Effect of Deborah number and phase difference on peristaltic transport of a third-order fluid in an asymmetric channel

The effect of a third-order fluid on the peristaltic transport in an asymmetric channel is studied. The wavelength of the peristaltic waves is assumed to be large compared to the varying channel width, whereas the wave amplitudes need not be small compared to the varying channel width. The channel asymmetry is produced by choosing the peristaltic wave train on the walls to have different amplitudes and phase. The flow is investigated in a wave frame of reference moving with velocity of the wave. The effects of Deborah number, phase difference, varying channel width and wave amplitudes on the pumping characteristics, streamline pattern and trapping phenomena are investigated. It is observed that the trapping regions increase as the channel becomes more and more symmetric and the trapped bolus volume decreases for increasing Deborah number, phase difference and varying channel width whereas it increases for increasing flow rate and wave amplitudes. Furthermore, the obtained results could also have applications to a range of peristaltic flows for a variety of non-Newtonian fluids such as aqueous solutions of high-molecular weight polyethylene oxide and polyacrylamide.     

Effect of variable viscosity on the peristaltic transport of a Newtonian fluid in an asymmetric channel

The effect of variable viscosity on the peristaltic flow of a Newtonian fluid in an asymmetric channel has been discussed. Asymmetry in the flow is induced due to travelling waves of different phase and amplitude which propagate along the channel walls. A long wavelength approximation is used in the flow analysis. Closed form analytic solutions for velocity components and longitudinal pressure gradient are obtained. The study also shows that, in addition to the effect of mean flow parameter, the wave amplitude also effect the peristaltic flow. This effect is noticeable in the pressure rise and frictional forces per wavelength through numerical integration.     

Non-linear peristaltic transport of a second-order fluid through a porous medium

The present paper investigates phenomena brought about into the classic peristaltic mechanism by inclusion of non-Newtonian effects through a porous space in a channel. The peristaltic motion of a second-order fluid through a porous medium was studied for the case of a planar channel with harmonically undulating extensible walls. The system of the governing nonlinear PDE is solved by using the perturbation method to second-order in dimensionless wavenumber. The analytic solution has been obtained in the form of a stream function from which the axial pressure gradient has been derived. 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 force. The features of the flow characteristics are analyzed by plotting graphs and discussed in detail.     

Influence of induced magnetic field on peristaltic flow in an annulus

This paper looks at the influence of the induced magnetic field on peristaltic transport through a uniform infinite annulus filled with an incompressible viscous and Newtonian fluid. The present theoretical model may be considered as mathematical representation to the movement of conductive physiological fluids in the presence of the endoscope tube (or catheter tube). The inner tube is uniform, rigid, while the outer tube has a sinusoidal wave traveling down its wall. The flow analysis has been developed for low Reynolds number and long wave length approximation. Exact solutions have been established for the axial velocity, stream function, axial induced magnetic field, current distribution and the magnetic force function. The effects of pertinent parameters on the pressure rise and frictional forces on the inner and outer tubes are investigated by means of numerical integrations, also we study the effect of these parameters on the pressure gradient, axial induced magnetic field and current distribution. The phenomena of trapping is further discussed.     

Influence of temperature dependent viscosity on peristaltic transport of a Newtonian fluid: Application of an endoscope

The effects of variable temperature dependent viscosity on peristaltic flow of Newtonian fluid in an annulus has been investigated with long wave length approximations. A regular perturbation method has been used to obtain explicit form for the velocity, temperature and relation between flow rate and pressure gradient. The expression for the pressure rise, friction force, velocity and temperature were plotted for different values of variable viscosity parameter β, radius ratio, amplitude ratio ?, heat absorption parameter β₁, and force convection parameter G_r. It is found that the pressure rise decrease as the viscosity parameter β increases and increases as the radius ratio as ? increases and β decreases.     

