Peristaltic flow of a Newtonian fluid through a porous medium in a vertical tube under the effect of a magnetic field

In this paper, we studied the effects of heat transfer and magnetic field with peristaltic flow of a viscous incompressible Newtonian fluid through a porous medium in a vertical tube under the assumptions of long wavelength and low Reynolds number. The closed form solutions of velocity field and temperature are obtained. The influence of various pertinent parameters on the flow characteristics, the temperature and the heat transfer coefficient are discussed through graphs

Peristaltic Pumping of Blood Through Small Vessels of Varying Cross-section

The paper is devoted to a study of the peristaltic motion of blood in the micro-circulatory system. The vessel is considered to be of varying cross-section. The progressive peristaltic waves are taken to be of sinusoidal nature. Blood is considered to be a Herschel-Bulkley fluid. Of particular concern here is to investigate the effects of amplitude ratio, mean pressure gradient, yield stress and the power law index on the velocity distribution, streamline pattern and wall shear stress. On the basis of the derived analytical expression, extensive numerical calculations have been made. The study reveals that velocity of blood and wall shear stress are appreciably affected due to the non-uniform geometry of blood vessels. They are also highly sensitive to the magnitude of the amplitude ratio and the value of the fluid index.Comment: Accepted for publication in ASME journal of Applied Mechanics. arXiv admin note: text overlap with arXiv:1108.1285v

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

Influence of MHD on Peristaltic Flow of Couple-Stress Fluid Through a Porous Medium with Slip Effect

This  paper investigates the  influence of MHD on a peristaltic flow of Newtonian fluid with couple stress through porous medium, where the no-slip assumption between  wall and the fluid is no longer valid. Along wavelength approximation and low Reynolds number are used in the flow analysis. The flow is considered in the  wave frame of reference moving with the velocity of the wave. Analytical solution for axial velocity, pressure gradient, frictional force, stream function, magnetic field are obtained. Effects of different physical parameters, reflecting couple-stress parameter, permeability parameter, slip parameter, Hartman  number, as well as amplitude ration on pumping characteristics and frictional force, stream lines pattern and trapping of peristaltic flow pattern studied with particular emphasis. This study are discussed through graphs. Keywords:  Peristaltic Transport, Couple-Stress,  Magnetic Field, Newtonian Fluid, Porous Medium, Reynolds Number

Effect of heat transfer on the peristaltic transport of MHD with couple-stress fluid through a porous medium with slip effect

This  paper concern with the Peristaltic transport of MHD Newtonian fluid in  asymmetric two dimensional channel with couple –stress through  a porous  medium under  the influence of heat  transfer analysis. For the formulation of the problem long wave length and low Reynold number  assumption is taken into account.  An  exact solution is presented for velocity field and the temperature field through solving a    non-homogenies partial differential equation that described the flow field. Effects of different physical parameters, reflecting couple-stress parameter, permeability parameter, slip parameter, Hartman  number, constant heat radiation factor and Grashof number, as well as amplitude ration on pumping characteristics and frictional force, stream lines pattern and trapping of peristaltic flow pattern studied with particular emphasis. This study are discussed through graphs. Keywords:  Peristaltic Transport, Couple-Stress,  Magnetic Field, Newtonian Fluid, Porous Medium, Reynolds Number, Heat transfer

Slip and hall current effects on Jeffrey fluid suspension flow in a peristaltic hydromagnetic blood micropump

The magnetic properties of blood allow it to be manipulated with an electromagnetic field. Electromagnetic blood flow pumps are a robust technology which provide more elegant and sustainable performance compared with conventional medical pumps. Blood is a complex multi-phase suspension with non-Newtonian characteristics which are significant in micro-scale transport. Motivated by such applications, in the present article a mathematical model is developed for magnetohydrodynamic (MHD) pumping of blood in a deformable channel with peristaltic waves. A Jeffery’s viscoelastic formulation is employed for the rheology of blood. A twophase fluid-particle (“dusty”) model is utilized to better simulate suspension characteristics (plasma and erythrocytes). Hall current and wall slip effects are incorporated to achieve more realistic representation of actual systems. A two-dimensional asymmetric channel with dissimilar peristaltic wave trains propagating along the walls is considered. The governing conservation equations for mass, fluid and particle momentum are formulated with appropriate boundary conditions. The model is simplified using of long wavelength and creeping flow approximations. The model is also transformed from the fixed frame to the wave frame and rendered non-dimensional. Analytical solutions are derived. The resulting boundary value problem is solved analytically and exact expressions are derived for the fluid velocity, particulate velocity, fluid/particle fluid and particulate volumetric flow rates, axial pressure gradient, pressure rise and skin friction distributions are evaluated in detail. Increasing Hall current parameter reduces bolus growth in the channel, particle phase velocity and pressure difference in the augmented pumping region whereas it increases fluid phase velocity, axial pressure gradient and pressure difference in the pumping region. Increasing the hydrodynamic slip parameter accelerates both particulate and fluid phase flow at and close to the channel walls, enhances wall skin friction, boosts pressure difference in the augmented pumping region and increases bolus magnitudes. Increasing viscoelastic parameter (stress relaxation time to retardation time ratio) decelerates the fluid phase flow, accelerates the particle phase flow, decreases axial pressure gradient, elevates pressure difference in the augmented pumping region and reduces pressure difference in the pumping region. Increasing drag particulate suspension parameter decelerates the particle phase velocity, accelerates the fluid phase velocity, strongly elevates axial pressure gradient and reduces pressure difference (across one wavelength) in the augmented pumping region. Increasing particulate volume fraction density enhances bolus magnitudes in both the upper and lower zones of the channel and elevates pressure rise in the augmented pumping region

