Hydromagnetic elastico-viscous fluid flow between two parallel walls: Velocity field.-I

Summary The effect of the elastic properties of the fluid on the MHD Couette flow of a conducting viscous fluid between two parallel walls is studied when one wall is fixed and the other is moving periodically in time. Exact solution for the velocity field in the boundary layer is obtained. Also expressions for the shear stress at different layers and the skin-friction at the two walls have been obtained.     

Hydromagnetic slip flow with heat transfer in an inclined channel

The problem of steady two-dimensional laminar flow in slip flow regime of a viscous incompressible and electrically conducting fluid through an inclined channel of rectangular cross-section in presence of a transverse magnetic field has been considered. The walls of the channel are assumed to have prescribed temperatures and finite conductivities. The expressions for the velocity component, induced magnetic field and the temperature are obtained and their numerical results are shown graphically.     

Investigation of Turbulent Transition in Plane Couette Flows Using Energy Gradient Method

The energy gradient method has been proposed with the aim of better understanding the mechanism of flow transition from laminar flow to turbulent flow. In this method, it is demonstrated that the transition to turbulence depends on the relative magnitudes of the transverse gradient of the total mechanical energy which amplifies the disturbance and the energy loss from viscous friction which damps the disturbance, for given imposed disturbance. For a given flow geometry and fluid properties, when the maximum of the function $K$ (a function standing for the ratio of the gradient of total mechanical energy in the transverse direction to the rate of energy loss due to viscous friction in the streamwise direction) in the flow field is larger than a certain critical value, it is expected that instability would occur for some initial disturbances. In this paper, using the energy gradient analysis, the equation for calculating the energy gradient function $K$ for plane Couette flow is derived. The result indicates that $K$ reaches the maximum at the moving walls. Thus, the fluid layer near the moving wall is the most dangerous position to generate initial oscillation at sufficient high $\operatorname{Re}$ for given same level of normalized perturbation in the domain. The critical value of $K$ at turbulent transition, which is observed from experiments, is about 370 for plane Couette flow when two walls move in opposite directions (anti-symmetry). This value is about the same as that for plane Poiseuille flow and pipe Poiseuille flow (385-389). Therefore, it is concluded that the critical value of $K$ at turbulent transition is about 370-389 for wall-bounded parallel shear flows which include both pressure (symmetrical case) and shear driven flows (anti-symmetrical case).     

Hall and Ion-Slip Effects in MHD Couette Flow with Heat Transfer

An analysis of the MHD Couette flow on taking into account the Hall and the ion-slip effects has been carried out for fully developed flow. Exact solutions to the velocity components, magnetic field components, axial and transverse components of the skin-friction, temperature and the rate of heat transfer have been derived. The numerical values of the transverse induced pressure gradient, the skin friction and the rate of heat transfer are entered in tables and the others have been shown on graphs. It has been observed that the flow may become unstable when M is small and ?e (Hall parameter) and ?i (ion-slip parameter) are large or at large value of M.     

纳米通道内气体剪切流动的分子动力学模拟

采用分子动力学模拟方法研究了表面力场对纳米通道内气体剪切流动的影响规律.结果显示通道内的气体流动分为两个区域:受壁面力场影响的近壁区域和不受壁面力场影响的主流区域.近壁区域内,气体流动特性和气体动力学理论预测差别很大,密度和速度急剧增大并出现峰值,正应力变化剧烈且各向异性,剪切应力在距壁面一个分子直径处出现突变.主流区域的气体流动特性与气体动力学理论预测相符合,该区域内的密度、正应力与剪切应力均为恒定值,速度分布亦符合应力-应变的线性响应关系.不同通道高度及密度下,近壁区域的归一化密度、速度及应力分布一致,表明近壁区域的气体流动特性仅由壁面力场所决定.随着壁面对气体分子势能作用的增强,气体分子在近壁区域的密度和速度随之增大,直至形成吸附层,导致速度滑移消失.通过剪切应力与切向动量适应系数(TMAC)的关系,得到不同壁面势能作用下的TMAC值,结果表明壁面对气体分子的势能作用越强,气体分子越容易在壁面发生漫反射.     

