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.     

Velocity profile measurement of the Taylor vortex flow of a magnetic fluid using the ultrasonic Doppler method

 A successful application of the ultrasound velocity profile (UVP) measuring technique to investigations on the flow of magnetic fluids is described. The flow structure of a magnetic fluid in a concentric annular geometry with a large aspect ratio of 20 and a radius ratio of 0.65 was investigated for a inner cylinder rotation. Axial velocity distributions were measured using the UVP measuring technique. A non-uniform magnetic field was applied to the flow field using a permanent magnet located on the outside of the cylinders. The energy spectral density was calculated from the periodic axial velocity profiles. The critical Reynolds number was obtained for various magnetic field strengths, and the apparent viscosity caused by the applied magnetic field was estimated. The UVP method was demonstrated to provide useful information on the structure of Taylor vortex flow in a magnetic fluid. Received: 27 May 1997/Accepted: 21 July 1998     

Interfacial instabilities in a stratified flow of two superposed fluids

Here we shall present a linear stability analysis of a laminar, stratified flow of two superposed fluids which are a clear liquid and a suspension of solid particles. The investigation is based upon the assumption that the concentration remains constant within the suspension layer. Even for moderate flow-rates the base-state results for a shear induced resuspension flow justify the latter assumption. The numerical solutions display the existence of two different branches that contribute to convective instability: long and short waves which coexist in a certain range of parameters. Also, a range exists where the flow is absolutely unstable. That means a convectively unstable resuspension flow can be only observed for Reynolds numbers larger than a lower, critical Reynolds number but still smaller than a second critical Reynolds number. For flow rates which give rise to a Reynolds number larger than the second critical Reynolds number, the flow is absolutely unstable. In some cases, however, there exists a third bound beyond that the flow is convectively unstable again. Experiments show the same phenomena: for small flow-rates short waves were usually observed but occasionally also the coexistence of short and long waves. These findings are qualitatively in good agreement with the linear stability analysis. Larger flow-rates in the range of the second critical Reynolds number yield strong interfacial waves with wave breaking and detached particles. In this range, the measured flow-parameters, like the resuspension height and the pressure drop are far beyond the theoretical results. Evidently, a further increase of the Reynolds number indicates the transition to a less wavy interface. Finally, the linear stability analysis also predicts interfacial waves in the case of relatively small suspension heights. These results are in accordance with measurements for ripple-type instabilities as they occur under laminar and viscous conditions for a mono-layer of particles.     

Stability of plane-parallel MHD flows in transverse magnetic field

We study within the framework of linear theory the stability of plane-parallel flows of a viscous, electrically conducting fluid in a transverse magnetic field. The magnetic Reynolds numbers are assumed small. The critical Reynolds number as a function of the Hartmann number is obtained over the entire range of variation of the latter. The small perturbation spectrum is studied in detail on the example of Hartmann flow. Neutral curves are constructed for symmetric and antisymmetric disturbances. The destablizing effect of a magnetic field is studied in the case of modified Couette flow. The results obtained agree with the calculations of Lock and Kakutani (where they meet) and are at variance with the results of Pavlov.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 11, No. 3, pp. 127–131, May–June, 1970.The authors wish to thank M. A. Gol'dshtik for his interest in this study.     

Stability of Poiseuille flow in the presence of a longitudinal magnetic field

The stability of the plane flow of an electrically conducting fluid with respect to small perturbations was studied at large Reynolds numbers in the presence of a longitudinal magnetic field. The dependence of the critical Reynolds number on the electrical conductivity is investigated. At large Reynolds numbers, a new branch of instability and a sudden change in the critical Reynolds numbers is found. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 45–53, May–June, 2008.     