Impact of Permeable Lining of the Wall on the Peristaltic Flow of Herschel Bulkley Fluid

The peristaltic motion is modeled for the Herschel Bulkley fluid, considered to flow in a non-uniform inclined channel. The channel wall is supposed to be lined with a non-erodible porous material. The flow is considered to be moving in a wave frame of reference moving with same velocity as of the sinusoidal wave. Low Reynolds number and long wave length assumptions are made to solve the model. Analytical solution is obtained for the pressure difference and also for the frictional force. Graphs are plotted, using Mathematica software, for both the results of pressure difference and frictional force against time average velocity. We observe that increasing the porous thickening, increases the pressure difference while, it decreases the frictional force. It is seen that the behavior of the pressure difference is opposite to the behavior of the frictional force for all the parameters considered

Peristaltic transport of bi-viscosity fluids through a curved tube : a mathematical model for intestinal flow

The human intestinal tract is a long curved tube constituting the final section of the digestive system in which nutrients and water are mostly absorbed. Motivated by the dynamics of chyme in the intestine, a mathematical model is developed to simulate the associated transport phenomena via peristaltic transport. Rheology of chyme is modelled using the Nakamura-Sawada bi-viscosity non-Newtonian formulation. The intestinal tract is considered as a curved tube geometric model. Low Reynolds number (creeping hydrodynamics) and long wavelength approximations are taken into consideration.Analytical solutions of the moving boundary value problem are derived for velocity field,pressure gradient and pressure rise. Streamline flow visualization is achieved with Mathematica symbolic software. Peristaltic pumping phenomenon and trapping of the bolus are also examined. The influence of curvature parameter, apparent viscosity coefficient (rheological parameter) and volumetric flow rate on flow characteristics is described. Validation of analytical solutions is achieved with a MAPLE17 numerical quadrature algorithm. The work is relevant to improving understanding of gastric hydrodynamics and provides a benchmark for further computational fluid dynamics (CFD) simulations

MHD Peristaltic Flow of a Couple Stress Fluids with Heat and Mass Transfer through a Porous Medium

In the present article, we have studied the effects of heat and mass transfer on the MHD flow of an incompressible, electrically conducting couple stress fluid through a porous medium in an asymmetric flexible channel over which a traveling wave of contraction and expansion is produced, resulting in a peristaltic motion. The flow is examined in a wave frame of reference moving with the velocity of the wave. Formulas of dimensionless velocity, temperature and concentration are obtained analytically under assumptions of long wavelength and low Reynolds number. The effects of various parameters of interest such as the couple stress fluid parameter, Darcy number, Hartmann number and Schmidt number on these formulas were discussed and illustrated graphically through a set of figures. Key words: peristalsis,  Couple stress fluid,  Porous medium,  MHD flow, Heat transfer,  Mass transfer

Effect of Slip Condition on Coup le Stress Fluid Flow in a Channel with Mild Stenosis in the Presence of Uniform Magnetic Field

The s teady flow of an incompressible couple stress fluid in a two dimensional uniform channel with stenosis under the influence of a magnetic field has been investigated. Assuming the stenosis to be mild, the flow equations have been analy tically solved using the slip condition and expressions for the resistance to flow and wall shear stress have been derived. The effects of various parameters on these flow variables have been studied. It is found that the resistance to flow as well as the wall shear stress increase with the height of the stenosis and decrease with the couple stress and magnetic parameters. The effects of other parameters on resistance to flow and the wall shear stress have been considered