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 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.     

Non-linear peristaltic flow of a non-Newtonian fluid under effect of a magnetic field in a planar channel

This paper is devoted to the study of peristaltic flow of a fourth grade fluid in a channel under the considerations of long wavelength and low-Reynolds number. The flow is examined in a wave frame of reference moving with velocity of the wave. The analytic solution has been obtained in the form of a stream function from which the axial velocity and axial pressure gradient have been derived. The results for the pressure rise and frictional force per wavelength have also been computed numerically. The computational results indicate that the pressure rise and frictional force per wavelength are increased in case of non-Newtonian fluid when compared with Newtonian fluid. Several graphs of physical interest are displayed and discussed.     

Non-linear peristaltic transport in an inclined asymmetric channel

The problem of peristaltic transport of a hydromagnetic (electrically conducting) viscous incompressible fluid in an inclined planar channel having electrically insulated walls has been investigated under long-wavelength and low-Reynolds number assumptions. 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 the velocity of the wave. Expressions for velocity field, shear stress and pressure gradient on the wall are obtained. The effects of different parameters entering into the problem are discussed numerically and explained graphically.     

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.     

Peristaltic transport of a Williamson fluid in asymmetric channels with permeable walls

The peristaltic flow of a Williamson fluid in asymmetric channels with permeable walls is investigated. The channel asymmetry is produced by choosing a peristaltic wave train on the wall with different amplitudes and phases. The solutions for stream function, axial velocity and pressure gradient are obtained for small Weissenberg number, We, via a perturbation expansion about We, while an exact solution method is discussed for large values of We. The exact solutions become singular as We tends to zero; hence the separate perturbation solutions are essential. Also, numerical results are obtained using the perturbation technique for the pumping and trapping phenomena, and these are used to bring out the qualitative features of the solutions. It is noted that the size of the trapped bolus decreases and its symmetry disappears for large values of the permeability parameter. The effects of various wave forms (namely, sinusoidal, triangular, square and trapezoidal) on the fluid flow are discussed.     

流变学流体的蠕动传输:食道中食物块的运动模型

研究食道中蠕动传输的流体力学.对任意的波形和任意的管道长度,建立起流变学流体蠕动传输的数学模型.用粘性流体的Ostwald-de Waele幂定律,描述非Newton流体的流动特性.解析公式化模型,详细且精确地给出食物块在食道中蠕动传输相关的一些重要性质.分析中应用了润滑理论,本研究特别适合于Reynolds数不大的情况.将食道看作环形的管道,通过食道壁周期性的收缩来传输食物块.就单个波和周期性收缩一组波的传播,研究与传输过程有关变量的变化,如压力、流速、食物颗粒轨迹以及流量等.局部压力的变化,对流变指数n有着高度的敏感性.研究结果清晰地表明,食物块在食道中蠕动传输时,Newton流体或流变学流体构成的连续流体,以组合波传播比大间隔单波传播,传输效率要高得多.     

Effect of Hall currents on interaction of pulsatile and peristaltic transport induced flows of a particle-fluid suspension

The interaction of purely periodic mean flow with a peristaltic induced flow is investigated within the framework of a two-dimensional analogue. The mathematical model considers a viscous incompressible fluid under the effect of transverse magnetic field, taking into account the effect of Hall currents for a magneto-fluid with suspended particles between infinite parallel walls on which a sinusoidal traveling wave is imposed. A perturbation solution to the complete set of Navier-Stokes equations is found for the case in which the frequency of the traveling wave and that of the imposed pressure gradient are equal. The ratio of the traveling wave amplitude to channel width is assumed to be small. For this case a first order steady flow is found to exist, as contrasted to a second order effect in the absence of the imposed periodic pressure gradient. The effect of Hall parameter, Hartmann number and the various parameters included in the problem are discussed numerically.     

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.     

Non-Newtonian characteristics of peristaltic flow of blood in micro-vessels

Of concern in the paper is a generalized theoretical study of the non-Newtonian characteristics of peristaltic flow of blood through micro-vessels, e.g. arterioles. The vessel is considered to be of variable cross-section and blood to be a Herschel–Bulkley type of fluid. The progressive wave front of the peristaltic flow is supposed sinusoidal/straight section dominated (SSD) (expansion/contraction type); Reynolds number is considered to be small with reference to blood flow in the micro-circulatory system. The equations that govern the non-Newtonian peristaltic flow of blood are considered to be non-linear. The objective of the study has been to examine the effect of amplitude ratio, mean pressure gradient, yield stress and the power law index on the velocity distribution, wall shear stress, streamline pattern and trapping. It is observed that the numerical estimates for the aforesaid quantities in the case of peristaltic transport of blood in a channel are much different from those for flow in an axisymmetric vessel of circular cross-section. The study further shows that peristaltic pumping, flow velocity and wall shear stress are significantly altered due to the non-uniformity of the cross-sectional radius of blood vessels of the micro-circulatory system. Moreover, the magnitude of the amplitude ratio and the value of the fluid index are important parameters that affect the flow behaviour. Novel features of SSD wave propagation that affect the flow behaviour of blood have also been discussed.     

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     

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.     

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.     

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     

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 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     

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.     

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.     

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.