Effect of induced magnetic field on peristaltic transport of a Carreau fluid

Magnetohydrodynamic (MHD) peristaltic flow of a Carreau fluid in a channel with different wave forms are analyzed in this investigation. The flow analysis is conducted in the presence of an induced magnetic field. Long wavelength approach is adopted. Mathematical expressions of stream function, magnetic force function and an axial induced magnetic field are constructed. Pressure rise and pumping phenomena are described.     

Effects of Poiseuille flow on peristaltic transport of a particulate suspension

The problem of peristaltic transport induced by sinusoidal waves of a particle-fluid mixture in the presence of a Poiseuille flow, is analysed. The governing equations of motion resulting from the Navier-Stokes equations for both the fluid and particle phases are solved and closed form solutions are obtained for limiting values of Reynolds number, wave number and the Poiseuille flow parameter while the method of Frobenius series solution is used for the general case. It is found that the mean flow is strongly dependent on the Poiseuille flow parameter. The effects of particle concentration in the fluid is well discharged throughout the analysis and the results are compared with the other studies in the literature.     

Influence of heat transfer on a peristaltic transport of Herschel–Bulkley fluid in a non-uniform inclined tube

Peristaltic transport in a two-dimensional non-uniform tube filled with Herschel–Bulkley fluid is studied under the assumptions of long wavelength and low Reynold number. The fluid flow is investigated in the wave frame of reference moving with the velocity of the peristaltic wave. Exact solution for the velocity field, the temperature profile, the stream functions and the pressure gradient are obtained. The physical behavior of τ, n, α and on the pressure rise versus flow rate are discussed through graphs. At the end of the article trapping phenomena for Herschel–Bulkley and also for Newtonian, Bingham and power law (which are the special cases of Herschel–Bulkley fluid) fluid are discussed.     

计及Hall和离子滑移电流的旋转流体在与时间相关初值条件下的MHDCouette流动

考虑Hall和离子滑移电流的影响,在旋转系统中研究导电流体非稳定的MHD Couette流动．在小数值磁场Reynolds数假定下,推导出基本的控制方程,使用著名的Laplace变换技术,数值地求解该基本方程．分两种情况:磁场相对于流体或者移动平板固定时,得到速度和表面摩擦力统一的闭式表达式．用图形讨论了问题的不同参数,对速度和表面摩擦力的影响．所得结果显示,主流速度u和次生速度v随着Hall电流而增大．离子滑移电流的增大,也会导致主流速度u的增大,但会使次生速度v减小．还给出了旋转、Hall和离子滑移参数的综合影响,确定了次生运动对流体流动的贡献．     

Impact of boundary conditions on entrainment and transport in gravity currents

Gravity currents have been studied numerically and experimentally both in the laboratory and in the ocean. The question of appropriate boundary conditions is still challenging for most complex flows. Gravity currents make no exception—appropriate, physically and mathematically sound boundary conditions are yet to be found. This task is further complicated by the technical limitations imposed by the current oceanographic techniques.     

Influence of induced magnetic field and heat transfer on peristaltic transport of a Carreau fluid

The effect of an induced magnetic field on peristaltic flow of an incompressible Carreau fluid in an asymmetric channel is analyzed. Perturbation solution to equations under long wavelength approximation is derived in terms of small Weissenberg number. Expressions have been constructed for the stream function, the axial induced magnetic field, the magnetic force function, the current density distribution and the temperature. Trapping phenomenon is examined with respect to emerging parameters of interest.     

Simulation of suspension gravity currents with different initial aspect ratio and layout of turbidity fence

A three-dimensional (3D) numerical model, using large eddy simulation (LES), is developed for simulating the motion of suspension gravity currents. The suitable values of model parameters are determined using the existing experimental data of a two-dimensional (2D) suspension (a mixture composed of water and glass bead particles) cloud. The simulated gravity current with different initial aspect ratio (length/breadth) of the suspension is compared with the reported data of 3D laboratory experiments to investigate the effect of initial aspect ratio on the flow characteristics and the diffusion of turbidity under the presence of a turbidity fence. The comparison of simulated results of such main flow characteristics as front height, front propagation velocity and particle deposition with the experimental data reveals that the model is capable of simulating the complex behavior of the 3D suspension gravity currents to a reasonably good accuracy under complex conditions.     

