Keywords (Extracted from title, table of contents and abstract of thesis)
oldroyd fluid, homotopy, nonnewtonian fluid, newtonian fluid, fluid dynamics, rate type fluids, equation of continuity, plane couette flow,plane poiseuille flow, generalized couette flow 
Abstract In recent years the study of nonNewtonian fluids has become of increasing importance. This is mainly due to their wide use in chemical process industries, food industry, construction engineering, petroleum production, power engineering, commercial and technological applications. The rheological concept for such fluids is of special importance owing to its application to many engineering problems. Rheological properties of fluids are specified, in general by their socalled constitutive equations. Because of the nonlinear relationship between stress and the rate of strain, the analysis of the behavior of the fluid motion of the nonNewtonian fluids tends to be really complicated and subtle in comparison with that of the Newtonian fluids. The governing equation that describes the flow of a Newtonian fluid is the NavierStokes equation. For the flow of nonNewtonian fluids there is not a single governing equation which describes all of their properties and thus these fluids cannot be described as Newtonian fluids. Therefore, many nonNewtonian models or constitutive equations have been proposed, most of them are empirical and semiempirical. The most important models for nonNewtonian fluids are the differential type and the rate type. However, the differential type fluids are incapable of predicting stress relaxation and therefore, have not been so successful for describing the flows of some polymeric suspensions. Of the numerous models that abound in nonNewtonian mechanics one that captures stress relaxation aspects of polymer suspensions, albeit only in a qualitative manner, and hence been accorded much scrutiny is rate type model which includes Oldroyd fluids. The most popular being an OldroydB fluid (3constant model). But unfortunately this fluid does not exhibit the nonNewtonian characteristics for steady unidirectional flow. Because of this shortfall, some steady flows may be well described by Oldroyd 6 and 8constant fluids, which do show the nonNewtonian characteristics. Another important aspect in the study of fluid dynamics is the consideration of slip boundary condition. The noslip condition is one of the central tenets of NavierStokes theory and the modern fluid dynamics. In the literature much of the analysis relies on noslip condition. This is convenient, and somewhat surprising, but hides the issue of whether the adherence boundary condition is infect a valid model of the fluidboundary interaction, and if not, how to determine and apply more realistic boundary condition. The adherence condition is inadequate when one considers nonNewtonian fluids such as polymer melts which exhibit macroscopic wall slip and that in general is governed by a nonlinear nonmonotone relation between the slip velocity and traction. This may be important factor in sharkskin, spurt and hysteresis effects. The existing theory for nonNewtonian fluids with wall slippage is scant. Motivated by these facts, the entire work in this thesis is divided into seven chapters. Chapter 0 is introductory in nature. The basic preliminaries regarding rate type fluids, governing laws and homotopy analysis method (HAM) are presented in chapter 1. In chapter 2, the governing nonlinear differential equation for an Oldroyd 6constant fluid has been modeled. Also, the analytical solutions of nonlinear equation for three fundamental flows (namely Couette, Poiseuille and generalized Couette) have been accomplished using HAM. It is noted that not only the nonNewtonian parameters appear in the solution even for steady flow which is distinct from the case of Oldroyd 3constant fluid but the solution is strongly dependent on these emerging nonNewtonian parameters. Chapter 3 is prepared to see the effects of slip on the flows considered in chapter 2. The analysis of this chapter treats the solvability of nonlinear equation subject to nonlinear conditions. The slip effects have been shown and analytical solutions are obtained. It is found that with the slip boundary condition, the reduced shearing force from the boundaries causes the velocity to become flatter than for noslip boundary condition. In chapters 4 and 5, the flows of magnetohydrodynamic (MHD) Oldroyd 8constant fluid are considered. These analyzes are important because the interaction of electromagnetic field with fluids gained importance in view of its promising applications in areas like nuclear fusion, chemical engineering, high speed noiseless printing, transformer cooling oil, etc. Chapter 4 describes the MHD flow analysis for three shearing flows which involve Oldroyd 8constant fluid. Both analytical and numerical solutions have been given and compared. It is observed that with an increase of the magnitude of the magnetic field the flow velocity decreases monotonically due to the effect of the magnetic force. In chapter 5, the MHD flow of an Oldroyd 8constant fluid between two coaxial cylinders is discussed analytically as well as numerically. It is noted that HAM and numerical solutions are in good agrement. Finally, the conclusions are presented in chapter 6.
