Magnetohydrodynamic peristaltic flow of a hyperbolic tangent fluid in a vertical asymmetric channel with heat transfer

In the present paper we discuss the magnetohydrodynamic (MHD) peristaltic flow of a hyperbolic tangent fluid model in a vertical asymmetric channel under a zero Reynolds number and long wavelength approximation. Exact solution of the temperature equation in the absence of dissipation term has been computed and the analytical ex- pression for stream function and axial pressure gradient are established. The flow is analyzed in a wave frame of reference moving with the velocity of wave. The expression for pressure rise has been computed numerically. The physical features of pertinent parameters are analyzed by plotting graphs and discussed in detail.     

Peristaltic transport of a couple-stress fluid

The problem of peristaltic transport of a couple-stress fluid has been investigated under a zero Reynolds number and long wavelength approximation. A comparison of the results with those for a Newtonian fluid model shows that the magnitude of the pressure rise under a given set of conditions is greater in the case of the couple-stress fluid. The pressure rise increases as the couple-stress parameter decreases. The difference between the pressure rise for a Newtonian and a couple-stress fluid increases with increasing amplitude ratio at zero flow rate. However, increasing the flow rate reduces this difference.     

Slip effects on the peristaltic flow of a Jeffrey fluid in an asymmetric channel under the effect of induced magnetic field

In the present study, we investigated the effects of slip and induced magnetic field on the peristaltic flow of a Jeffrey fluid in an asymmetric channel. The governing two‐dimensional equations for momentum, magnetic force function and energy are simplified by using the assumptions of long wavelength and low but finite Reynolds number. The reduced problem has been solved by Adomian decomposition method (ADM) and closed form solutions have been presented. Further, the exact solution of the proposed problem has also been computed and the mathematical comparison shows that both solutions are almost similar. The effects of pertinent parameters on the pressure rise per wavelength are investigated using numerical integration. The expressions for pressure rise, friction force, velocity, temperature, magnetic force function and the stream lines against various physical parameters of interest are shown graphically. Moreover, the behavior of different kinds of wave shape are also discussed. Copyright © 2009 John Wiley & Sons, Ltd.     

Peristaltic transport and heat transfer of a MHD Newtonian fluid with variable viscosity

The influence of temperature‐dependent viscosity and magnetic field on the peristaltic flow of an incompressible, viscous Newtonian fluid is investigated. The governing equations are derived under the assumptions of long wavelength approximation. A regular perturbation expansion method is used to obtain the analytical solutions for the velocity and temperature fields. The expressions for the pressure rise, friction force and the relation between the flow rate and pressure gradient are obtain. In addition to analytical solutions, numerical results are also computed and compared with the analytical results with good agreement. The results are plotted for different values of variable viscosity parameter β, Hartmann number M, and amplitude ratio ?. It is found that the pressure rise decreases as the viscosity parameter β increases and it increases as the Hartmann number M increases. Finally, the maximum pressure rise (σ=0) increases as M increases and β decreases. Copyright © 2009 John Wiley & Sons, Ltd.     

Peristaltic flow of Sisko fluid in a uniform inclined tube

We have analyzed an incompressible Sisko fluid through an axisymmetric uniform tube with a sinusoidal wave propagating down its walls. The present analysis of non- Newtonian fluid is investigated under the considerations of long wavelength and low Reynolds number approximation. The analytic solution is obtained using （i） the regular perturbation method （ii） the Homotopy analysis method （HAM）. The comparison of both the solutions is presented graphically. The results for the pressure rise, frictional force and pressure gradient have been calculated numerically and the results are studied for various values of the physical parameters of interest, such as α （angle of inclination）, b^＊ （Sisko fluid parameter）, Ф （amplitude ratio） and n （power law index）. Trapping phenomena is discussed at the end of the article.     

Endoscopic effects on the peristaltic flow of an Eyring–Powell fluid

This study investigates the peristaltic flow of Eyring–Powell fluid in an endoscope. The governing equations for Eyring–Powell are modeled in cylindrical coordinates under the assumption of long wavelength and low Reynolds number approximation. The resulting nonlinear differential equations are solved analytically and numerically by employing perturbation method and shooting technique. Numerical integration have been done for pressure rise and frictional forces. Comparative study have been made for both the solutions to see the validity of the results. The effects of various emerging parameters are investigated for five different peristaltic waves. (Basically peristaltic phenomena is a natural phenomena so it is not necessary that peristaltic wave be always a sinusoidal wave it could be multisinusoidal, triangular, trapezoidal and square waves for example heartbeats.) Streamlines have been plotted at the end of the article.     

