MHD peristaltic flow of a third order fluid in an asymmetric channel

This study is concerned with peristaltic flow of a magnetohydrodynamic (MHD) fluid in an asymmetric channel. Asymmetry in the flow is induced by waves on the channel walls having different amplitudes and phase. A systematic approach based on an expansion of Deborah number is used for the solution series. Analytic expressions have been developed for the stream function, axial velocity and axial pressure gradient. The pressure rise over a wavelength has been addressed through numerical integration. Particular attention has been given to the effects of Hartman number and Deborah number on the pressure rise over a wavelength and the trapping phenomenon. Several limiting solutions of interest are obtained as the special cases of the presented analysis by taking the appropriate parameter(s) to be zero. Copyright © 2009 John Wiley & Sons, Ltd.     

Boundary element method solution of MHD flow in a rectangular duct

The magnetohydrodynamic (MHD) flow of an incompressible, viscous, electrically conducting fluid in a rectangular duct with an external magnetic field applied transverse to the flow has been investigated. The walls parallel to the applied magnetic field are conducting while the other two walls which are perpendicular to the field are insulators. The boundary element method (BEM) with constant elements has been used to cast the problem into the form of an integral equation over the boundary and to obtain a system of algebraic equations for the boundary unknown values only. The solution of this integral equation presents no problem as encountered in the solution of the singular integral equations for interior methods. Computations have been carried out for several values of the Hartmann number (1 ? M ? 10). It is found that as M increases, boundary layers are formed close to the insulated boundaries for both the velocity and the induced magnetic field and in the central part their behaviours are uniform. Selected graphs are given showing the behaviours of the velocity and the induced magnetic field.     

Transport and deposition of neutral particles in magnetohydrodynamic turbulent channel flows at low magnetic Reynolds numbers

The effect of Lorentz force on particle transport and deposition is studied by using direct numerical simulation of turbulent channel flow of electrically conducting fluids combined with discrete particle simulation of the trajectories of uncharged, spherical particles. The magnetohydrodynamic equations for fluid flows at low magnetic Reynolds numbers are adopted. The particle motion is determined by the drag, added mass, and pressure gradient forces. Results are obtained for flows with particle ensembles of various densities and diameters in the presence of streamwise, wall-normal or spanwise magnetic fields. It is found that the particle dispersion in the wall-normal and spanwise directions is decreased due to the changes of the underlying fluid turbulence by the Lorentz force, while it is increased in the streamwise direction. The particle accumulation in the near-wall region is diminished in the magnetohydrodynamic flows. In addition, the tendency of small inertia particles to concentrate preferentially in the low-speed streaks near the walls is strengthened with increasing Hartmann number. The particle transport by turbophoretic drift and turbulent diffusion is damped by the magnetic field and, consequently, particle deposition is reduced.     

Direct simulation of MHD flows in dual-coolant liquid metal fusion blanket using a consistent and conservative scheme

Direct simulation of 3-D MHD (magnetohydrodynamics) flows in liquid metal fusion blanket with flow channel insert (FCI) has been conducted. Two kinds of pressure equilibrium slot (PES) in FCI, which are used to balance the pressure difference between the inside and outside of FCI, are considered with a slot in Hartmann wall or a slot in side wall, respectively. The velocity and pressure distribution of FCI made of SiC/SiC_f are numerically studied to illustrate the 3-D MHD flow effects, which clearly show that the flows in fusion blanket with FCI are typical three-dimensional issues and the assumption of 2-D fully developed flows is not the real physical problem of the MHD flows in dual-coolant liquid metal fusion blanket. The optimum opening location of PES has been analyzed based on the 3-D pressure and velocity distributions.     