Effects of Hall current and heat transfer on rotating flow of a second grade fluid through a porous medium

The effects of Hall current and heat transfer on the rotating flow of a second grade fluid past a porous plate with variable suction are examined. The medium considered is porous and suction and external flow velocities vary periodically. The plate is assumed to be at a higher temperature than the fluid. The influences of the Hall parameter and porosity of the medium have been seen and discussed on the velocity and temperature profiles. Moreover, these influences have also been seen on the drag and lateral stress. Finally, the obtained solutions are also compared with the previous studies in the literature and found quite agreement.     

Hall电流对表面热通量均匀的竖直可渗透平板上MHD自然对流的影响

在横向磁场作用下,研究Hall电流对竖直可渗透平板上MHD自然对流的影响,平板具有均匀的热通量.和外部磁场相比,假设感应磁场可以忽略不计.利用自由变量公式化(FVF)和流函数公式化(SFF),将边界层方程简化为适当的形式.对局部蒸发系数ζ的整个取值范围,由FVF得到的抛物型方程,用简明的有限差分法进行数值积分;另一方面,由SFF得到的非相似方程,采用局部非相似法求解.有些区域,如局部蒸发系数ζ值足够大或足够小时,用正规的摄动法求解.对低值Prandtl数Pr,例如Pr=0.005,0.01,0.05时,用图形表示磁场参数M和Hall参数m,对局部表面摩擦因数和局部Nusselt数的影响.最后对不同的局部蒸发系数ζ值,给出流体的速度和温度分布.     

Periodic solutions of a nonlinear suspension bridge equation with damping and nonconstant load

The paper is concerned with the existence of periodic solutions for the Lazer-McKenna suspension bridge equation with damping and nonconstant load. By using the Lyapunov-Schmidt reduction methods, the author discuss the relationship between the sign-changing solutions and the source terms. The result answers partly the open problem in Lazer and McKenna (SIAM Rev. 32 (1990) 537-578).     

Effect of homogeneous and heterogeneous chemical reactions on peristaltic transport of an MHD micropolar fluid with wall effects

In this paper, the influence of magnetic field on the dispersion of a solute in peristaltic flow of an incompressible micropolar fluid is studied as a model of fluid transport in the human intestinal system with wall properties. Long wavelength approximation, Taylor's limiting condition, and dynamic boundary conditions at the flexible walls are used to obtain the average effective dispersion coefficient in the presence of combined homogeneous and heterogeneous chemical reactions. The effects of various pertinent parameters on the effective dispersion coefficient are discussed. Average effective dispersion coefficient increases with amplitude ratio, which implies that dispersion is more in the presence of peristalsis. It also increases with the cross‐viscosity coefficient, heterogeneous chemical reaction rate, and wall parameters. Further, dispersion decreases with micropolar parameter, magnetic parameter, and homogeneous chemical reaction rates. Copyright © 2015 John Wiley & Sons, Ltd.     

Hall effect on unsteady MHD Couette flow and heat transfer of a Bingham fluid with suction and injection

The unsteady magnetohydrodynamic flow of an electrically conducting viscous incompressible non-Newtonian Bingham fluid bounded by two parallel non-conducting porous plates is studied with heat transfer considering the Hall effect. An external uniform magnetic field is applied perpendicular to the plates and the fluid motion is subjected to a uniform suction and injection. The lower plate is stationary and the upper plate moves with a constant velocity and the two plates are kept at different but constant temperatures. Numerical solutions are obtained for the governing momentum and energy equations taking the Joule and viscous dissipations into consideration. The effect of the Hall term, the parameter describing the non-Newtonian behavior, and the velocity of suction and injection on both the velocity and temperature distributions are studied.     