Thermal analysis of a flow of immiscible couple stress fluids in a channel

An analytical study of the entropy generation rate and heat transfer in a flow of immiscible couple stress fluids between two horizontal parallel plates under a constant pressure gradient is performed. Both plates are kept at different and constant temperatures higher than that of the fluid. The Stokes couple stress flow model is employed. The classical no-slip condition is prescribed at the plates, and continuity of the velocity, rotation, couple stress, shear stress, temperature, and heat flux is imposed at the interfaces. The velocity and temperature distributions are found analytically, and they are used to compute the entropy generation number and Bejan number. The effects of the couple stress parameter and Reynolds number on the velocity, temperature, entropy generation number, and Bejan number are investigated. It is observed that the friction near the plates in couple stress fluids decreases as the couple stress increases.     

Peristaltic flow of a couple stress fluid under the effect of induced magnetic field in an asymmetric channel

The present paper investigates the peristaltic transport of a couple stress fluid in an asymmetric channel with the effect of the induced magnetic field. The exact solutions of momentum and the magnetic field equations have been calculated under the assumptions of long wave length and low but finite Reynolds number. The expression for pressure rise has been computed numerically using mathematics software Mathematica. The graphical results have been presented to discuss the physical behavior of various physical parameters of interest. Finally, the trapping phenomena have been discussed for various physical parameters.     

Peristaltic transport of a power-law fluid: Application to the ductus efferentes of the reproductive tract

The problem of peristaltic transport of a non-Newtonian (power-law) fluid in uniform and non-uniform two-dimensional channels has been investigated under zero Reynolds number with long wavelength approximation. A comparison of the results with those for a Newtonian fluid model shows that the magnitude of pressure rise, under a given set of conditions, is smaller in the case of the non-Newtonian fluid (power-law indexn < 1) at zero flow rate. Further, the pressure rise is smaller asn decreases from 1 at zero flow rate, is independent ofn at a certain value of flow rate and becomes greater if flow rate increases further. Also, at a given flow rate, an increase in wavelength leads to a decrease in pressure rise and increase in the influence of non-Newtonian behaviour. Pressure rise in the case of non-uniform geometry, is found to be much smaller than the corresponding value in the case of uniform geometry. Finally, the analysis is applied and compared with observed flow rates in the ductus efferentes of the male reproductive tract.     

Effects of heat and mass transfer peristaltic flow of?Williamson fluid in a vertical annulus

In the present investigation, we have studied the effects of mixed convection heat and mass transfer on peristaltic flow of Williamson fluid model in a vertical annulus. The governing equations of Williamson fluid model are simplified using the assumptions of long wavelength and low Reynold’s number. An approximated analytical and numerical solutions are found for the velocity field using (i) Perturbation method (ii) Shooting method. The comparisons of analytical and numerical solutions have been presented. The expressions for pressure rise, velocity against various physical parameter are discussed through graphs.     

Combined effects of heat and chemical reactions on the peristaltic flow of carreau fluid model in a diverging tube

The study of peristaltic flow of a Carreau fluid in a non‐uniform tube under the consideration of long wavelength in the presence of heat and mass transfer is presented. The flow is investigated in a wave frame of reference moving with velocity of the wave c. Two types of analytical solutions have been evaluated (i) perturbation method (ii) homotopy analysis method for velocity, temperature and concentration field. Numerical integration have been used to obtain the graphical results for pressure rise and frictional forces. The effects of various emerging parameters are investigated for five different peristaltic waves. Copyright © 2010 John Wiley & Sons, Ltd.     

MHD peristaltic flow of a third order fluid in an asymmetric channel

This study is concerned with peristaltic flow of a magnetohydrodynamic (MHD) fluid in an asymmetric channel. Asymmetry in the flow is induced by waves on the channel walls having different amplitudes and phase. A systematic approach based on an expansion of Deborah number is used for the solution series. Analytic expressions have been developed for the stream function, axial velocity and axial pressure gradient. The pressure rise over a wavelength has been addressed through numerical integration. Particular attention has been given to the effects of Hartman number and Deborah number on the pressure rise over a wavelength and the trapping phenomenon. Several limiting solutions of interest are obtained as the special cases of the presented analysis by taking the appropriate parameter(s) to be zero. Copyright © 2009 John Wiley & Sons, Ltd.     

Peristaltic flow of a Johnson-Segalman fluid through a deformable tube

To understand theoretically the flow properties of physiological fluids we have considered as a model the peristaltic motion of a Johnson–Segalman fluid in a tube with a sinusoidal wave traveling down its wall. The perturbation solution for the stream function is obtained for large wavelength and small Weissenberg number. The expressions for the axial velocity, pressure gradient, and pressure rise per wavelength are also constructed. The general solution of the governing nonlinear partial differential equation is given using a transformation method. The numerical solution is also obtained and is compared with the perturbation solution. Numerical results are demonstrated for various values of the physical parameters of interest.      

