Similarity Solution for Flow of a Micro-Polar Fluid Through a Porous Medium

The equations of two dimensional incompressible steady micro-polar fluid flows through a porous medium are studied. Lie group analysis is employed and the solutions corresponding to the translational symmetry are developed. A boundary value problem is investigated and the results are sketched graphically. The effect on the flow of the porosity coefficient of the porous medium and the micro-polar parameters are observed

The Flow Separation of Peristaltic Transport for Maxwell Fluid between Two Coaxial Tubes

We study the peristaltic mechanism of an incompressible non-Newtonian biofluid (namely, Maxwell model) in the annular region between two coaxial tubes. The inner tube represents the endoscope tube. The system of the governing nonlinear PDE is solved by using the perturbation method to the first order in dimensionless wavenumber. The modified Newton-Raphson method is used to predict the flow separation points along the peristaltic wall and the endoscope tube. The results show that the presence of the endoscope (catheter) tube in the artery increases the pressure gradient and shear stress. Such a result seems too reasonable from the physical and medical point of view

A Study of Nonlinear Variable Viscosity in Finite-Length Tube with Peristalsis

Peristaltic motion of an incompressible Newtonian fluid with variable viscosity induced by periodic sinusoidal traveling wave propagating along the walls of a finite-length tube has been investigated. A perturbation method of solution is sought. The viscosity parameter α (α << 1) is chosen as a perturbation parameter and the governing equations are developed up to the first-order in the viscosity parameter (α). The analytical solution has been derived for the radial velocity at the tube wall, the axial pressure gradient across the length of the tube, and the wall shear stress under the assumption of low Reynolds number and long wavelength approximation. The impacts of physical parameters such as the viscosity and the parameter determining the shape of the constriction on the pressure distribution and on the wall shear stress for integral and non-integral number of waves are illustrated. The main conclusion that can be drawn out of this study is that the peaks of pressure fluctuate with time and attain different values with non-integral numbers of peristaltic waves. The considered problem is very applicable in study of biological flow and industrial flow

Peristaltic Transport of a Physiological Fluid in an Asymmetric Porous Channel in the Presence of an External Magnetic Field

The paper deals with a theoretical investigation of the peristaltic transport of a physiological fluid in a porous asymmetric channel under the action of a magnetic field. The stream function, pressure gradient and axial velocity are studied by using appropriate analytical and numerical techniques. Effects of different physical parameters such as permeability, phase difference, wave amplitude and magnetic parameter on the velocity, pumping characteristics, streamline pattern and trapping are investigated with particular emphasis. The computational results are presented in graphical form. The results are found to be in perfect agreement with those of a previous study carried out for a non-porous channel in the absence of a magnetic field

Peristaltic Flow of a Magneto-Micropolar Fluid: Effect of Induced Magnetic Field

We carry out the effect of the induced magnetic field on peristaltic transport of an incompressible conducting micropolar fluid in a symmetric channel. The flow analysis has been developed for low Reynolds number and long wavelength approximation. Exact solutions have been established for the axial velocity, microrotation component, stream function, magnetic-force function, axial-induced magnetic field, and current distribution across the channel. Expressions for the shear stresses are also obtained. The effects of pertinent parameters on the pressure rise per wavelength are investigated by means of numerical integrations, also we study the effect of these parameters on the axial pressure gradient, axial-induced magnetic field, as well as current distribution across the channel and the nonsymmetric shear stresses. The phenomena of trapping and magnetic-force lines are further discussed

Influence of Lateral Walls on Peristaltic Flow of a Couple Stress Fluid in a Non-Uniform Rectangular Duct

In the present investigation we have studied the peristaltic flow of a couple stress fluid in a non-uniform rectangular duct. The flow is investigated in a wave frame of reference moving with the velocity c away from the fixed frame. The peristaltic waves propagating on the horizontal side walls of a non-uniform rectangular duct is studied under lubrication approach. The exact solutions of velocity and pressure gradient have been found under lubrication approach. The pumping characteristics, axial pressure gradient, velocity field and trapping phenomena have been discussed to highlight the physical features of emerging parameters of couple stress fluid