الفهرس 
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Abstract
Flows occur in all elds of our natural and technical environment.
Without ows our natural and technical world would be dierent, and might not even exist at all [26].
The magnetohydrodynamic (MHD) ows and boundary layer ows have a great signicance both from a mathematical as well as a physical
standpoint. Such ows are very important in electromagnetic propulsion.
The MHD systems are used eectively in many applications including power generators, pumps, accelerators, electrostatic lters,droplet lters, the design of heat exchangers, the cooling of reactors,
etc [71].
MHD boundarylayer ows have been studied by several researchers.
Yih [76] and Ishak et al. [40] transformed the partial dierential boundary-layer equations into the non-similar boundarylayer equations
and a system of ordinary dierential equations, respectively, then they used Keller box method to solve them.
The steady laminar ow passing over the surface of a wedge was rst analyzed in the early 1930s by Falkner and Skan [29] to illustrate the application of Prandtls boundarylayer theory. The FalknerSkan equation has been the subject of much research. For instance, Xenos et al. [75] examined compressible turbulent boundary layer ow over a wedge which has signicant application in the eld of aerodynamics.
Recently, Alizadeh et al. [6] discussed the hydrodynamic FalknerSkan ow by using the Adomian decomposition method (ADM).
Spectral methods are famous ways to solve these kinds of problems.
Abbasbandy and Hayat [1, 2] have solved the the MHD FalknerSkan ow by homotopy analysis and HankelPad methods, respectively.
Very recently, Parand et al. [59] developed pseudospectral method to solve MHD FalknerSkan by Hermite functions pseudospectral method.
Aim this thesis is to study numerically some problems of computational uid dynamics and their dierent applications by applying the
Chebyshev pseudospectral dierentiation matrix (ChPDM), approach that has been introduced by Aly et al. [8] and Guedda et al. [34].
The numerical computations have done and all gures have drawn the Mathematica program. This thesis consists of four chapters, which are followed by lists of references.
CHAPTER(1)
In this chapter we review some basic information for computational uid dynamics and some of the characteristics and types of uid ows and the ow of the boundary layer and their governing equations. As well as review some methods for using matrix to obtain derivatives of dierent functions such as Chebyshev collocation methods (Chebyshev pseudospectral methods) .
CHAPTER(2)
In this chapter, we studied the eect of magnetic eld on uid ow in boundarylayer. It is mentioned that the problem depends on the magnetic parameter M. In this study the basic equations for boundary layer have been converted into a set of nonlinear ordinary dierential equations by using similarity transformations. Moreover,the resulting equations are solved numerically by applying the Chebyshev
pseudospectral dierentiation matrix (ChPDM), approach that has been introduced by Aly et al. [8] and Guedda et al. [34]. The results for the similar stream function, velocity and skin friction coe cient are presented and discussed for various parameters. Finally,the conclusion is summarized. The work in this chapter is preparing
to submission.
CHAPTER(3)
In this chapter, we studied the eect of magnetic eld on uid ow in boundarylayer through porous media. It is mentioned that the problem depends on the magnetic parameter M and porosity parameter K. In this chapter the basic equations for boundary layer have been converted into a set of nonlinear ordinary dierential equations by usiv
ing similarity transformations. Moreover, the resulting equations are solved numerically by applying the Chebyshev pseudospectral di
erentiation matrix (ChPDM). The results for the similar stream function,velocity and skin friction coecient are presented and discussed for
various parameters. Finally, the conclusion is summarized. The work in this chapter is preparing to submission.
CHAPTER(4)
In this Chapter, we studied the eect of magnetic eld on viscoelastic uid ow in boundarylayer through porous media. It is mentioned that the problem depends on the magnetic parameter M,
porosity parameter K and elastic parameter E. In this chapter the basic equations for boundarylayer have been converted into a set
of nonlinear ordinary dierential equations by using similarity transformations.
Moreover, the resulting equations are solved numerically by applying the Chebyshev pseudospectral dierentiation matrix (Ch-
PDM). The results for the similar stream function, velocity and skin friction coecient are presented and discussed for various parameters.
Finally, the conclusion is summarized. The work in this chapter is preparing to submission.
(This problem accepted for publication on Journal of Applied Sciences Research.)