Peristaltic motion of a magnetohydrodynamic generalized second‐order fluid in an asymmetric channel

We investigate the peristaltic motion of a magnetohydrodynamic (MHD) generalized second‐order fluid in an asymmetric channel. The governing equations are first modeled and then numerically solved under the long wavelength approximation. Attention has been focused to analyze the shear‐thinning and shear‐thickening effects of the investigated non‐Newtonian fluid, the influence of the magnetic force on the flow, especially the trapping, pumping characteristics caused by the peristalsis of the walls. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011     

Peristaltic mechanism of a Maxwell fluid in an asymmetric channel

The peristaltic flow of a Maxwell fluid in an asymmetric channel is studied. Asymmetry in the flow is induced by taking peristaltic wave train of different amplitudes and phase. The viscoelasticity of the fluid is induced in the momentum equation. An analytic solution is obtained through a series of the wave number. The leading velocity term denotes the Newtonian result. The first and second order terms are the viscoelastic contribution to the flow. Expressions for stream function and longitudinal pressure gradient are obtained analytically. Numerical computations have been performed for the pressure rise per wavelength and discussed.     

Peristaltic flow of a Carreau fluid in a channel with different wave forms

This investigation deals with the peristaltic motion of a Carreau fluid in a planar channel by employing long wavelength approximation. Five wave forms are chosen. Explicit solutions of longitudinal velocity and pressure gradient are derived. The pumping and trapping phenomena are properly examined. Comparison is made for the flow characteristics of the various selected wave forms. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010     

Peristaltic motion of micropolar fluid in circular cylindrical tubes: Effect of wall properties

In this paper, peristaltic motion of micropolar fluid in a circular cylindrical flexible tube with viscoelastic or elastic wall properties has been considered. A finite difference scheme is developed to solve the governing equations of motion resulting from a perturbation technique for small values of amplitude ratio. The time mean axial velocity profiles are presented for the case of free pumping and analysed to observe the influence of wall properties for various values of micropolar fluid parameters. In the case of viscoelastic wall, the effect of viscous damping on mean flow reversal at the boundary is seen.     

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.     

Peristaltic flow of viscoelastic fluid with fractional Maxwell model through a channel

The paper presents the transportation of viscoelastic fluid with fractional Maxwell model by peristalsis through a channel under long wavelength and low Reynolds number approximations. The propagation of wall of channel is taken as sinusoidal wave propagation (contraction and relaxation). Homotopy perturbation method (HPM) and Adomian decomposition method (ADM) are used to obtain the analytical approximate solutions of the problem. The expressions of axial velocity, volume flow rate and pressure gradient are obtained. The effects of fractional parameters (α), relaxation time (λ₁) and amplitude (?) on the pressure difference and friction force across one wavelength are calculated numerically for different particular cases and depicted through graphs.     

Numerical simulation of pressure-driven startup laminar flows through a planar T-junction channel

A start-up flow of a viscous incompressible fluid in a T-junction channel is studied numerically. The flow starting from rest is driven by a constant pressure drops suddenly applied between the entries and exits of a planar T-junction channel. The Navier-Stokes equations in primitive variables are solved numerically using finite-volume techniques. Predicted variations with time of the volume flow rates and the flow patterns are presented for several values of pressure drops. It has been shown that a start-up flow can pass through different regimes (or different flow direction) before asymptotically reaching steady state distribution.     

Peristaltic transport of a Newtonian fluid in a vertical asymmetric channel with heat transfer and porous medium

The problem of peristaltic flow of a Newtonian fluid with heat transfer in a vertical asymmetric channel through 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 channel asymmetry is produced by choosing the peristaltic wave train on the walls to have different amplitudes and phase. The analytical solution has been obtained in the form of temperature from which an axial velocity, stream function and pressure gradient have been derived. The effects of permeability parameter, Grashof number, heat source/sink parameter, phase difference, varying channel width and wave amplitudes on the pressure gradient, velocity, pressure drop, the phenomenon of trapping and shear stress are discussed numerically and explained graphically.     

Peristaltic motion of a magnetohydrodynamic micropolar fluid in a tube

This study is concerned with the magnetohydrodynamic flow of a micropolar fluid in a circular cylindrical tube. The equations governing the flow are modeled using the assumptions of long wavelength and low Reynolds number. It is found that the governing equations are coupled partial differential equations for the flow velocity and the microrotation. The finite difference scheme is used to integrate the equations and the results are graphically presented and discussed. Special emphasis is given to the effects of micropolar fluid parameters, tube wall peristaltic amplitude and magnetic parameter on the transverse profiles of velocity and microrotation as well as pumping characteristics and trapping phenomena.     

Peristaltic flow of a Williamson fluid in an asymmetric channel

In this work, we have presented a peristaltic flow of a Williamson model in an asymmetric channel. The governing equations of Williamson model in two dimensional peristaltic flow phenomena are constructed under long wave length and low Reynolds number approximations. A regular perturbation expansion method is used to obtain the analytical solution of the non-linear problem. The expressions for stream function, pressure gradient and pressure rise have been computed. The pertinent features of various physical parameters have been discussed graphically. It is observed that, (the non-dimensional Williamson parameter) for large We , the curves of the pressure rise are not linear but for very small We it behave like a Newtonian fluid.     