Peristaltic transport of a Jeffrey fluid under the effect of magnetic field in an asymmetric channel

The peristaltic flow of a Jeffrey fluid in an asymmetric channel is studied under long wavelength and low Reynolds number assumptions. The fluid is electrically conducting by a transverse magnetic field. 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. The expressions for stream function, axial velocity and axial pressure gradient have been obtained. The effects of various emerging parameters on the flow characteristics are shown and discussed with the help of graphs. The pumping characteristics, axial pressure gradient and trapping phenomenon have been studied. Comparison of various wave forms (namely sinusoidal, triangular, square and trapezoidal) on the flow is discussed.     

Peristaltic flow of Johnson-Segalman fluid in asymmetric channel with convective boundary conditions

This work is concerned with the peristaltic transport of the Johnson-Segalman fluid in an asymmetric channel with convective boundary conditions. The mathematical modeling is based upon the conservation laws of mass, linear momentum, and energy. The resulting equations are solved after long wavelength and low Reynolds number are used. The results for the axial pressure gradient, velocity, and temperature profiles are obtained for small Weissenberg number. The expressions of the pressure gra-dient, velocity, and temperature are analyzed for various embedded parameters. Pumping and trapping phenomena are also explored.     

Multiple-scale modelling of acoustic sources in low Mach-number flow

The main difficulty in the calculation of sound generated by fluid flow at low Mach numbers is the occurrence of different scales. The fluid flow is characterized by small spatial structures containing a large amount of energy that may propagate with a small convective velocity, such as small vortices in a turbulent flow. The radiated acoustic waves have small amplitudes and carry a small amount of energy, but have a long wavelength due to their fast propagation velocity. In this paper a perturbation method is used to calculate noise generation and propagation in combination with fluid flow based on the incompressible equations. The idea for the numerical modelling is to introduce a fine grid for the resolution of the fluid flow that is embedded into a larger acoustical domain with a coarse grid adapted to the long wavelength acoustics. To get an appropriate restriction of the acoustic source terms from the fine CFD-grid to the coarse CAA-grid, a multi-scale expansion with one time and two space scales is introduced. To cite this article: C.-D. Munz et al., C. R. Mecanique 333 (2005).     

Bio-fluid flow analysis based on heat transfer and variable viscosity

This study investigates the cilia transport phenomenon from the perspectives of the heat transfer and variable viscosity in a bending channel. The rightward wall is maintained at a temperature of T_0, and the leftward wall has a temperature of T_1. Each wall has a metachronal wave that travels along its wall. The structures of the ciliary assemblies are calculated by the well-known simplifying suppositions of the large wavelength and the small Reynolds number approximation. The flow phenomenon for the Newtonian fluid is described as a function of cilia and a metachronal wave velocity. The pressure rise is calculated with MATHEMATICA. The theme of the cilia beating flow is inspected with scheming plots, and its features are discussed at the end of the article.     

Effective equations describing the flow of a viscous incompressible fluid through a long elastic tubeEquations efficaces décrivant l'écoulement d'un fluide visqueux incompressible dans un tuyau long et élastique

We study the flow of a viscous incompressible fluid through a long and narrow elastic tube whose walls are modeled by the Navier equations for a curved, linearly elastic membrane. The flow is governed by a given small time dependent pressure drop between the inlet and the outlet boundary, giving rise to creeping flow modeled by the Stokes equations. By employing asymptotic analysis in thin, elastic, domains we obtain the reduced equations which correspond to a Biot type viscoelastic equation for the effective pressure and the effective displacement. The approximation is rigorously justified by obtaining the error estimates for the velocity, pressure and displacement. Applications of the model problem include blood flow in small arteries. We recover the well-known Law of Laplace and provide a new, improved model when shear modulus of the vessel wall is not negligible. To cite this article: S. ?ani?, A. Mikeli?, C. R. Mecanique 330 (2002) 661–666.     

Peristaltic flow of MHD Jeffrey fluid through finite length cylindrical tube

The present investigation studies the peristaltic flow of the Jeffrey fluid through a tube of finite length. The fluid is electrically conducting in the presence of an applied magnetic field. Analysis is carried out under the assumption of long wavelength and low Reynolds number approximations. Expressions of the pressure gradient, volume flow rate, average volume flow rate, and local wall shear stress are obtained. The effects of relaxation time, retardation time, Hartman number on pressure, local wall shear stress, and mechanical efficiency of peristaltic pump are studied. The reflux phenomenon is also investigated. The case of propagation of a non-integral number of waves along the tube walls, which are inherent characteristics of finite length vessels, is also examined.