Some Problems of Bio- uids Motion through Di erent Surfaces under the Action of External Forces with its Applications

Abstract

Chapter (1): is a general introduction. We give in it some information about the following topics: Fluid mechanics and bio-fluid mechanics, some types of fluids flow, Newtonian fluids, non Newtonian fluids, some models of non-Newtonian fluids, peristaltic transport, blood, stenosis, heat transfer, nano-fluids, the flow through porous media, basic equations of motion, non-dimensional numbers, stability in fluid dynamics, Electrostatics and Electrohydrodynamics (EHD), Maxwell's equations, the EHD linear Kelvin-Helmholtz instability, the viscous potential theory, boundary and interfacial conditions, multiple-scale analysis.

Chapter( 2): in this chapter, we investigated the peristaltic transport of a blood flow through a circular symmetric tapered tube. By considering a Casson model, the nature of blood in small arteries are mathematically analyzed. The analysis is carried out for an artery with mild stenosis. The wall motion is governed by a wave of contraction propagating along the wall of the tube which contracts in the radial direction. The analytical solutions of equations of motion are based on a perturbation technique. Analytical expressions for the stream function, the axial velocity and the wall shear stress distributions have been computed. The influences of pertinent parameters, such as the Reynolds number, wave number, yield stress and amplitude ratio, are shown and discussed in some details. The numerical results show that, in case of the diverging tapered artery, the curves of the axial velocity are greater than those in case of the non tapered one as well as the convergent tapered artery. Streamlines have been also depicted. It is observed that the size of the trapped bolus increases with the increasing of both the wave number and the yield stress. Furthermore, it decreases with the increasing of both the Reynolds number and the taper angle.

Chapter (3): in this chapter, we studied the effect of a vertical alternating current (AC) electric field and heat transfer on peristaltic flow of a dielectric Oldroydian viscoelastic fluid. This analysis involved a uniform and non-uniform annulus having a mild stenosis. The analytical solutions of equations of motion are based on a perturbation technique. This technique depends on two parameters. Firstly, the amplitude ratio. Secondly, the small wave number. A numerical calculations are adopted to obtain the effects of several parameters, such as the electrical Rayleigh number, the adverse temperature parameter, the Reynolds number, the wave number, the maximum height of stenosis and the Weissenberg numbers, on the distributions of velocity, temperature, electric potential and wall shear stress. The stream lines are also depicted. It is found that, in case of convergent tapered tube, the above distributions are larger than those in case of the non tapered one as well as the diverging tapered tube. The present study is very important in many medical applications, such as the gastric juice motion in the small intestine when an endoscope is inserted through it.

Chapter (4) : this chapter investigates the effect of peristaltic flow of a Jeffrey nanofluid in endoscope. The flow is streaming through a tapered artery having a mild stenosis. The influences of heat and nanoparticle concentration on blood flow are also taken into account. Both velocity and thermal slip conditions are considered. The governing equations of motion, energy and nanoparticles are based on a perturbation technique. this technique depends on two parameters. Firstly, the amplitude ratio. Secondly, the small wave number. The distributions of the axial velocity, temperature and nanoparticle volume fraction are analytically derived. The pressure rise and friction force are numerically calculated. The numerical calculations are adopted to obtain the effects of several physical parameters, such as the slip parameter, Brownian motion parameter, thermophoresis parameter, the Reynolds number, the taper angle, nanoparticles Rayleigh number, thermal Rayleigh number and the maximum height of stenosis. It is found that the axial velocity increases with the decrease of the slip parameter. Meanwhile, it increases with the increase of both the nanoparticles Rayleigh number and the thermal Rayleigh number in the region of stenosis. The stream lines are also depicted. It is observed that the trapped bolus decreases in size with the increase of both the Brownian motion parameter and the thermophoresis parameter. In addition, the trapped bolus increases in size with the increase of both the maximum height of stenosis and the taper angle.

Chapter (5): This chapter investigates the effect of partial slip on peristaltic flow of a Sisko fluid through a porous medium. The flow is streaming through a tapered artery having a mild stenosis. The influences of heat and chemical reactions on blood flow are also taken into account. The governing equations of motion, energy and concentration are simplified by using the long wavelength and low Reynolds number approximations. The analytical solutions of these equations are obtained by considering a perturbation technique for small non-Newtonian Sisko fluid parameter. The pressure rise and friction force are numerically calculated. The numerical calculations with the help of graphs are adopted to obtain the effects of several parameters, such as the slip parameter, permeability parameter, the taper angle, Brickmann number, Soret number and the maximum height of stenosis, upon the distributions of velocity, temperature, concentration, pressure rise and friction force. It is found that the axial velocity increases with the increase of slip parameter. Meanwhile, it decreases with the increase of permeability parameter. The stream lines are also depicted. It is observed that the trapped bolus increases in size with the increase of both the slip parameter and the maximum height of stenosis.

Chapter (6): In this chapter, In the light of a viscous potential flow analysis, the nonlinear Kelvin-Helmholtz instability of two superposed semi-infinite fluid layers is investigated. The flows are streaming through porous media. The Sisko model is employed to describe the rheological behavior of a non-Newtonian fluid. A uniform tangential electric field is applied at the interface between two media in the absence of surface charges. A weakly nonlinear theory of wave propagation is adopted, which depends on solving the linearized equations of motion with the appropriate nonlinear boundary conditions. The effect of the surface tension is, also, taken into account. The normal mode technique is applied to obtain the solution of the linear equations of motion. A general dispersion relation is derived. Also, the transition curves are plotted at the different parameters of the considered system. The Hurwitz criterion of a quadratic dispersion equation is utilized to determine the stability of the system. Regions of stability and instability are determined and discussed in some details. The method of the multiple time scale with the aid of the Taylor's expansion are employed in order to obtain the well-known Ginzburg-Landau equation. This equation describes the behavior of the system in a nonlinear approach. The conditions of the stability are theoretically attained. Stability diagrams are characterized through di_erent physical quantities. Due to nonlinear effects, new regions of stability and instability are illustrated.