Hydrodynamic instability of premixed flame propagating in narrow planar channel in the presence of gas flow

The paper analyses the hydrodynamic instability of a flame propagating in the space between two parallel plates in the presence of gas flow. The linear analysis was performed in the framework of a two-dimensional model that describes the averaged gas flow in the space between the plates and the perturbations development of two-dimensional combustion wave. The model includes the parametric dependences of the flame front propagation velocity on its local curvature and on the combustible gas velocity averaged along the height of the channel. It is assumed that the viscous gas flow changes the surface area of the flame front and thereby affects the propagation velocity of the two-dimensional combustion wave. In the absence of the influence of the channel walls on the gas flow, the model transforms into the Darrieus–Landau model of flame hydrodynamic instability. The dependences of the instability growth rate on the wave vector of disturbances, the velocity of the unperturbed gas flow, the viscous friction coefficients and other parameters of the problem are obtained. It is shown that the viscous gas flow in the channel can lead, in some cases, to a significant increase in instability compared with a flame propagating in free space. In particular, the instability increment depends on the direction of the gas flow with respect direction of the flame propagation. In the case when the gas flow moves in the opposite direction to the direction of the flame propagation, the pulsating instability can appear.     

Magnetic fluid behavior in uniform DC,AC, and rotating magnetic fields

New flows and instabilities are demonstrated for magnetic fluids and by dual analogy to dielectric fluids. If a fluid drop is contained in a thin gap between two glass plates (Hele–Shaw cell) with a simultaneously applied in-plane rotating field and a DC axial field, smooth spirals or an abrupt transformation to many small droplets can occur. A preliminary minimum magnetization and surface energy analysis is presented to model the abrupt transformation in ferrofluids. An analysis of effective DC magnetoviscosity is also presented for planar Couette flow with an applied uniform DC field transverse to a duct axis with the effective magnetoviscosity and flow spin velocity calculated as a function of field strength. Related Couette viscometer measurements of ferrofluid viscosity show zero and negative magnetoviscosity values for rotating magnetic fields.     

Effects of hall current on MHD Couette flow in a rotating system with arbitrary magnetic field

Author has studied the MHD Couette flow in a rotating environment with non- conducting walls in the presence of an arbitrary magnetic field. The solution in dimensionless form contains four pertinent flow parameters, viz. the Hartmann number, the rotation parameter which is the reciprocal of the Ekman number, the Hall current parameter, and the angle of inclination of the magnetic field to the positive direction of the axis of rotation. An interplay of hydromagnetic force and Coriolis force with an inclusion of Hall current plays a significant role in determining the MHD flow behaviour. The velocity and induced magnetic field distributions are depicted graphically. Also, the numerical results of shear stresses and the rate of mass flows are presented graphically.     

Shear Stress in a Couette Flow of Liquid-Particle Suspensions

The mechanisms of momentum transfer and shear stress of liquid-particle suspensions in two-dimensional Couette flow are studied using direct numerical simulation by lattice-Boltzmann techniques. The results obtained display complex flow phenomena that arise from the two-phase nature of the fluid including a nonlinear velocity profile, layering of particles, and apparent slip near the solid walls. The general rheological behaviour of the suspension is dilatant. A detailed study of the various momentum transfer mechanisms that contribute to the total shear stress indicates that the observed shear thickening is related to enhanced relative solid phase stress for increasing shear rates.     

