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.     

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.     

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.     

Elastoviscoplastic fluid flow in non-circular tubes: Transversal field and interplay of elasticity and plasticity

An analytical study of elastoviscoplastic fluid flow in tubes of non-circular cross section is presented. The constitutive structure of the fluid is described by a linear frame invariant combination of the Phan-Thien−Tanner model of viscoelastic fluids and the Bingham model of plastic fluids. Non-circular tube cross sections are modeled by the shape factor method a one-to-one mapping of the circular base contour into a wide spectrum family of arbitrary tube contours. Field variables are expanded into asymptotic series in terms of the elasticity measure, the Weissenberg number We, coupled with an asymptotic expansion in terms of the geometrical mapping parameter ε leading to a set of hierarchical momentum balance equations which are solved successively up to and including the third order in We when the secondary field appears for the first time. The computational algorithm developed is applied to the study of the non-rectilinear flow in tubes with triangular and square cross sections. We find that the presence of the yield stress dampens the intensity of the purely viscoelastic vortices, the higher the yield stress the lower the intensity of the vortices in the cross-section, and the further away the vortices are from the center of the cross section as compared to the purely viscoelastic vortices. The results also evidence that viscoelasticity increases the axial flow for given viscoplastic conditions and pressure drop, and consequently increases the rate of flow, a phenomenon that may find applications in optimizing material transportation.     

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.     

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 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.     

Parametric study of liquid droplets impinging on porous surfaces

This work presents a numerical simulation of the fluid dynamics of a liquid droplet during impact/absorption onto a porous medium. The main focus of this paper is on a parametric study of the influence of the governing parameters upon the fluid flow characteristics. The problem is described in a non-dimensional form, and the influence of the main governing parameters is investigated, including their variation along the range of physical configurations of interest. This procedure revealed 7 main governing parameters: Reynolds number (Re), Darcy number (Da), porosity (ε), Froude number (Fr), Weber number (We), contact angle (θ) and the ratio between pore and particle diameter size in the porous substrate (α). The results indicate that the values of Da and Re are more related to the amount of momentum dissipation due to the drag of the solid matrix of the substrate, while the values of We, α and θ can be mainly related to capillary pressure.     

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.     

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.     

Slip effects in peristalsis

Taking slip condition into account the magnetohydrodynamic peristaltic flow in an asymmetric channel is theoretically analyzed. The analytic solutions for stream function, longitudinal pressure gradient, and temperature have been found in closed form by employing long wavelength and low Reynolds number approximations. A discussion for pressure rise and frictional forces is provided through numerical integration. Finally, the effects of various key parameters are discussed with the help of graphs and tables. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 1003–1015, 2011     

Heat transfer in a peristaltic flow of MHD fluid with partial slip

In the present note, we have discussed the effects of partial slip on the peristaltic flow of a MHD Newtonian fluid in an asymmetric channel. The governing equations of motion and energy are simplified using a long wave length approximation. A closed form solution of the momentum equation is obtained by Adomian decomposition method and an exact solution of the energy equation is presented in the presence of viscous dissipation term. The expression for pressure rise is calculated using numerical integration. The trapping phenomena is also discussed. The graphical results are presented to interpret various physical parameter of interest. It is found that the temperature field decreases with the increase in slip parameter L, and magnetic field M, while with the increase in P_r and E_c, the temperature field increases.     

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.     

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     

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.     

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.     

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.     

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.     

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.