Numerical study of magnetohydrodynamic viscous plasma flow in rotating porous media with Hall currents and inclined magnetic field influence

A numerical solution is developed for the viscous, incompressible, magnetohydrodynamic flow in a rotating channel comprising two infinite parallel plates and containing a Darcian porous medium, the plates lying in the x–z plane, under constant pressure gradient. The system is subjected to a strong, inclined magnetic field orientated to the positive direction of the y-axis (rotational axis, normal to the x–z plane). The Navier–Stokes flow equations for a general rotating hydromagnetic flow are reduced to a pair of linear, viscous partial differential equations neglecting convective acceleration terms, for primary velocity (u′) and secondary velocity (v′) where these velocities are directed along the x and y axes. Only viscous terms are retained in the momenta equations. The model is non-dimensionalized and shown to be controlled by a number of dimensionless parameters. The resulting dimensionless ordinary differential equations are solved using a robust numerical method, Network Simulation Methodology. Full details of the numerics are provided. The present solutions are also benchmarked against the analytical solutions presented recently by Ghosh and Pop [Ghosh SK, Pop I. An analytical approach to MHD plasma behaviour of a rotating environment in the presence of an inclined magnetic field as compared to excitation frequency. Int J Appl Mech Eng 2006;11(4):845–856] for the case of a purely fluid medium (infinite permeability). We study graphically the influence of Hartmann number (Ha, magnetic field parameter), Ekman number (Ek, rotation parameter), Hall current parameter (Nh), Darcy number (Da, permeability parameter), pressure gradient (Np) and also magnetic field inclination (θ) on primary and secondary velocity fields. Additionally we investigate the effects of these multiphysical parameters on the dimensionless shear stresses at the plates. Both primary and secondary velocity are seen to be increased with a rise in Darcy number, owing to a simultaneous reduction in Darcian drag force. Primary velocity is seen to decrease with an increase in Hall current parameter (Nh) but there is a decrease in secondary velocity. The study finds important applications in magnetic materials processing, hydromagnetic plasma energy generators, magneto-geophysics and planetary astrophysics.     

Effect of Hall currents and chemical reaction on hydromagnetic flow of a stretching vertical surface with internal heat generation/absorption

The problem of steady, laminar, hydromagnetic, simultaneous heat and mass transfer by laminar flow of a Newtonian, viscous, electrically conducting and heat generating/absorbing fluid over a continuously stretching surface in the presence of the combined effect of Hall currents and mass diffusion of chemical species with first and higher order reactions is investigated. The fluid is permeated by a strong transverse magnetic field imposed perpendicularly to the plate on the assumption of a small magnetic Reynolds number. Certain transformations are employed to transform the governing differential equations to a local similarity form which are solved numerically. Comparisons with previously published work have been conducted and the results are found to be in good agreement. A parametric study is performed to illustrate the influence of the magnetic field parameter, Hall parameter, the coefficients of space-dependent and temperature-dependent internal heat generation/absorption, the chemical reaction parameter and order of reaction on the fluid velocity, temperature and concentration distributions. Numerical data for the local skin-friction coefficient, the local Nusselt number and the local Sherwood number have been tabulated for various values of parametric conditions.     

Effects of pulsatile flow and straight length on low-density lipoprotein transport in a curved arterial wall

Abnormal accumulation of macromolecules such as low-density lipoproteins (LDLs) in the arterial wall causes narrowing and blockage of vessels, which leads to atherosclerosis. Effects of pulsatile nature of blood flows as well as the initial length on transport of the LDL species in the arterial boundary layer region are analyzed numerically in the present work. The set of governing equations consisting of continuity, Navier-Stokes, and species transport is solved using a projection method based on the second-order central difference discretization. The obtained results are in excellent agreement with the pertinent data. The computational results imply that the flow field and concentration distribution are time dependent but the variation of the filtration velocity can be ignored. The LDL concentration boundary layer thickness decreases in the outer part and increases in the inner part for both with or without straight length. Presence of initial straight length generates about 26% growth in the boundary layer thickness, although its effect on the LDL surface concentration (LSC) is negligible. The maximum LSC is related to the regions with minimum wall shear stress in the inner part of the curved artery, which have more potential for formation of atherosclerosis. A new numerical correlation between the LSC and boundary layer thickness is proposed and examined.