Effects of rotation and magnetic field on the nonlinear peristaltic flow of a second-order fluid in an asymmetric channel through a porous medium

In this paper, the effects of both rotation and magnetic field of the peristaltic transport of a second-order fluid through a porous medium in a channel are studied analytically and computed numerically. The material is represented by the constitutive equations for a second-order fluid. Closed-form solutions under the consideration of long wavelength and low Reynolds number is presented. The analytical expressions for the pressure gradient, pressure rise, friction force, stream function, shear stress, and velocity are obtained in the physical domain. The effects of the non-dimensional wave amplitude, porosity, magnetic field, rotation, and the dimensionless time-mean flow in the wave frame are analyzed theoretically and computed numerically. Numerical results are given and illustrated graphically in each case considered. Comparison was made with the results obtained in the presence and absence of rotation, magnetic field, and porosity. The results indicate that the effects of the non-dimensional wave amplitude, porosity, magnetic field, rotation, and the dimensionless time-mean flow are very pronounced in the phenomena.     

MHD flow study of viscous fluid through a complex wavy curved surface due to biomimetic propulsion under porosity and second-order slip effects

The steady laminar flow of viscous fluid from a curved porous domain under a radial magnetic field is considered. The fluid flow by a curved domain is due to peristaltic waves present at the boundary walls. The whole analysis is based on porosity(Darcy number) effects. Moreover, the effects of second-order slip on the rheology analysis are also discussed. Due to the complex nature of the flow regime, we have governed the rheological equations by using curvilinear coordinates in the fixed frame. The physical influence of magnetic(Hartmann number) and porosity(Darcy number)parameters on the rheological features of peristaltic transportation are argued in detailed(in the wave frame). Additionally, in the current study, the complex wavy pattern on both boundary walls of the channel is used. The whole rheological study is based on ancient, but medically valid,assumptions of creeping phenomena and long wavelength assumptions. Analytical solutions of the governing equations are obtained by using the simple integration technique in Mathematica software 11.0. The core motivation of the present analysis is to perceive the physical influence of embedded parameters, such as the dimensionless radius of the curvature parameter, magnetic parameter, porosity parameter, different amplitude ratios of complex peristaltic waves, first-and second-order slip parameters, on the axial velocity, pressure gradient, local wall shear stress,tangential component of the extra-stress tensor, pumping and trapping phenomena.     

Heat transfer in MHD flow of dusty viscoelastic (Walters’ liquid model-B) stratified fluid in porous medium under variable viscosity

The paper investigates the effects of heat transfer in MHD flow of viscoelastic stratified fluid in porous medium on a parallel plate channel inclined at an angle θ. A laminar convection flow for incompressible conducting fluid is considered. It is assumed that the plates are kept at different temperatures which decay with time. The partial differential equations governing the flow are solved by perturbation technique. Expressions for the velocity of fluid and particle phases, temperature field, Nusselt number, skin friction and flow flux are obtained within the channel. The effects of various parameters like stratification factor, magnetic field parameter, Prandtl number on temperature field, heat transfer, skin friction, flow flux, velocity for both the fluid and particle phases are displayed through graphs and discussed numerically.     

Hydromagnetic Blood Flow of Sisko Fluid in a Non-uniform Channel Induced by Peristaltic Wave

In this paper, a smooth repetitive oscillating wave traveling down the elastic walls of a non-uniform twodimensional channels is considered. It is assumed that the fluid is electrically conducting and a uniform magnetic field is perpendicular to flow. The Sisko fluid is grease thick non-Newtonian fluid can be considered equivalent to blood. Taking long wavelength and low Reynolds number, the equations are reduced. The analytical solution of the emerging non-linear differential equation is obtained by employing Homotopy Perturbation Method(HPM). The outcomes for dimensionless flow rate and dimensionless pressure rise have been computed numerically with respect to sundry concerning parameters amplitude ratio ?, Hartmann number M, and Sisko fluid parameter b1. The behaviors for pressure rise and average friction have been discussed in details and displayed graphically. Numerical and graphical comparison of Newtonian and non-Newtonian has also been evaluated for velocity and pressure rise. It is observed that the magnitude of pressure rise is maximum in the middle of the channel whereas for higher values of fluid parameter it increases. Further, it is also found that the velocity profile shows converse behavior along the walls of the channel against multiple values of fluid parameter.     

The influence of heat transfer and magnetic field on peristaltic transport of a Newtonian fluid in a vertical annulus: Application of an endoscope

This Letter discusses the influence of heat transfer and magnetic field on the peristaltic flow of Newtonian fluid in a vertical annulus under a zero Reynolds number and long wavelength approximation. The inner tube is uniform, rigid, while the outer tube has a sinusoidal wave traveling down its wall. The flow is investigated in a wave frame of reference moving with velocity of the wave. Numerical calculations are carried out for the pressure rise and frictional forces. The features of the flow characteristics are analyzed by plotting graphs and discussed in detail.     