Peristaltic flow of a Maxwell fluid in a channel with compliant walls

This paper describes the peristaltic motion of a non-Newtonian fluid in a channel having compliant boundaries. Constitutive equations for a Maxwell fluid have been used. Perturbation method has been used for the analytic solution. The influence of pertinent parameters is analyzed. Comparison of the present analysis of Maxwell fluid is made with the existing results of viscous fluid.     

Peristaltic transport of non-Newtonian fluid in a diverging tube with different wave forms

The present study investigates the peristaltic transport of non-Newtonian fluid, modeled as power law and Bingham fluid, in a diverging tube with different wall wave forms: sinusoidal, multi-sinusoidal, triangular, trapezoidal and square waves. Fourier series is employed to get the expressions for temporal and spatial dependent wall shapes. Solutions for time average pressure rise — flow rate relationship are computed for different amplitude ratios, φ, power law indices, n, yield stresses, τ₀, and wave shapes. Results indicate that φ and n play a vital role in peristalsis. When φ of the sinusoidal wave is increased from 0.6 to 0.8, the maximum pressure rise, increased by a factor of 10. Increasing n from 0.6 to 1 increased the by a factor of 3. For Bingham fluid with φ=0.5, a 25% increase in is obtained when τ₀, is reduced from 1 (non-Newtonian) to 0 (Newtonian). Of all the wave shapes considered, obtained is maximum for the square wave and minimum for the triangular wave (4–15 times less depending on φ). Finally, pathlines of massless particles are traced to investigate the occurrence of reflux. It is observed that, even for zero flow rate, reflux occurs near the tube wall and the thickness and shape of the reflux region strongly depends on φ, n, and shape of the peristaltic waves.     

Hydromagnetic rotating flow of a fourth‐order fluid past a porous plate

The rotating flow in the presence of a magnetic field is a problem belonging to hydromagnetics and deserves to be more widely studied than it has been to date. In the non‐linear regime the literature is scarce. We develop the governing equations for the unsteady hydromagnetic rotating flow of a fourth‐order fluid past a porous plate. The steady flow is governed by a boundary value problem in which the order of differential equations is more than the number of available boundary conditions. It is shown that by augmenting the boundary conditions based on asymptotic structures at infinity it is possible to obtain numerical solutions of the nonlinear hydromagnetic equations. Effects of uniform suction or blowing past the porous plate, exerted magnetic field and rotation on the flow phenomena, especially on the boundary layer structure near the plate, are numerically analysed and discussed. The flow behaviours of the Newtonian fluid and second‐, third‐ and fourth‐order non‐Newtonian fluids are compared for the special flow problem, respectively. Copyright © 2004 John Wiley & Sons, Ltd.     

Thermocapillary motion of deformable fluid particles in tubes

The boundary integral technique is used to study the effect of deformation on the steady, creeping, thermocapillary migration of a fluid particle under conditions of axisymmetry, negligible thermal convection and an insulated tube wall. The spherical radius of the fluid particle (i.e. the radius as if the particle were a sphere, a ′= (3V _p ^′ /4π)^1/3, V _p ^′ is the particle volume) and that of the tube are denoted, respectively, by a′and b′. For small capillary numberCa = 0.05, only for a large fluid particle (a′/b′ = 0.8) is deformation significant. Fora′/b′= 0.8, hydrodynamic stresses squeeze the particle, reduce the interaction of the particle with the wall and thereby increase the terminal velocity. For small particles a′/b′< 0.8 and Ca = 0.05 the fluid particles translate as spheres, due to the fact that the fluid particle is too far away from the wall to be subject to distending hydrodynamic stresses. The deformable particle moves faster than a spherical one in the thermocapillary migration. The increase in velocity with capillary number is larger for thermocapillary motion than for buoyancy.     

Peristaltic motion of a Jeffrey fluid under the effect of a magnetic field in a tube

This study is concerned with the analysis of peristaltic motion of a Jeffrey fluid in a tube with sinusoidal wave travelling down its wall. The fluid is electrically conducting in the presence of a uniform magnetic field. Analytic solution is carried out for long wavelength and low Reynolds number considerations. The expressions for stream function, axial velocity and axial pressure gradient have been obtained. The results for pressure rise and frictional force per wavelength obtained in the analysis have been evaluated numerically and discussed briefly. The significance of the present model over the existing models has been pointed out by comparing the results with other theories. It is further noted that under the long wavelength approximation, the retardation time has no effect in the present analysis.     

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.     

Linearized viscoelastic Oldroyd fluid motion in an almost periodic environment

In most of the linear homogenization problems involving convolution terms so far studied, the main tool used to derive the homogenized problem is the Laplace transform. Here we propose a direct approach enabling one to tackle both linear and nonlinear homogenization problems that involve convolution sequences without using Laplace transform. To illustrate this, we investigate in this paper the asymptotic behavior of the solutions of a Stokes–Volterra problem with rapidly oscillating coefficients describing the viscoelastic fluid flow in a fixed domain. Under the almost periodicity assumption on the coefficients of the problem, we prove that the sequence of solutions of our ?‐problem converges in L² to a solution of a rather classical Stokes system. One important fact is that the memory disappears in the limit. To achieve our goal, we use some very recent results about the sigma‐convergence of convolution sequences. Copyright © 2013 John Wiley & Sons, Ltd.