الفهرس 
Introduction and BasicsOnly 14 pages are availabe for public view
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Abstract
Differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology. In pure mathematics, differential equations are studied from several different perspectives, mostly concerned with their solutions the set of functions that satisfy the equation. Only the simplest differential equations are solvable by explicit formulas; however, some properties of solutions of a given differential equation may be determined without finding their exact form. If a self-contained formula for the solution is not available, the solution may be numerically approximated using computers. The theory of dynamical systems puts emphasis on qualitative analysis of systems described by differential equations, while many analytical methods have been developed to determine solutions with a given degree of accuracy. One of the effective semi-analytical methods is named by the differential transform method (DTM), which is a semi-analytical method for solving integral equations, ordinary and partial differential equations. The method provides the solution in terms of convergent series with easily computable components. In this thesis, we use the generalized methods of DTM by new techniques named by Pade’-approximation differential transform method (Pade’-DTM) and the Multi-step differential transform method (Ms-DTM) to solve the highly nonlinear systems of fluid mechanics, and especially peristaltic flow problems
In the following, we conclude with a brief description of each chapter:
• Chapter (1): Introduction and Basics
This chapter introduces some information about methods of solutions that used in our thesis such as, Parametric ND Solve Method, Finite Difference Method, Differential transform method and Multi-step differential transform method. In addition, presents some acquaintances concerning with the classification of fluids, heat and mass transfer, the flow through a porous medium, magnetohydrodynamic (MHD), peristalsis, nanotechnology and mathematical models of the governing equations of the fluid.
• Chapter (2): Numerical simulation of the motion of a micropolar Casson fluid over a stretching surface with two different numerical and semi-analytical methods
This chapter examines the motion of a micropolar non-Newtonian Casson fluid through a porous medium over a stretching surface. The system is pervaded by an external uniform magnetic field. The heat transfer and heat generation are taken into consideration. The problem is modulated mathematically by a system of nonlinear partial differential equations which describe the equations of continuity, momentum and energy. Suitable similarity solutions are utilized to transform the system of equation to ordinary nonlinear differential equations. In accordance with the appropriate boundary conditions, they are numerically solved by means of the finite difference technique. Also, the system is solved by using multistep differential transform method. The effects of the various physical parameters, of the problem at hand, are illustrated through a set of diagrams.
• Chapter (3): A semi-analytical solution to nonlinear peristaltic flow of Jeffrey nanofluid with variable viscosity and thermal conductivity: Application of multi-step differential transform method.
A semi-analytical solution of the peristaltic motion of Jeffrey nanofluid with heat and mass transfer inside an asymmetric channel is introduced in this chapter. The influences of variable viscosity and thermal conductivity are taken into account. Hall currents, Joule heat and viscous dissipation are taken into consideration. The problem is modulated mathematically by a system of non-linear partial deferential equations which describe the fluid velocity, temperature and concentration. This system is analyzed under the approximations of long wavelength and low Renolds number. It is solved by using the multi-step deferential transform method (Ms-DTM) to obtain the velocity, temperature and concentration distributions, pressure rise and pressure gradient. These solutions are obtained as functions of the physical parameters of the problem. Tables and figures are discussed to see the effects of the pertinent parameters. It is found that the thermal conductivity parameter causes an increasing in the pressure gradient, while it reduces the pressure rise. Also, it is seen that behavior of the Brownian and thermophoresis parameters on nanoparticles concentration field are quite reverse.
• Chapter (4): Peristaltic blood flow with Gold nanoparticles on a Carreau nanofluid through a non-Darcian porous medium The chapter investigates the influences of a variable thermal conductivity and wall slip on a peristaltic motion of Carreau nanofluid. The model is considered with heat and mass transfer inside asymmetric channel. The blood is considered as the base Carreau non-Newtonian fluid and gold (Au) as nanoparticles stressed upon. The system is stressed upon a strong magnetic field and the Hall currents are completed. The problem is modulated mathematically by a system of non-linear partial differential equations which describe the fluid velocity, temperature and concentration. The system is reformulated under the approximation of long wavelength and low Reynolds number. It is solved on using multi-step differential transform method (Ms-DTM) as a semi-analytical method. A gold nanoparticle has increased the temperature distribution which is of great importance in destroying the cancer cells.
• Chapter (5): Mixed convective peristaltic flow of Eyring Prandtl fluid with chemical reaction and variable electrical conductivity in a tapered asymmetric channel
The influence of variable electrical conductivity and chemical reaction on the peristaltic motion of non-Newtonian Eyring Prandtl fluid inside a tapered asymmetric channel is investigated in this chapter. The system is expressed by a uniform external magnetic field. The heat and mass transfer are considered. The problem is controlled mathematically by a system of non-linear partial differential equations which describe the velocity, temperature and Nanoparticle concentration of the fluid. By means of long wavelength and low Reynolds numbers our system is simplified. It is solved by using multi-step differential transform method (Ms-DTM) as a semi-analytical technique. The distributions of velocity, temperature, nanoparticle concentration as well as pressure gradient and pressure rise are obtained as a function of the physical parameters of the problem. The effects of these parameters on these distributions are deliberated numerically and illustrated graphically through a set of figures. Results indicate that the parameters play a significant role to control the velocity, temperature, Nanoparticle concentration, pressure gradient and pressure rise.
• Chapter (6): A semi-analytical technique for MHD peristalsis of pseudoplastic nanofluid with temperature-dependent viscosity: Application in drug delivery system
An analysis has been performed to study the influences of temperature dependent viscosity and magneto-hydrodynamics on peristaltic flow of pseudoplastic nanofluid in a tapered asymmetric channel through a porous medium. Chemical reaction, Ohmic dissipation and heat generation are taken into consideration. The present problem is discussed under the approximation of long wavelength and low Reynolds number approximation. Two models of temperature dependent viscosity are discussed. Model-1, all non-dimensional parameters, which are functions of viscosity, has been considered as constants within the flow. Model-2, all these mentioned parameters have been regarded to vary with temperature. Comparisons between the obtained solutions are found in a very good agreement. Attention is focused to the variable viscosity, chemical reaction, and Brownian motion and thermophoresis parameters. The governing equations for each case have been solved by an easy and highly accurate series, based on multi-step differential transform method (Ms-DTM) using the Mathematica 11 mathematical software and compared to available numerical results. It is found that the thermal conductivity parameter causes the increasing of the pressure gradient while reduces the pressure rise.
Chapter (7): A treatment of the effect of thermal diffusion on the Carreau nanofluid utilizing the Pade’ - DTM approximation
In this chapter, the system of nonlinear boundary-layer flow of Carreau nanofluid over a moving stretching sheet is modulated. Thermal diffusion and diffusion thermo effects are considered. Then it has been solved by using the multi-step differential transformation method and the differential transformation method (DTM) with Padé approximation (Pade’-DTM). These methods represent approximations with a high degree of accuracy and minimal computational effort for studying the particle motion in a steady boundary layer flow and heat transfer over a porous moving plate in presence of thermal radiation. In addition, the velocity, temperature and concentration profiles are obtained and depicted graphically in the current study.