Pulsatile magneto-biofluid flow and mass transfer in a non-Darcian porous medium channel

A numerical study of pulsatile flow and mass transfer of an electrically conducting Newtonian biofluid via a channel containing porous medium is considered. The conservation equations are transformed and solved under boundary conditions prescribed at both walls of the channel, using a finite element method with two-noded line elements. The influence of magnetic field on the flow is studied using the dimensionless hydromagnetic number, Nm, which defines the ratio of magnetic (Lorentz) retarding force to the viscous hydrodynamic force. A Darcian linear impedance for low Reynolds numbers is incorporated in the transformed momentum equation and a second order drag force term for inertial (Forchheimer) effects. Velocity and concentration profiles across the channel width are plotted for various values of the Reynolds number (Re), Darcy parameter (λ), Forchheimer parameter (Nf), hydro-magnetic number (Nm), Schmidt number (Sc) and also with dimensionless time (T). Profiles of velocity varying in space and time are also provided. The conduit considered is rigid with a pulsatile pressure applied via an appropriate pressure gradient term. Increasing the hydromagnetic number (Nm) from 1 to 15 considerably depresses biofluid velocity (U) indicating that a magnetic field can be used as a flow control mechanism in, for example, medical applications. A rise in Nf from 1 to 20 strongly retards the flow development and decreases the velocity, U, across the width of the channel. The effects of other parameters on the flowfield are also discussed at length. The flow model also has applications in the analysis of electrically conducting haemotological fluids flowing through filtration media, diffusion of drug species in pharmaceutical hydromechanics, and also in general fluid dynamics of pulsatile systems.     

Effects of shear-thinning/thickening nature on the stability of Couette-like flow with uniform crossflow

The linear stability of wall-injected pressure- driven Couette-like flow in power-law fluids is studied. Previous study on this kind of flow for Newtonian fluids by Nicoud and Angilella [Phys. Rev. E 56, 3000 （1997）] was extended to power-law fluids to understand the effects of shear-thinning/thickening nature on the flow stability. A related expression between the critical crossflow Reynolds number for Newtonian fluids and that for power-law fluids is obtained as the streamwise Reynolds number is large enough based on numerical computations, and verified theoretically in the case of a limiting condition with the power-law index.     

Frottements et pertes de pression des fluides non newtoniens dans des conduites non circulaires

The study of fluid flow in a duct requires characteristic parameters of the flow and dimensionless numbers to correlate and compare experimental results. For Newtonian fluids in simple configurations, the definition of the Reynolds number is quite standard, but for non-Newtonian fluid flows in ducts with arbitrary shape of cross section, the dependence of the apparent viscosity with the shear rate requires a generalization of this dimensionless number. This note proposes a general method valid for a large class of non-Newtonian fluids and for all duct shapes. An application is developed for a viscoelastic flow through a rectangular duct. Results obtained in the present investigation are in a good agreement with available correlations. To cite this article: M. Mahfoud et al., C. R. Mecanique 333 (2005).     

Steady plane-parallel flow of a magnetic fluid

In the hydrodynamics of a Newtonian fluid, nonlinear effects are connected only with the presence of convective derivatives in the equations and therefore disappear when plane-parallel flows are considered. Non-Newtonian effects are usually taken into account either phenomenologically in the expression for the stress tensor or by explicitly considering additional degrees of freedom. A theory of the effective viscosity of a magnetic fluid is constructed in [1] by regarding a magnetic fluid as a medium with internal rotation. It was shown that the flow of fluid in a magnetic field is non-Newtonian. Later, many authors (see, for example, [2, 3]) studied one- and two-dimensional flows under the influence of a pressure difference. However, the study was usually limited to continuous and smooth solutions. In the present work, we study the plane-parallel flow of a magnetic fluid in a homogeneous magnetic field under the influence of a longitudinal pressure gradient. We also consider discontinuous solutions. It is shown that for large longitudinal pressure gradients and sufficiently great intensities of the magnetic field, the problem has an infinite number of steady solutions which differ in the number and position of discontinuities of the magnetization and the associated abrupt changes in the velocity profile. Steady regimes and their stability are studied numerically with allowance for weak diffusion of magnetization and internal angular momentum. It is shown that the degeneracy is then lifted; however, in a certain region of parameters several stable steady regimes still exist.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 57–64, November–December, 1984.The authors would like to thank M. I. Shliomis for his constant interest in this work.     

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.     

