الفهرس 
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Abstract
This thesis contains numerical and analytical solutions for systems
of nonlinear equations governing
uid
ow, heat transfer and the concentration
of some nonNewtonian
uids through di erent geometric
shapes. Also presented a study to the error analysis in numerical
methods by comparing it with the analytical methods and previously
published work. It should be noted that the solution of the current results
is obtained by designing Fortran, Matlab and Mathematica programmes
and then the present graphics is drawn by designing Excel
and Matlab programmes. This thesis consists of six chapters, which
are followed by lists of references.
Chapter(1)
The introductory chapter is considered as a background for the material
included in the thesis. The purpose of this chapter is to present
a short introduction on numerical analysis and
uid mechanics, a brief
survey of famous numerical and analytical methods which using to
solve
uid mechanics problems,
uid properties and the basic
ow
equations. Moreover, it contains a short survey of some needed concepts
of the material used in this thesis.
Chapter(2)
The purpose of this chapter is to study the e ect of Papanastasiou
viscosity on steady MHD
ow and heat transfer between two parallel
plates in the presence of dissipations and radiation. The dimensional
quantities are applied to transform the governing equations into nonlinear
partial di erential equations. In addition, the resulting equations
solved numerically by using the nite di erence method (FDM). Moreover, numerical results are presented for the distribution of velocity,
temperature and local Nusselt number pro les for various parametric
conditions. The e ects of varying the yield stress parameter
D, the Hartman number Ha, Brinkman number Br and the radiation
parameter are determined. In order to verify the eciency of the
proposed method in comparison with Di erential transform method
(DTM), a comparison is presented in tables and gures for di erent
values of di erent parameters. The tables and gures clearly show
that the results by (FDM) are in good agreement with the results of
analytical solution by using (DTM). Furthermore, at the end of this
chapter the conclusions are summarized. Some results of this chapter
was published in (Eleventh International Conference of Fluid
Dynamics (ICFD11)), December 1921, 2013, Alexandria, Egypt.
Chapter(3)
The aim of this chapter is to study the e ect of chemical reaction
and radiation on heat and mass transfer of stagnation point
ow of
micropolar
uid through a porous medium. The governing equations
are transformed into nonlinear ordinary di erential equations by applying
the similarity transformation and then solved numerically by
applying (FDM). The solutions are found to be governed by six parameters,
the porosity parameter M, the material parameter K, the
thermal radiation parameter Rd, the Prandtl number Pr, the Schmidt
number Sc and the reactionrate parameter . Numerical results are
presented the distribution of velocity, temperature and concentration
pro les. Furthermore, comparisons of the present results with previously
published work show that the present results have high accuracy
and are found to be a good agreement. At the end of this chapter, the
conclusions are summarized. Some results of this chapter are accepted
for (INTERNATIONAL JOURNAL OF APPLIED MATHE-
MATICS AND PHYSICS).
Chapter(4)
The main goal of this chapter is to study numerical and analytical
treatment of MHD natural convection of an incompressible
uid
between two in nite parallel vertical plates through a porous medium using (FDM) and Multistep di erential transform method (MDTM).
The governing equations are transformed into nonlinear partial di erential
equations by applying the similarity variables and then solved
numerically by applying (FDM) and analytically by using (MDTM).
Figures illustrate the e ects of dimensionless nonNewtonian viscosity
, Prandtl number Pr, Eckert number E, porosity parameter Mp and
magnetic parameter Mm on the nondimensional velocity and temperature.
The gures and tables clearly show that the results by (FDM)
and (MDTM) are in good agreement with the results of analytical solution
of previously published works by using Homotopy perturbation
method (HPM), Adomian decomposition method (ADM), Homotopy
analysis method (HAM) and Di erential transform method (DTM).
The work in this chapter is preparing to publication.
Chapter(5)
The main aim of this chapter is to study comparison between numerical
and analytical solution of free convection of Casson
uid
ow with
constant heat sources in a porous channel with suction and injection.
In addition, the governing equations are transformed into nonlinear
ordinary di erential equations by applying the dimensionless quantities
and then solved numerically by applying (FDM). Moreover, the
solutions are found to be governed by ve parameters, the heat source
parameter , the suction Reynolds number R, the Prandtl number Pr,
the dimensionless group parameter Q and the yield stress parameter
D. Numerical results are presented the distribution of velocity and
temperature pro les. In order to verify the accuracy of the present
results, we have compared these results with analytical solution of
present work in Newtonian case by using (DTM) and previously published
work. It is observed that this approximate numerical solution is
in good agreement with analytical solution by using (DTM) and previously
published work. At the end of this chapter the conclusions are
summarized. The work in this chapter is preparing to publication.
Chapter(6)
The goal of this chapter is to study the three dimensional entrance
heat transfer to MHD Bingham
uid
ow in a square duct with joule and viscous dissipations. Using suitable dimensional quantities the
governing equations are transformed into dimensional nonlinear partial
di erential equations and solved numerically by using (FDM). The
solutions are found to be governed by three parameters, the Hartman
number Ha, the yield stress parameter D and the Brinkman number
Br. Moreover, numerical and graphical results for the velocity, temperature
and local Nusselt number pro les are presented and discussed for
various parametric conditions. Furthermore, tables shows comparison
between numerical solution by using (FDM) and previously published
work to verify the accuracy of the numerical solution of present work by
using (FDM). It is observed that this approximate numerical solution
is in good agreement with the corresponding solutions. Finally, at the
end of this chapter the conclusions are summarized. Some results of
this chapter was published in (Eleventh International Conference
of Fluid Dynamics (ICFD11)), December 1921, 2013, Alexandria,
Egypt.