Non-linear peristaltic transport of a Newtonian fluid in an inclined asymmetric channel through a porous medium

Peristaltic transport of an incompressible viscous fluid in an inclined asymmetric channel through a porous medium is studied under long-wavelength and low-Reynolds number assumptions. The flow is examined in a wave frame of reference moving with the velocity of the wave. The analytical solution has been obtained in the form of a stream function from which the axial velocity and pressure gradient have been derived. The results for the pressure drop and shear stress have also been computed numerically. The effects of various physical parameters are discussed through graphs and the phenomenon of trapping is also discussed. Comparison of various wave forms (namely sinusoidal, triangular, square and trapezoidal) on the flow is discussed.     

Existence of a Hartmann layer in the peristalsis of Sisko fluid

Analytical solutions for the peristaltic flow of a magneto hydrodynamic(MHD) Sisko fluid in a channel, under the effects of strong and weak magnetic fields, are presented. The governing nonlinear problem, for the strong magnetic field,is solved using the matched asymptotic expansion. The solution for the weak magnetic field is obtained using a regular perturbation method. The main observation is the existence of a Hartman boundary layer for the strong magnetic field at the location of the two plates of the channel. The thickness of the Hartmann boundary layer is determined analytically. The effects of a strong magnetic field and the shear thinning parameter of the Sisko fluid on the velocity profile are presented graphically.     

Simultaneous effects of magnetic field and space porosity on compressible Maxwell fluid transport induced by a surface acoustic wave in a microchannel

Peristaltic motion induced by a surface acoustic wave of a viscous, compressible and electrically conducting Maxwell fluid in a confined parallel-plane microchannel through a porous medium is investigated in the presence of a constant magnetic field. The slip velocity is considered and the problem is discussed only for the free pumping case. A perturbation technique is employed to analyze the problem in terms of a small amplitude ratio. The phenomenon of a “backward flow” is found to exist in the center and at the boundaries of the channel. In the second order approximation, the net axial velocity is calculated for various values of the fluid parameters. Finally, the effects of the parameters of interest on the mean axial velocity, the reversal flow, and the perturbation function are discussed and shown graphically. We find that in the non-Newtonian regime, there is a possibility of a fluid flow in the direction opposite to the propagation of the traveling wave. This work is the most general model of peristalsis created to date with wide-ranging applications in biological, geophysical and industrial fluid dynamics.     

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     

Parallel flow in hele-shaw cells with ferrofluids

Parallel flow in a Hele-Shaw cell occurs when two immiscible liquids flow with relative velocity parallel to the interface between them. The interface is unstable due to a Kelvin-Helmholtz type of instability in which fluid flow couples with inertial effects to cause an initial small perturbation to grow. Large amplitude disturbances form stable solitons. We consider the effects of applied magnetic fields when one of the two fluids is a ferrofluid. The dispersion relation governing mode growth is modified so that the magnetic field can destabilize the interface even in the absence of inertial effects. However, the magnetic field does not affect the speed of wave propogation for a given wave number. We note that the magnetic field creates an effective interaction between the solitons.     

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.     

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.     

Effect of the induced magnetic field on peristaltic flow of a couple stress fluid

We have analyzed the MHD flow of a conducting couple stress fluid in a slit channel with rhythmically contracting walls. In this analysis we are taking into account the induced magnetic field. Analytical expressions for the stream function, the magnetic force function, the axial pressure gradient, the axial induced magnetic field and the distribution of the current density across the channel are obtained using long wavelength approximation. The results for the pressure rise, the frictional force per wave length, the axial induced magnetic field and distribution of the current density across the channel have been computed numerically and the results were studied for various values of the physical parameters of interest, such as the couple stress parameter γ, the Hartmann number M, the magnetic Reynolds number Rm and the time averaged mean flow rate θ. Contour plots for the stream and magnetic force functions are obtained and the trapping phenomena for the flow field is discussed.     

On the possibility of natural formation of a transverse wave with a phase velocity lower than the velocity of light

The formation of a transverse wave with a phase velocity lower than the velocity of light, which can exist in an equilibrium plasma without a slow-wave structure in zero magnetic field, is described. It involves the transformation of a transverse wave with trapped electrons, traveling along the magnetic field, into a slow transverse wave after the removal of the magnetic field. During the evolution of the wave with trapped electrons, the magnetic induction decreases very slowly in the direction of the wave propagation. As a result, the velocity at which electrons are in resonant interaction with the wave increases; therefore, the electrons fall to the bottom of potential wells. Under the influence of the trapped electrons, the phase velocity of the wave decreases and becomes lower than the velocity of light. It becomes equal to the velocity at which the electrons are in resonance interaction with the wave at the instant when the magnetic field vanishes. It is demonstrated that a transverse wave with a velocity lower than the velocity of light can exist in an equilibrium plasma even after the magnetic field vanishes; in this case, the flow of trapped electrons serves as a slow-wave structure.     

