N.S. Gad

Abstract: This paper describes the peristaltic transport under the effect of Hall currents in a channel having compliant boundaries. The fluid–solid interaction problem is investigated by considering equations of motion of both the fluid and the deformable boundaries. A perturbation solution of the stream function for zeroth, first and second in a small amplitude ratio is obtained. The phenomenon of the “mean flow reversal” is found to exist both at the center and at the boundaries of the channel. The effect of wall damping, wall tension, Hall parameter and Hartmann number on the mean axial velocity and reversal flow is investigated. The numerical results show that the flow reversal increases by increasing the wall damping and Hall parameter while it decreases by increasing the wall tension and Hartmann number.

Abstract: 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.

Abstract: 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 flow through a porous medium 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 and the effect of the permeability parameter and the various parameters including in the problem are discussed numerically.

Abstract: Experimental studies and observations in the human brain indicate that interstitial fluid and solutes, such as amyloid-beta (Abeta), are eliminated from grey matter of the brain along pericapillary and periarterial pathways. It is unclear, however, what constitutes the motive force for such transport within blood vessel walls, which is in the opposite direction to blood flow. In this paper the potential for global pressure differences to achieve such transport are considered. A mathematical model is constructed in order to test the hypothesis that perivascular drainage of interstitial fluid and solutes out of brain tissue is driven by pulsations of the blood vessel walls. Here it is assumed that drainage occurs through a thin layer between astrocytes and endothelial cells or between smooth muscle cells. The model suggests that, during each pulse cycle, there are periods when fluid and solutes are driven along perivascular spaces in the reverse direction to the flow of blood. It is shown that successful drainage may depend upon some attachment of solutes to the lining of the perivascular space, in order to produce a valve-like effect, although an alternative without this requirement is also postulated. Reduction in pulse amplitude, as in ageing cerebral vessels, would prolong the attachment time, encourage precipitation of Abeta peptides in vessel walls, and impair elimination of Abeta from the brain. These factors may play a role in the pathogenesis of cerebral amyloid angiopathy and in the accumulation of Abeta in the brain in Alzheimer's disease.

Abstract: In this paper, the effects of heat transfer and Hall current on the sinusoidal motion of solid particles through a planar channel has been discussed. The walls of the channel are considered as comp...

Abstract: Impact of applied magnetic field on the peristaltic transport of Carreau–Yasuda fluid in a curved conduit is analyzed in this article Hall effects are also taken into consideration Lubrication approach is utilized in problem formulation Resulting nonlinear system is solved numerically Results for axial velocity, pressure gradient, pressure rise per wavelength and stream function are obtained and studied graphically Results revealed that for small values of curvature parameter the fluid velocity is not symmetric about the centerline Also increase in the value of Hall parameter balances the magnetic influence of applied magnetic field by some extent Further, the Carreau–Yasuda fluid possesses large size of trapped bolus when compared with the Newtonian fluid

Abstract: This study examines the peristaltic transport of silver-water nanofluid in the presence of constant applied magnetic field. Ohmic heating and Hall effects are also taken into account. Present attempt includes the velocity and thermal slip effects. Mathematical modeling is carried out employing the lubrication approach. The resulting system of equations is numerically solved. Effects of sundry parameters on the quantities of interest are studied through graphs. Results show that addition of 5% silver nanoparticles reduces the velocity of base fluid (water in this case) by almost 10% and its temperature by 16%. Further presence of Hall effects lessens the changes brought by an applied magnetic field in the state of nanofluid. Maximum velocity of nanofluid decreases with an increase in the value of velocity slip parameter whereas maximum temperature enhances by increasing the thermal slip parameter. It is hoped that the presented analysis is of considerable importance in the modern drug delivery systems in biomedical engineering.

Abstract: In this paper, the effects of both rotation and magnetic field of a micropolar fluid through a porous medium induced by sinusoidal peristaltic waves traveling down the channel walls are studied analytically and computed numerically. Closed-form solutions under the consideration of long wavelength and low-Reynolds number is presented. The analytical expressions for axial velocity, pressure rise per wavelength, mechanical efficiency, spin velocity, stream function and pressure gradient are obtained in the physical domain. The effect of the rotation, density, Hartmann number, permeability, coupling number, micropolar parameter and the non-dimensional wave amplitude in the wave frame is analyzed theoretically and computed numerically. Numerical results are given and illustrated graphically in each case considered. Comparison was made with the results obtained in the presence and absence of rotation and magnetic field. The results indicate that the effect of rotation, density, Hartmann number, permeability, coupling number, micropolar parameter and the non-dimensional wave amplitude are very pronounced in the phenomena.