The DRBEM solution of incompressible MHD flow equations

This paper presents a dual reciprocity boundary element method (DRBEM) formulation coupled with an implicit backward difference time integration scheme for the solution of the incompressible magnetohydrodynamic (MHD) flow equations. The governing equations are the coupled system of Navier‐Stokes equations and Maxwell's equations of electromagnetics through Ohm's law. We are concerned with a stream function‐vorticity‐magnetic induction‐current density formulation of the full MHD equations in 2D. The stream function and magnetic induction equations which are poisson‐type, are solved by using DRBEM with the fundamental solution of Laplace equation. In the DRBEM solution of the time‐dependent vorticity and current density equations all the terms apart from the Laplace term are treated as nonhomogeneities. The time derivatives are approximated by an implicit backward difference whereas the convective terms are approximated by radial basis functions. The applications are given for the MHD flow, in a square cavity and in a backward‐facing step. The numerical results for the square cavity problem in the presence of a magnetic field are visualized for several values of Reynolds, Hartmann and magnetic Reynolds numbers. The effect of each parameter is analyzed with the graphs presented in terms of stream function, vorticity, current density and magnetic induction contours. Then, we provide the solution of the step flow problem in terms of velocity field, vorticity, current density and magnetic field for increasing values of Hartmann number. Copyright © 2010 John Wiley & Sons, Ltd.     

Stability analysis in spatial mode for channel flow of fiber suspensions

Different from previous temporal evolution assumption, the spatially growing mode was employed to analyze the linear stability for the channel flow of fiber suspensions. The stability equation applicable to fiber suspensions was established and solutions for a wide range of Reynolds number and angular frequency were given numerically . The results show that, the flow instability is governed by a parameter H which represents a ratio between the axial stretching resistance of fiber and the inertial force of the fluid. An increase of H leads to a raise of the critical Reynolds number, a decrease of corresponding wave number, a slowdown of the decreasing of phase velocity , a growth of the spatial attenuation rate and a diminishment of the peak value of disturbance velocity. Although the unstable region is reduced on the whole, long wave disturbances are susceptible to fibers.     

Linear stability analysis of flow in a periodically grooved channel

We have conducted the linear stability analysis of flow in a channel with periodically grooved parts by using the spectral element method. The channel is composed of parallel plates with rectangular grooves on one side in a streamwise direction. The flow field is assumed to be two‐dimensional and fully developed. At a relatively small Reynolds number, the flow is in a steady‐state, whereas a self‐sustained oscillatory flow occurs at a critical Reynolds number as a result of Hopf bifurcation due to an oscillatory instability mode. In order to evaluate the critical Reynolds number, the linear stability theory is applied to the complex laminar flow in the periodically grooved channel by constituting the generalized eigenvalue problem of matrix form using a penalty‐function method. The critical Reynolds number can be determined by the sign of a linear growth rate of the eigenvalues. It is found that the bifurcation occurs due to the oscillatory instability mode which has a period two times as long as the channel period. Copyright © 2003 John Wiley & Sons, Ltd.     

EFFECTS OF TENSOR CLOSURE MODELS AND 3-D ORIENTATION ON THE STABILITY OF FIBER SUSPENSIONS IN A CHANNEL FLOW

IntroductionFlowoffibresuspensionshasbeenveryfamiliarinmanyindustrialfields.Fibreadditivesplayanimportantroleindragreductioninmanytypesofflow[1- 3].Inthesuspensions,somebehavioroftheflowmaybealteredbythefibres.Oneoftheimportantexamplesisthehydrodynamicsta…     

Spontaneous swirling in axisymmetric MHD flows of an ideally conducting fluid with closed streamlines

The region of instability of the Hill-Shafranov viscous MHD vortex with respect to azimuthal axisymmetric perturbations of the velocity field is determined numerically as a function of the Reynolds number and magnetization in a linear formulation. An approximate formulation of the linear stability problem for MHD flows with circular streamlines is considered. The further evolution of the perturbations in the supercritical region is studied using a nonlinear analog model (a simplified initial system of equations that takes into account some important properties of the basic equations). For this model, the secondary flows resulting from the instability are determined. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 40–50, May–June, 2007.     

