الفهرس 
INTRODUCTION AND LITERATURE REVIEWOnly 14 pages are availabe for public view
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Abstract
In this thesis, a study of some non-linear models in fluid mechanics is presented and its applications. The aim is to obtain numerical solutions for three important non-darcian flow models in porous medium of a Newtonian fluid with different geometries. It should be mentioned that the non-Darcy flow in a porous medium deals with the analysis in which the differential equations governing the fluid motion are based on the non-Darcy law (Darcy -Forchheimer flow model) that accounts for the drag exerted by the porous medium, in addition to the inertial effect.
In the first problem, the steady non-Darcian flow through a porous medium of a viscous incompressible fluid due to the uniform rotation of a disk of infinite extent is studied. The governing nonlinear differential equations are integrated numerically using finite difference approximations. The effect of the porosity of the medium and the inertial effects on the steady velocity fields as well as the radial and tangential wall shear stresses are analyzed. The study indicates the resisting effect of the porosity on the flow velocities. This resisting effect increases in case of other inertial effects on the fluid flow besides the pore resistance, which summarizes and investigates the non-Darcian flow behavior. It is also showed that the porosity and non-Darcian parameters are inversely proportional to both the magnitude of the radial wall shear stress and the axial flow towards the disk, while they show direct proportionality with the tangential wall shear stress.
In the second problem, the unsteady non-darcian flow of a dusty fluid through a circular pipe in a porous medium is investigated. The carrier fluid is assumed viscous and incompressible. The particle phase is considered incompressible, inviscid and pressureless that the particles are being dragged along with the fluid-phase where the motion of the dust particles is governed by Newton’s second law applied in the axial direction. The flow in the pipe starts from rest through the application of a constant axial pressure gradient. The governing momentum equations for both the fluid and particle-phases are solved numerically using the finite difference approximations. The effect of the porosity of the medium and the inertial effects on the velocity distributions of the fluid and particle-phases are reported. It is showed that increasing the porosity parameter decreases the velocity of the fluid and dust particles, while increasing the non-Darcian parameter decreases more the velocity of the fluid and dust particles for all values of the porosity parameter. The skin-friction coefficient for the fluid and the volumetric flow rates for both the fluid and particle phases are defined, and their steady state values are computed.
In the third problem, the unsteady non-Darcian flow between two parallel plates in a porous medium of a viscous incompressible fluid considering heat transfer is studied. The study presented in two parts; in the first part the fluid flow is between two stationary parallel plates, while in the second part; a Couette flow is considered where the upper plate moves with a uniform velocity and the lower plate is stationary. In each part the flow is discussed in two cases, firstly, when the fluid motion is subjected to a constant pressure gradient and secondly when the fluid is acted upon by an exponential decaying pressure gradient applied in the axial direction. The flow is subjected to a uniform suction from above and a uniform injection from below. The two plates are kept at two different but constant temperatures. The viscous dissipation is taken into consideration in the energy equation. The governing momentum and energy equations are solved numerically using the finite difference approximations. The inclusion of the porosity effect, inertial effects as well as the velocity of suction or injection leads to some interesting effects, on both the velocity and temperature fields. The study includes investigations of the non-Darcian flow in porous medium passing through the case of Darcian flow and finally the Newtonian fluid flow through non-porous medium obtaining the easiest quick path for the flow.