paired configuration were successfully used to control mass transport in redox-based, magnetohydrodynamics (MHD). Control of fluid flow based on magnetic fields has potential for use in portable lab-on-a-chip (LOAC) and analytical devices. Bonded magnets, composed of magnetic powder and organic binder materials, are less expensive and easier to fabricate and pattern than electromagnets and sintered permanent magnets, which have been previously used in MHD studies on electrochemical systems. The ability to pattern bonded magnets near and around the electrodes is expected to allow for better control over the magnetic field distribution and solution flow. Current was generated at an 800-microm-radius platinum disk electrode in a solution of 0.06 M nitrobenzene and 0.5 M tetra-n-butylammonium hexafluorophosphate in acetonitrile. Increases in limiting current in the presence of the magnetic field, which indicate enhancement in mass transport, for sintered (210+/-14%, N = 4, where B(r) = 1.23 T and magnetic field strength is 0.55 T) and bonded (94+/-8%, N = 4, where B(r) = 0.41 T and magnetic field strength is 0.20 T) magnets, were similar to those obtained using an electromagnet with the same magnetic flux densities. The magnetic field strength and not the magnet type is important in controlling fluid flow, which is encouraging for integration of bonded permanent magnets into LOAC devices.     

Manipulation of self-assembled structures of magnetic beads for microfluidic mixing and assaying

We present an original concept of manipulation of magnetic microbeads in a microchannel. It is based on the dynamic motion of a self-assembled structure of ferrimagnetic beads that are retained within a microfluidic flow using a local alternating magnetic field. The latter induces a rotational motion of the magnetic particles, thereby strongly enhancing the fluid perfusion through the magnetic structure that behaves as a dynamic random porous medium. The result is a very strong particle-liquid interaction that can be controlled by adjusting the magnetic field frequency and amplitude, as well as the liquid flow rate, and is at the basis of very efficient liquid mixing. The principle is demonstrated using a microfluidic chip made of poly(methyl methacrylate) with integrated soft ferromagnetic plate structures. The latter are part of an electromagnetic circuit and serve to locally apply a magnetic field over the section of the microchannel. Starting from a laminar flow pattern of parallel fluorescein dye and nonfluorescent liquid streams, we demonstrate a 95% mixing efficiency using a mixing length of only 400 microm and at liquid flows of the order of 0.5 cm/s. We anticipate that the intense interaction between the fluid and magnetic particles with functionalized surfaces holds large potential for the development of future bead-based assays.     

Theoretical magnetohydrodynamic analysis of mixed convection boundary-layer flow over a wedge with uniform suction or injection

Summary The purpose of this work is to study the effects of an applied magnetic field on the mixed convection boundary-layer flow over a wedge with suction or injection. The fluid is assumed to be viscous, incompressible and electrically conducting, and the magnetic field is applied transversally to the direction of the flow. Such a flow model has great significance not only of its own theoretical interest, but also for applications to aerodynamics and engineering. The governing partial differential equations of this problem, subjected to their boundary conditions, are solved numerically by applying an efficient solution scheme for local nonsimilarity boundary-layer analysis. Numerical calculations are carried out for different values of the dimensionless parameters of the problem, and the analysis of the obtained results showed that the flow field is appreciably influenced by the applied magnetic field.     

MHD boundary-layer flow of a micropolar fluid past a wedge with variable wall temperature

Summary The steady laminar MHD boundary-layer flow past a wedge immersed in an incompressible micropolar fluid in the presence of a variable magnetic field is investigated. The governing partial differential equations are transformed to the ordinary differential equations using similarity variables, and then solved numerically using a finite-difference scheme known as the Keller-box method. Numerical results show that the micropolar fluids display drag reduction and consequently reduce the heat transfer rate at the surface, compared to the Newtonian fluids. The opposite trends are observed for the effects of the magnetic field on the fluid flow and heat transfer characteristics.     

Electroosmotic and pressure-driven flow in open and packed capillaries: velocity distributions and fluid dispersion

The flow field dynamics in open and packed segments of capillary columns has been studied by a direct motion encoding of the fluid molecules using pulsed magnetic field gradient nuclear magnetic resonance. This noninvasive method operates within a time window that allows a quantitative discrimination of electroosmotic against pressure-driven flow behavior. The inherent axial fluid flow field dispersion and characteristic length scales of either transport mode are addressed, and the results demonstrate a significant performance advantage of an electrokinetically driven mobile phase in both open-tubular and packed-bed geometries. In contrast to the parabolic velocity profile and its impact on axial dispersion characterizing laminar flow through an open cylindrical capillary, a pluglike velocity distribution of the electroosmotic flow field is revealed in capillary electrophoresis. Here, the variance of the radially averaged, axial displacement probability distributions is quantitatively explained by longitudinal molecular diffusion at the actual buffer temperature, while for Poiseuille flow, the preasymptotic regime to Taylor-Aris dispersion can be shown. Compared to creeping laminar flow through a packed bed, the increased efficiency observed in capillary electrochromatography is related to the superior characteristics of the electroosmotic flow profile over any length scale in the interstitial pore space and to the origin, spatial dimension, and hydrodynamics of the stagnant fluid on the support particles' external surface. Using the Knox equation to analyze the axial plate height data, an eddy dispersion term smaller by a factor of almost 2.5 than in capillary high-performance liquid chromatography is revealed for the electroosmotic flow field in the same column.