Analytic solution to the problem of the couette flow in a plane channel with infinitely large parallel walls

An analytic (in the form of a Neuman series) solution to the problem of the Couette flow in a plane channel with infinitely large parallel walls is constructed using the kinetic approach in the isothermal approximation. For the basic equation, the Bhatnagar-Gross-Krook (BGK) model of the kinetic Boltzmann equation is used, while the boundary condition is determined by the diffuse reflection model. The mass flux through half the channel thickness in the direction parallel to the channel walls as well as the nonzero component of the viscous stress tensor are calculated taking into account the constructed distribution function. The results are compared with analogous data obtained by numerical methods.     

Couette flow in ferrofluids with magnetic field

Instability of a viscous, incompressible ferrofluid flow in an annular space between two coaxially rotating cylinders in the presence of axial magnetic field has been investigated numerically. The magnetic field perturbations in fluid in the gap between the cylinders have been taken into consideration and these have been observed to stabilize the Couette flow.     

Comments on “hydromagnetic slip flow with heat transfer in an inclined channel”

The hydromagnetic slip flow of a viscous incompressible and electrically conducting fluid through an inclined channel of rectangular cross section in the presence of a transverse magnetic field has been analysed. The walls of the channel are assumed to have prescribed temperatures and finite conductivities. The boundary conditions for both velocity and temperature are properly rectified. The expressions for the velocity, induced magnetic field and the temperature are obtained both analytically and numerically.     

Effect of couple stresses on transient MHD poiseuille flow

The unsteady laminar flow of an electrically conducting viscous fluid between parallel insulating plates subject to a transverse magnetic field is considered. The plates are fixed and flow is due to a constant pressure gradient. The induced field is taken into account. The fluid is incompressible and of couple stress type. The defining equations are coupled and numerical solutions for different values of couple stress parameter are obtained. The velocity and induced magnetic field profiles are sketched as functions of time, Hartmann number, and magnetic Prandtl number. The velocity decreases with increase in couple stress parameter.     

Three-dimensional MHD flow over a shrinking sheet: Analytical solution and stability analysis

The magnetohydrodynamic(MHD) steady and unsteady axisymmetric flows of a viscous fluid over a two-dimensional shrinking sheet are addressed. The mathematical analysis is carried out in the presence of a large magnetic field. The steady state problem results in a singular perturbation problem having an infinite domain singularity. The secular term appearing in the solution is removed and a two-term uniformly valid solution is derived using the Lindstedt–Poincaré technique. This asymptotic solution is validated by comparing it with the numerical solution. The solution for the unsteady problem is also presented analytically in the asymptotic limit of large magnetic field. The results of velocity profile and skin friction are shown graphically to explore the physical features of the flow field. The stability analysis of the unsteady flow is made to validate the asymptotic solution.     

Rapid measurement of transient velocity evolution using GERVAIS

Rapid velocity measurements using GERVAIS (Gradient Echo Rapid Velocity and Acceleration Imaging Sequence), an EPI (Echo Planar Imaging) based technique capable of measuring velocity over an observation time of several milliseconds, are performed on a wide-gap Couette Rheo-NMR cell for the first time. A variable delay time between a control signal to initiate a transition in flow and the start of the measurement sequence is incorporated to allow investigation of the transient evolution of the velocity field following a step change in rotation rate. Both the commencement and the cessation of imposed shear stress are investigated for (i) a shear banding micellar solution of CPyCl (cetylpyridiniumchloride)/NaSal (sodium salicylate) in brine and (ii) a low molecular weight PDMS (polydimethylsiloxane) oil. With respect to the micellar solution, an elastic shear wave is seen to propagate across the cell following the commencement of shear stress whilst an oscillatory ‘recoil’ is observed following the cessation of shear stress; neither of these phenomena were observed for the PDMS oil which exhibited a purely viscous response as expected for an incompressible Newtonian fluid. This technique has potential applications across a wide range of transient rheological investigations, particularly with respect to optically opaque materials.     