Wave propagation in viscoelastic single-walled carbon nanotubes with surface effect under magnetic field based on nonlocal strain gradient theory

The governing equation of wave motion of viscoelastic SWCNTs (single-walled carbon nanotubes) with surface effect under magnetic field is formulated on the basis of the nonlocal strain gradient theory. Based on the formulated equation of wave motion, the closed-form dispersion relation between the wave frequency (or phase velocity) and the wave number is derived. It is found that the size-dependent effects on the phase velocity may be ignored at low wave numbers, however, is significant at high wave numbers. Phase velocity can increase by decreasing damping or increasing the intensity of magnetic field. The damping ratio considering surface effect is larger than that without considering surface effect. Damping ratio can increase by increasing damping, increasing wave number, or decreasing the intensity of magnetic field.     

Operation of microsecond plasma opening switches

Closing and breaking of current in microsecond megaampere plasma opening switches are considered. Conductivity current scaling in the switch due to plasma acceleration by a magnetic piston is discussed and compared with experimental data. Two ways of determining the width of a current channel are taken up. This channel results from the diffusion of the magnetic field in the plane of the piston followed by the convective ejection of the field “frozen” in the accelerated plasma flow behind the shock wave into the bridge. Based on experimental data, a scaling law for the voltage on the switch according to the switch parameters is derived. The problem of reverse closing, which limits the efficiency of storage energy extraction into the load, is considered.     

对称槽道涡波流场流动特征的POD分析

为深入分析层流状态下对称槽道内涡波流场的流动特性及其变化规律,对流场进行了二维粒子图像测速(2DPIV)测量获取瞬态速度矢量数据,利用本征正交分解(POD)技术进行模态分解以及涡波流场的重构,然后根据重构的流场对对称槽道内涡波流场进行了平均速度剖面、流场脉动强度以及特征点的速度和频谱分布等方面的分析。结果表明:POD的前15阶模态能够表征涡波流场的主导结构,第1,3阶模态主要表现为一对旋向相反的涡对特征,第2阶模态具有涡旋和波状主流的特征;提取了5个涡旋涡核的位置作为流场流动特性的特征点;根据POD重构流场分析发现流向平均速度呈抛物线形状分布,法向平均速度呈对称分布特征;流向脉动强度受壁面的影响较大,法向脉动强度呈现抛物线形状分布;距离中心主流较近的1#,4#,5#特征点的速度脉动程度受主流的脉动强度影响较大,速度的脉动主频0.15 Hz与次频、流场的自然频率0.35 Hz共同影响特征点的速度分布;2#,3#特征点的流向速度呈衰减趋势,法向速度在初期幅度变化较大。     

Magnetic field rotation in the screw gallium flow

The magnetic field induced by the nonstationary screw flow of gallium in a toroidal channel has been investigated experimentally using a gallium prototype of the sodium apparatus developed in the frame of the experimental dynamo program at the Institute of Continuous Media Mechanics, Perm, Russia. The experimental set-up is a rapidly rotating toroidal channel subjected to abrupt braking. The screw flow is initiated by inertial forces pushing liquid gallium through diverters. The regular structure of the induced magnetic field is generated about 0.1 s after the stop of the channel and persists up to 1 s. The induced field is measured by sensors placed outside the channel. The inductive effects observed are attributed to the mean screw flow. The decay laws of the induced regular magnetic field and turbulent magnetic fluctuations are studied.Received: 27 August 2004, Published online: 5 November 2004PACS: 47.65. + a Magnetohydrodynamics and electrohydrodynamics - 07.55.Dd Generation of magnetic fields     

Flow of a Bose-Einstein condensate in a quasi-one-dimensional channel under the action of a piston

The problem of the flow of a Bose—Einstein condensate in a channel under the action of a piston is considered. Problems of this kind are topical in connection with experiments on condensate flow control in quasi-one-dimensional (cigar-shaped) traps, in wh ich the repulsive potential produced by a laser beam focused across the trap acts as a piston. A dispersive shock wave characterized by rapid oscillations of the condensate density and flow velocity is shown to be formed in the condensate flow after some instant of time for an arbitrary law of piston motion. The Whitham averaging method is used to obtain a solution for the main parameters of the dispersive shock wave in the case of a uniformly accelerated piston motion. The evolution of the dispersive shock wave immediately after the breaking time, when the dispersionless solution is well approximated by a cubic parabola for the coordinate dependence of the density, is analyzed in the case of an arbitrary piston motion. Comparison shows good agreement of the numerical calculation with the approximate analytical theory. The developed theory complements the previously considered case of a piston moving with a constant velocity and is important for describing the condensate transport in atomic chips.