Magnetohydrodynamic peristaltic flow of a hyperbolic tangent fluid in a vertical asymmetric channel with heat transfer

In the present paper we discuss the magnetohydrodynamic (MHD) peristaltic flow of a hyperbolic tangent fluid model in a vertical asymmetric channel under a zero Reynolds number and long wavelength approximation. Exact solution of the temperature equation in the absence of dissipation term has been computed and the analytical ex- pression for stream function and axial pressure gradient are established. The flow is analyzed in a wave frame of reference moving with the velocity of wave. The expression for pressure rise has been computed numerically. The physical features of pertinent parameters are analyzed by plotting graphs and discussed in detail.     

MHD non-Newtonian micropolar fluid flow and heat transfer in channel with stretching walls

A study is presented for magnetohydrodynamics （MHD） flow and heat transfer characteristics of a viscous incompressible electrically conducting micropolar fluid in a channel with stretching walls. The micropolar model introduced by Eringen is used to describe the working fluid. The transformed self similar ordinary differential equations together with the associated boundary conditions are solved numerically by an algorithm based on quasi-linearization and multilevel discretization. The effects of some physical parameters on the flow and heat transfer are discussed and presented through tables and graphs. The present investigations may be beneficial in the flow and thermal control of polymeric processing.     

On the stability of a thermally stratified conducting fluid under the action of aligned magnetic field

The stability of a thermally stable stratified viscous electrically conducting shear flow is investigated in the presence of an impressed uniform aligned magnetic field. Only two-dimensional disturbances are studied in this paper because Squire's theorem does not apply in general, owing to the presence of the aligned magnetic field. The analysis is partly analytical and partly numerical. The asymptotic solutions for non-viscous fluid are first obtained analytically and they are then improved by introducing viscous and thermal diffusion terms (but only for =1) to get a uniformly valid solution. The neutral stability curves are numerically computed for a range of values of Richardson and Stuart numbers, which show that the flow is completely stabilized when a Stuart number exceeds a certain value for a given R _i>0. It is shown that the combined effects of magnetic field and stratification is to make the system stable to two-dimensional disturbances at lower Stuart number than the one given by Stuart (1954) in the absence of thermal stratification.     

The stability of nonisothermal plasma flow in a flat MHD channel

Papers [1, 2] were devoted to questions of the stability of the laminar flow of a conducting fluid in a transverse magnetic field with Hartmann flow. It was assumed in these papers, however, that the transport coefficients are quantities independent of the flow characteristics; in particular, the temperature and the effect of energy dissipation were not taken into account. When these factors are allowed for it turns out that even for relatively small subsonic velocities, when the medium may be regarded as incompressible, the temperature distribution exerts a considerable influence on the dynamic flow characteristics. Papers [3,4] deal with this type of flow in an MHD channel which will be called nonisothermal in what follows. It has been shown that under specific conditions the velocity profiles are grossly deformed, and non-monotonic profiles with inflection points may even appear.However, the influence of nonisothermal flow on stability is not confined to an alteration of the stability criteria as a result of the change in the velocity profile. When energy dissipation and the fact that the transport coefficients are not constant are taken into account new dissipative instability branches appear, as, for example, the overheat instability [5, 8], This article considers the problem of the hydrodynamic stability of a nonisothermal plasma flow in constant crossed electric and magnetic fields in a flat channel with dielectric walls. The system of equations derived in this paper for the perturbations does, of course, take into account all the instability mechanisms mentioned above, but is difficult to solve. The general system of equations may be investigated in two limiting cases corresponding to the overheat and hydrodynamic instabilities.The author is most grateful to V. Kalitenko for writing the computer programs and to S. Filippov for advice and discussions.     

Lie group analysis of viscoelastic MHD aligned flow and heat transfer

Exact solutions for an incompressible, viscoelastic, electrically conducting MHD aligned fluid are obtained for velocity components and temperature profiles. Lie Group method is applied to obtain the solution and the symmetries used are of translational type.The English text was polished by Keren Wang and Yunming Chen.     