Thermoconvective flow velocity in a high-speed magnetofluid seal after it has stopped

Convective flow is investigated in the high-speed (linear velocity of the shaft seal is more than 1 m/s) magnetofluid shaft seal after it has been stopped. Magnetic fluid is preliminarily heated due to viscous friction in the moving seal. After the shaft has been stopped, nonuniform heated fluid remains under the action of a high-gradient magnetic field. Numerical analysis has revealed that in this situation, intense thermomagnetic convection is initiated. The velocity of magnetic fluid depends on its viscosity. For the fluid with viscosity of 2 × 10^?4 m²/s the maximum flow velocity within the volume of magnetic fluid with a characteristic size of 1 mm can attain a value of 10 m/s.     

On the theory of the magnetoviscous effect in ferrofluids

The microscopic origin of viscoelastic effects in ferrofluids is studied theoretically. The growth kinetics of chain aggregates formed by magnetic ferroparticles under the action of the dipole-dipole interaction between them is analyzed. It is shown that the evolution rate for an ensemble of chains determines the rate of variation in the macroscopic stress of the medium upon a change in the applied external field and/or in the shear flow velocity. Consequently, the viscoelastic properties of magnetic fluids can be explained by the chain formation-destruction processes. The proposed microscopic model of a ferrofluid makes it possible (apparently, for the first time) to estimate the characteristic time of viscoelasticity corresponding to experimental results.     

Measurement of diffusion in the presence of shear flow

We demonstrate here a method whereby molecular diffusion coefficients may be measured in the presence of the deformational flow field of a rheo-NMR cell. The method, which uses a repetitive CPMG train of rf pulses interspersed with magnetic field gradient pulses, allows the anisotropic diffusion spectrum to be directly probed. We focus on the cylindrical Couette cell, for which the radial, tangential, and axial directions correspond to the hydrodynamic velocity gradient, velocity, and vorticity directions. While ideal Couette flow does not perturb the vorticity direction, it does perturb diffusion measurements for the velocity gradient direction, and to a lesser extent, the velocity direction. We show that with closely spaced gradient pulses operating in a flow-compensating mode, there exists a diffusion limit below which one cannot measure, that scales as T(2)gamma(4), where gamma is the shear rate and T the gradient pulse repetition period. For a typical rheo-NMR cell, and for the more challenging velocity gradient direction, diffusion rates above 10(-12) m(2) s(-1) can be accurately measured (to 1% error) at shear rates up to 3s(-1). We demonstrate the use of the method in measuring the diffusion spectrum of a lyotropic lamellar phase under shear.     

微尺度振荡Couette流的格子Boltzmann模拟

采用有效多松弛时间-格子Boltzmann方法(Effective MRT-LBM)数值模拟了微尺度条件下的振荡Couette和Poiseuille流动. 在微流动LBM中引入Knudsen边界层模型,对松弛时间进行修正. 模拟时平板或外力以正弦周期振动,Couette流中考虑了单平板振动、上下板同相振动这两类情况. 研究结果表明,修正后的MRT-LBM模型能有效用于这类非平衡的微尺度流动模拟;对于Couette流,随着Kn数的增大,壁面滑移效应变得越明显. St越大,板间速度剖面的非线性特性越剧烈;两板同相振荡时,若Kn,St均较小,板间流体受到平板拖动剪切的影响很小,板间速度几乎重叠在一起;在振荡Poiseuille流动中,St数增大到一定值时,相位滞后现象减弱;相对于Kn数,St数对振荡Couette 和Poiseuille流中不同位置处速度相位差的产生有较大影响. 关键词： 格子Boltzmann方法 有效MRT模型 Knudsen层 振荡流     

Free convection effects on HMD horizontal channel flow with Hallcurrents

An exact solution of MHD channel flow between two horizontal parallel plates taking into account free convection currents and the Hall currents is presented. Solutions for the primary and secondary velocity, the induced magnetic field, the skin friction, and the temperature are derived. The velocity field and magnetic field are shown on graphs, and the values of the skin friction and the rate of heat transfer are indicated on tables. The results are discussed in terms of the hall parameter, the Hartmann number, and the Grashof number