الفهرس 
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Abstract
This thesis is mainly concerned with some various stability problems for non-Newtonian fluid flows. The structure of this thesis is as follows:
We start in Chapter one by giving an introduction to the thesis as follows:
The basic governing equations that describe the fluid flow, and the main concepts for the non-Newtonian models that is used in our study are presented. Linear stability theory of the fluid flow is introduced in brief. Finally, a review on the previous investigations concerned with our thesis is presented.
In Chapter two; The effect of transverse magnetic field on the hydrodynamic stability of plane Poiseuille and Couette flow of an upper convected Maxwell fluid is investigated by the linearized method of small disturbances, assuming that the magnetic Prandtl number is sufficiently small. The equations of stability are solved numerically using Chebyshev-Tau method. It is found that the magnetic field has a stabilizing effect on the Poiseuille flow. For plane Couette flow and at certain value of elasticity, it is shown that as the Hartmann number increases, the minimum critical Reynolds number decreases and it does not increase again in contrast to the Newtonian case.
The work that has been done in chapter two is extended in Chapter three
to include a more mathematical complicated model, Oldroyd-B fluid, instead of the upper convected Maxwell fluid. The equations of stability are solved numerically using Chebyshev collocation method with QZ-Algorithm. It is found that the magnetic field has a stabilizing effect on Poiseuille flow, while it has both destabilizing and stabilizing effects on the Couette flow.
In Chapter four; Linear stability analysis is carried out to examine the effect of shear thinning and shear thickening on the stability of plane Couette flow with viscous heating for a power-law fluid. The resulting eigenvalues are calculated using the Chebyshev collocation method with QZ-Algorithm. It is found that, for shear thinning/thckening fluid, the instability occurs at a lower/highervalues of the Brinkman number Br than in Newtonian case. Also, the results indicate, for both the Newtonian and non-Newtonian fluids, that two modes of the instability occur: one termed an inviscid mode, and the second a coupled mode not a viscous mode as conjectured in a previous study [89].
Influence of non-Newtonian parameters of Powell-Eyring fluid flow between
two vertical planes, on the stability of natural convection, is considered in Chapter
five. Cheybshev collocation method with QZ-Algorithm is used to solve the
stability equations. The non-Newtonian parameter characterized Powell-Eyring
fluid is found to have a stabilizing effect on the stationary wave modes, while it
has a stabilizing/destabilizing effect on the travelling wave modes at lower/higher
values of the Prandtl number. Also, it is found, at the point of transition from
stationary to travelling wave modes, that the Prandtl number is decreased with
the non-Newtonian parameter.