Linear stability of channel entrance flow

The spatial stability of two dimensional, steady channel flow is investigated in the downstream entry zone for both exponentially and algebraically growing disturbances. A model based on previous work is presented for the base flow which represents a small deformation of plane Poiseuille flow. The base flow evolution towards the fully developed state comes from the experimental and theoretical study of M. Asai and J.M. Floryan [M. Asai, J.M. Floryan, Certain aspects of channel entrance flow, Phys. Fluids 16 (2004) 1160–1163]. This flow is found to be more stable than the parabolic Poiseuille flow. The most destabilizing base flow defect is then calculated using a variational method. The compromise between the destabilizing effect of the defect, which diffuses downstream, and the instability growth is found to be insufficient to provoke transition in the downstream laminar flow.     

MHD flow of a viscous fluid on a nonlinear porous shrinking sheet with homotopy analysis method

The present paper investigates the magnetohydrodynamic（MHD） flow of a viscous fluid towards a nonlinear porous shrinking sheet.The governing equations are simplified by similarity transformations.The reduced problem is then solved by the homotopy analysis method.The pertinent parameters appearing in the problem are discussed graphically and presented in tables.It is found that the shrinking solutions exist in the presence of MHD.It is also observed from the tables that the solutions for f（0） with different values of parameters are convergent.     

MHD flow and heat transfer of micropolar fluid between two porous disks

A numerical study is carried out for the axisymmetric steady laminar incompressible flow of an electrically conducting micropolar fluid between two infinite parallel porous disks with the constant uniform injection through the surface of the disks. The fluid is subjected to an external transverse magnetic field. The governing nonlinear equations of motion are transformed into a dimensionless form through von Karman’s similarity transformation. An algorithm based on a finite difference scheme is used to solve the reduced coupled ordinary differential equations under associated boundary conditions. The effects of the Reynolds number, the magnetic parameter, the micropolar parameter, and the Prandtl number on the flow velocity and temperature distributions are discussed. The results agree well with those of the previously published work for special cases. The investigation predicts that the heat transfer rate at the surfaces of the disks increases with the increases in the Reynolds number, the magnetic parameter, and the Prandtl number. The shear stresses decrease with the increase in the injection while increase with the increase in the applied magnetic field. The shear stress factor is lower for micropolar fluids than for Newtonian fluids, which may be beneficial in the flow and thermal control in the polymeric processing.     

Gas-Dynamic Processes in Two-Phase Flows in MHD Generators

A plane problem of a two-phase monodisperse flow of combustion products of plasma-forming composite solid propellants in the duct of a Faraday's MHD generator with continuous electrodes, including an accelerating nozzle, MHD channel, and diffuser, is considered. An algorithm based on the pseudo-transient method is developed to solve the system of equations describing the two-phase flow. Gas-dynamic processes in the channels of the Pamir-1 setup are numerically studied. It is shown that shock-free deceleration of a supersonic flow to velocities close to the equilibrium velocity of sound in a two-phase mixture and significantly lower than the velocity of sound in the gas is possible in two-phase flows.     

Magnetohydrodynamic flow in an infinite channel

The magnetohydrodynamic (MHD) flow of an incompressible, viscous, electrically conducting fluid in an infinite channel, under an applied magnetic field has been investigated. The MHD flow between two parallel walls is of considerable practical importance because of the utility of induction flowmeters. The walls of the channel are taken perpendicular to the magnetic field and one of them is insulated, the other is partly insulated, partly conducting. An analytical solution has been developed for the velocity field and magnetic field by reducing the problem to the solution of a Fredholm integral equation of the second kind, which has been solved numerically. Solutions have been obtained for Hartmann numbers M up to 200. All the infinite integrals obtained are transformed to finite integrals which contain modified Bessel functions of the second kind. So, the difficulties associated with the computation of infinite integrals with oscillating integrands which arise for large M have been avoided. It is found that, as M increases, boundary layers are formed near the nonconducting boundaries and in the interface region for both velocity and magnetic fields, and a stagnant region in front of the conducting boundary is developed for the velocity field. Selected graphs are given showing these behaviours.