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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 dierent 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 eect 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 dierential equations. In addition, the resulting equations solved numerically by using the nite dierence method (FDM). Moreover, numerical results are presented for the distribution of velocity, temperature and local Nusselt number proles for various parametric conditions. The eects 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 Dierential transform method (DTM), a comparison is presented in tables and gures for dierent values of dierent 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 eect 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 dierential 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 proles. 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 innite parallel vertical plates through a porous medium using (FDM) and Multistep dierential transform method (MDTM). The governing equations are transformed into nonlinear partial dierential equations by applying the similarity variables and then solved numerically by applying (FDM) and analytically by using (MDTM). Figures illustrate the eects 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 Dierential 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 dierential 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 proles. 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 dierential 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 proles 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. |