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.     

Effects of an induced magnetic field on the peristaltic flow of a third‐order fluid

In this article, we carry out the effect of an induced magnetic field on the peristaltic transport of an incompressible conducting third order fluid in a symmetric channel. The flow analysis has been developed for low Reynolds number and long wave length approximation. Analytical solutions have been established for the axial velocity, stream function, magnetic force function, and axial‐induced magnetic field. The effects of pertinent parameters on the pressure rise per wavelength are investigated by using numerical integration. Besides this, we study the effect of these parameters on the pressure gradient and axial induced magnetic field. The phenomena of trapping and pumping are also discussed. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010     

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.     

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.     

Influence of heat and mass transfer on peristaltic flow of a third order fluid in a diverging tube

In the present investigation we have discussed the heat and mass transfer analysis on peristaltic flow of a third order fluid in a diverging tube. The assumption of low Reynolds number and long wavelength have been used to simplify the complicated problem into relatively simple problem. Two types of analytical solutions named as perturbation solution and solution have been evaluated for velocity, temperature and concentration field. The expression for pressure rise and frictional forces are calculated using numerical integration. In addition, the quantitative effects of pressure rise, frictional forces, temperature and concentration profile are displayed graphically. Trapping phenomena is also discussed at the end of the article.     

Numerical and analytical simulation of peristaltic flow of a Jeffrey-six constant fluid

This paper describes the Peristaltic flow of a Jeffrey-six constant fluid in an endoscope. The two-dimensional equation of Jeffrey-six constant fluid is simplified by making the assumptions of long wave length and low Reynolds number. The reduced momentum equations are solved with three methods, namely (i) Perturbation method, (ii) Homotopy analysis method, and (iii) shooting method. The comparison of the three solutions shows a very good agreement between the three results. The expressions for pressure rise and frictional forces per wave length have been also computed numerically. Finally, the pressure rise, frictional forces are plotted for different parameters of interest.     

Effects of heat transfer and space porosity on peristaltic flow in a vertical asymmetric channel

This article discusses the effect of heat transfer on the peristaltic flow of a Newtonian fluid through a porous space in a vertical asymmetric channel. Long wavelength approximation is used to linearize the governing equations. The system of the governing nonlinear PDE is solved by using the perturbation method. The solutions are obtained for the velocity and the temperature fields. 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, frictional forces, and the features of the flow and temperature characteristics are analyzed by plotting graphs and discussed in detail. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010     

Peristaltic flow of a micropolar fluid through a porous medium in the presence of an external magnetic field

This paper presents an analytical study of the MHD flow of a micropolar fluid through a porous medium induced by sinusoidal peristaltic waves traveling down the channel walls. Low Reynolds number and long wavelength approximations are applied to solve the non-linear problem in the closed form and expressions for axial velocity, pressure rise per wavelength, mechanical efficiency and stream function are obtained. The impacts of pertinent parameters on the aforementioned quantities are examined by plotting graphs on the basis of computational results. It is found that the pumping improves with Hartman number but degrades with permeability of the porous medium.     

Effects of temperature dependent viscosity on peristaltic flow of a Jeffrey-six constant fluid in a non-uniform vertical tube

This paper deals with the influence of heat transfer and temperature dependent viscosity on peristaltic flow of a Jeffrey-six constant fluid. The two-dimensional equations of Jeffrey-six constant fluid are simplified by making the assumptions of long wave length and low Reynolds number. The arising equations are solved for temperature, velocity profile and axial pressure gradient using regular perturbation method and homotopy analysis method. The integration appeared in the pressure rise is treated numerically to find the solution. The expressions for pressure rise, temperature, pressure gradient and stream functions are sketched for various embedded parameters and interpreted. The graphical results are also presented for five different wave shapes.     

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.     

On the flow of a dusty viscous liquid through a circular pipe

Analytical solution of the flow problem of a dusty viscous liquid through a circular pipe in case of axial symmetry is obtained when pressure gradient varies harmonically with time. It is found that the effect of the fine dust is to make the velocity of sedimentation zero and when dust is sufficiently coarse, the effect of the dust is equivalent to an extra frictional force proportional to the fluid velocity.     

Effects of an endoscope and magnetic field on the peristalsis involving Jeffrey fluid

This paper looks at the influence of an endoscope on the peristaltic flow of a Jeffrey fluid through tubes. The considered fluid is incompressible and electrically conducting. The governing partial differential equations are modeled. Exact analytic solutions for velocity components and pressure gradient are established under long wavelength assumption. 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.     

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 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.     

The influence of heat transfer on peristaltic transport of a Jeffrey fluid in a vertical porous stratum

The peristaltic flow of a Jeffrey fluid in a vertical porous stratum with heat transfer is studied under long wavelength and low Reynolds number assumptions. The nonlinear governing equations are solved using perturbation technique. The expressions for velocity, temperature and the pressure rise per one wave length are determined. The effects of different parameters on the velocity, the temperature and the pumping characteristics are discussed. It is observed that the effects of the Jeffrey number λ₁, the Grashof number Gr, the perturbation parameter N = EcPr, and the peristaltic wall deformation parameter ϕ are the strongest on the trapping bolus phenomenon. The results obtained for the flow and heat transfer characteristics reveal many interesting behaviors that warrant further study on the non-Newtonian fluid phenomena, especially the shear-thinning phenomena. Shear-thinning reduces the wall shear stress.     

Effect of wall compliance on compressible fluid transport induced by a surface acoustic wave in a microchannel

Effects of complaint wall properties on the flow of a Newtonian viscous compressible fluid has been studied when the wave propagating (surface acoustic wave, SAW) along the walls in a confined parallel‐plane microchannel is conducted by considering the slip velocity. A perturbation technique has been employed to analyze the problem where the amplitude ratio (wave amplitude/half width of channel) is chosen as a parameter. In the second order approximation, the net axial velocity is calculated for various values of the fluid parameters and wall parameters. The phenomenon of the “mean flow reversal” is found to exist both at the center and at the boundaries of the channel. The effect of damping force, wall tension, and compressibility parameter on the mean axial velocity and reversal flow has been investigated, also the critical values of the tension are calculated for the pertinent flow parameters. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 621–636, 2011 Keywords:     

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.