الفهرس 
CHAPTER 1: Introduction and Literature SurveyOnly 14 pages are availabe for public view
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Abstract
This study is divided into two parts
Part A) Numerical Study:
The current study presents comparisons between four different discretization schemes for non-orthogonal grids in the skewed cavity and highly skewed flow in the curved cavity.
These schemes are upwind differencing scheme (UDS), upwind differencing scheme with numerical diffusion (UDS-ND), central differencing scheme (CDS) and Quadratic upwind interpolation for convective kinematics (QUICK). The comparison between the selected
schemes for highly skewed flow in the curved cavity indicated that the upwind differencing scheme with numerical diffusion is the best choice in terms of accuracy and computational cost. Besides, the comparison between the present results and previous results from the literature indicates that the current procedure, which is more suitable for general purpose codes, can produce computational results which are in close agreement with those obtained
from body fitted and polar coordinates system. For the case of non-orthogonal grids in the skewed cavity, all the tested schemes produce close results when they are compared with benchmark solution. However, the UDS-ND requires a smaller number of iteration and
shorter computational time. Despite the upwind differencing scheme with numerical diffusion is the first-order scheme, its accuracy is very close to the second and third-order schemes. Therefore, the UDS-ND is recommended for general-purpose code because its
stability is higher than the higher-order scheme and computational time is lower. The blood flow is assumed as a two-phase (liquid-solid) model with the Eulerian-Lagrangian approach.
The plasma of the blood is treated as a continuous phase while the red blood cells are treated as a solid phase. The effect of hematocrit change and different Reynolds numbers had been validated with the available experimental data. For the best of our knowledge, the effect of red blood cell concentration on the flow characteristics had been studied only through simple geometries as a pipe. The validation of the blood flow through the pipe gives very
good prediction with the experimental results. An increase of the red blood cell concentration will cause a decrease in the flow velocity near the centerline of the pipe while the velocity near the wall will be increased. The four-way coupling between the two-phases had been used. The effect of drag, shear lift, Magnus lift, and gravity forces have been taken into consideration
Part B) Analytical Study:
Stenotic geometry in the blood flow is one of the important sections in the human arteries. Understanding the behavior of blood flows in this section is necessary because it is playing a role in causing a die from heart attacks. Many different mathematical models and solution techniques are dealing with blood flows. A two-phase (liquid-solid) model solved
by a perturbation method will be introduced. Effects of hematocrit, Reynolds number, area reduction, and different geometries of the stenotic channel are studied on the velocity,
pressure gradient, and streamlines. The flow characteristics (velocity and pressure) give a great increase as the stenosis classified as a sever stenosis. It is found that the stenosis
geometry has a great effect on the pressure gradient in the axial direction, and there is a change in velocity profile in each cross section of the geometry. The hematocrit has a
noticed effect on the flow velocity and pressure gradient, in which as the hematocrit increases the maximum velocity decreases before the throat while it increases after that
section. The blood vessels can be treated with a slip boundary condition assumption because of the nature of the blood and the walls of the living organism vessels as mentioned by many
previous authors. The effect of the slip boundary conditions is studied with the same previous parameters on the channel with a narrowing taking in consideration the effect of
Knudsen number. The results show that the slip boundary condition at the wall affects on the velocity distribution and the pressure gradient.
The thesis is divided to six chapters.
Chapter 1 deals with the introduction and literature survey about numerical and analytical mathematical models for blood flow through the stenosis.
Chapter 2 introduces mathematical modeling and solution procedure for the generalized coordinates system for the continuous phase (fluid flow) and discreet phase (solid particles).
This chapter introduces different discretization schemes for the convective term in a generalized coordinate system for the single-phase (liquid phase).
Chapter 3 shows the numerical results for three different cases, the first case is the flow in a highly skewed flow through a curved cavity. The second case is the flow in non-orthogonal grids in a skewed cavity. The last case is a validation for the blood flow through a pipe under the effect of different hematocrits.
Chapter 4 presents the analysis of a different stenotic geometry on two-phase flow by using the perturbation analytical method up to the second order. Effects of different parameters
are introduced.
Chapter 5 presents the slip wall velocity analysis through a stenotic geometry. The effect of the Knudson number is presented with the same parameters of the previous chapter.
Chapter 6 includes the conclusions of this work as well as recommendations for further studies.