Laminar unsteady magnetohydrodynamic flow in an annular channel under a radial magnetic field

Summary The paper discusses the unsteady flow of an electrically conducting viscous fluid in the region between two coaxial cylinders in the presence of a radial magnetic field emanating from the common axis in planes perpendicular to it. In the special case when the magnetic Reynolds number of the flow is the same as its Reynolds number, an exact solution in terms of Bessel functions has been obtained which after infinite time tends to the steady flow discussed by Globe.     

Electromagnetohydrodynamic flows and mass transport in curved rectangular microchannels

Curved microchannels are often encountered in lab-on-chip systems because the effective axial channel lengths of such channels are often larger than those of straight microchannels for a given per unit chip length. In this paper, the effective diffusivity of a neutral solute in an oscillating electromagnetohydrodynamic(EMHD)flow through a curved rectangular microchannel is investigated theoretically. The flow is assumed as a creeping flow due to the extremely low Reynolds number in such microflow systems. Through the theoretical analysis, we find that the effective diffusivity primarily depends on five dimensionless parameters, i.e., the curvature ratio of the curved channel, the Schmidt number, the tidal displacement, the angular Reynolds number, and the dimensionless electric field strength parameter. Based on the obtained results, we can precisely control the mass transfer characteristics of the EMHD flow in a curved rectangular microchannel by appropriately altering the corresponding parameter values.     

Magnetorheology in an aging, yield stress matrix fluid

Field-induced static and dynamic yield stresses are explored for magnetorheological (MR) suspensions in an aging, yield stress matrix fluid composed of an aqueous dispersion of Laponite? clay. Using a custom-built magnetorheometry fixture, the MR response is studied for magnetic field strengths up to 1?T and magnetic particle concentrations up to 30?v%. The yield stress of the matrix fluid, which serves to inhibit sedimentation of dispersed carbonyl iron magnetic microparticles, is found to have a negligible effect on the field-induced static yield stress for sufficient applied fields, and good agreement is observed between field-induced static and dynamic yield stresses for all but the lowest field strengths and particle concentrations. These results, which generally imply a dominance of inter-particle dipolar interactions over the matrix fluid yield stress, are analyzed by considering a dimensionless magnetic yield parameter that quantifies the balance of stresses on particles. By characterizing the applied magnetic field in terms of the average particle magnetization, a rheological master curve is generated for the field-induced static yield stress that indicates a concentration–magnetization superposition. The results presented herein will provide guidance to formulators of MR fluids and designers of MR devices who require a field-induced static yield stress and a dispersion that is essentially indefinitely stable to sedimentation.     

Effect of magnetic Reynolds number on the two‐dimensional hydromagnetic flow around a cylinder

Numerical experiments have been conducted to study the effect of magnetic Reynolds number on the steady, two‐dimensional, viscous, incompressible and electrically conducting flow around a circular cylinder. Besides usual Reynolds number Re, the flow is governed by the magnetic Reynolds number R_m and Alfvén number β. The flow and magnetic field are uniform and parallel at large distances from the cylinder. The pressure Poisson equation is solved to find the pressure fields in the entire flow region. The effects of the magnetic field and electrical conductivity on the recirculation bubble, drag coefficient, standing vortex and pressure are presented and discussed. For low interaction parameter (N<1), the suppression of the flow‐separation is nearly independent of the conductivity of the fluid, whereas for large interaction parameters, the conductivity of the fluid strongly influences the control of flow‐separation. Copyright © 2008 John Wiley & Sons, Ltd.     

Two-layer flow of magnetic fluids

The plane two-layer flow of viscous incompressible fluids with differentmagnetic properties between two horizontal rigid planes in a nonuniform traveling magnetic field is investigated. An arbitrary nonuniform periodic traveling magnetic field generates wavelike changes in the interface between the media and fluid flows with nonzero flow rates. From the given magnetic field the interface shape and the velocities, pressures and mean flow rates of the fluids are calculated. The cases of a cosine magnetic force and of the magnetic field created by ferromagnetic cylinders moving in a uniform magnetic field are considered. The effect of various parameters on the mean flow rates of the fluids is investigated.     

A thermal LBM-LES model in body-fitted coordinates: Flow and heat transfer around a circular cylinder in a wide Reynolds number range

In order to apply the lattice Boltzmann method (LBM) for modeling passive heat transfer at high Reynolds numbers, a number of models were proposed by introducing the large eddy simulation (LES) into the LBM framework to improve numerical stability. Our study finds that the generalized form of interpolation-supplemented LBM (GILBM), likewise, can locally modify the dimensionless relaxation time, thus enhancing the numerical stability at high Reynolds numbers. Given additional advantages of the GILBM in dealing with complicated geometries and improving computing accuracy, a thermal LBM-LES model in body-fitted coordinates is established in this paper. Numerical validation is performed by investigating the flow and heat transfer around a circular cylinder over a wide range of Reynolds numbers. The obtained results agree well with both experimental and numerical data in the previous work. Meanwhile, the effects of Reynolds number and Prandtl number on thermodynamic features of flow past a circular cylinder are revealed. It is found out that when the Reynolds number exceeds the critical value, the local Nusselt number fluctuates rapidly in a specific region of the rear cylinder surface affected by the Prandtl number. In the near-wake region, the temperature field exhibits significant dependence on the Prandtl number at moderate Reynolds numbers, while such effects turn to be slight at high Reynolds numbers.     

Instabilities of a gas-liquid flow between two inclined plates analyzed using the Navier–Stokes equations

The paper is devoted to a theoretical analysis of a counter-current gas-liquid flow between two inclined plates. We linearized the Navier–Stokes equations and carried out a stability analysis of the basic steady-state solution over a wide variation of the liquid Reynolds number and the gas superficial velocity. As a result, we found two modes of the unstable disturbances and computed the wavelength and phase velocity of their neutral disturbances varying the liquid and gas Reynolds number. The first mode is a “surface mode” that corresponds to the Kapitza's waves at small values of the gas superficial velocity. We found that the dependence of the neutral disturbance wavelength on the liquid Reynolds number strongly depends on the gas superficial velocity, the distance between the plates and the channel inclination angle for this mode. The second mode of the unstable disturbances corresponds to the transition to a turbulent flow in the gas phase and there is a critical value of the gas Reynolds number for this mode. We obtained that this critical Reynolds number weakly depends on both the channel inclination angle, the distance between the plates and the liquid flow parameters for the conditions considered in the paper. Despite a thorough search, we did not find the unstable modes that may correspond to the instability in frame of the viscous (or inviscid) Kelvin–Helmholtz heuristic analysis.     

Stability of a perturbed conducting gas flow in a magnetic field for arbitrary magnetic Reynolds numbers

A numerical calculation is made which describes the conversion into a T-layer of a finite perturbation in electrical conductivity imposed on a one-dimensional supersonic flow of a compressible medium for a finite value of the magnetic Reynolds number. The development of the injected perturbation is significantly affected by the magnetic Reynolds number of the unperturbed flow, and to each value of this number there corresponds a particular boundary region in which the perturbation is taken up by the magnetic field into an induced T-layer. The stability is investigated in the linear approximation for a minimal perturbation, and the dispersion equation is solved with allowance for gradients in the unperturbed parameters. It is shown that an overheating instability can arise in the system and lead to the formation of a T-layer.Translated from Zhurnal Prikladnoi Mekhaniki i Teknicheskoi Fiziki, No. 3, pp. 3–9, May–June, 1973.The authors thank L. M. Degtyarev, L. A. Zaklyaz'minskii, and A. P. Favorskii for useful discussions and advice during the completion of this work.     

Application of a non-linear local analysis method for the problem of mixed convection instability

We consider the problem of laminar mixed convection flow between parallel, vertical and uniformly heated plates where the governing dimensionless parameters are the Prandtl, Rayleigh and Reynolds numbers. Using the method based on the centre manifold theorem which was derived from the general theory of dynamical systems, we reduce a three-dimensional simplified model of ordinary differential amplitude equations emanating from the original Navier-Stokes system of the problem in the vicinity of a trivial stationary solution. We have found that when the forcing parameter, the Rayleigh number, increases beyond the critical value Ra_s, the stationary solution is a pitchfork bifurcation point of the system.