Abstract There are many models which are used to investigate different types of fluid mechanics problems. It is difficult to characterize in general way all necessary requirements since each problem is unique. However, we can broadly classify many of the problems on the basis of the general nature of the flow and the fluid and subsequently develop some general characteristics of model designs in each of these classifications. Amongst these models, the model of Newtonian fluid is the simplest one for which the NavierStokes equations can describe the flow problem. However, there are many fluids with complex microstructure such as biological fluids, as well as polymeric liquids, suspensions, liquid crystals which are used in current industrial processes and show nonlinear viscoelastic behaviour that cannot be characterized by NavierStokes equations. Because of the fluids complexity, many constitutive equations have been proposed. The nonNewtonian models that have been developed to describe the other rheological characteristics can be classified under the following three categories: fluids of differential type, rate type and integral type. Amongst these types, the differential fluids have received the special attention from the recent researchers in order to describe the several nonstandard features such as normal stress effects, rod climbing, shear thinning and shear thickening. The governing equations for such fluids are more nonlinear and higher order than the NavierStokes equations. In the literature much attention has been focused on the flows of second grade fluid which is simplest subclass of differential type fluids. The second grade fluid model is able to predict the normal stress differences but it does not take into account the shear thinning or shear thickening phenomena that many fluids show. The third grade fluid model represents a further, although inconclusive attempt toward a more comprehensive description of the behaviour of nonNewtonian fluids. Due to this fact in mind, the model in the present thesis is a third grade. Another aspect in the study of nonNewtonian fluids is the slip boundary condition. Although there are rigorous mathematical researches on flows of Newtonian fluids with slip condition but due attention has not been given to flows of nonNewtonian fluids with slip condition. The nonNewtonian fluids such as polymer melts often exhibit macroscopic wall slip governed by a nonlinear and nonmonotone relation between the slip velocity and the traction. The fluids that exhibit boundary slip are important from technological point of view for example, the polishing of artificial heart valves. Keeping the above facts in view, the present thesis is organized as follows: Chapter zero provides the introduction of the thesis. Basic preliminaries relevant to nonNewtonian fluids, governing laws and techniques are given in Chapter one. Equation which governs the rotating flow of a third grade fluid over a porous surface is also modeled here. Chapter two describes the steady flow of a third grade fluid in a rotating frame by using noslip condition. The same problem has been solved employing another set of dimensionless variables for the influence of dynamic viscosity. Later, this problem is solved using partial slip boundary condition. Chapter three describes the oscillatory rotating flow of a third grade fluid passed a porous plate. An asymptotic solution has been obtained. Two cases of noslip and partial slip have been considered. Homotopy analysis method is used to obtain the analytic solutions for the problems in chapters two and three. Convergence of the obtained solutions developed in these chapters is also ensured. Chapter four has been prepared for the numerical solutions of the two partial slip boundary value problems. A reasonable agreement between the HAM and numerical solutions is presented through graphs. The concluding remarks are made at the end of each Chapter. However, a brief summary of the important results from the thesis has been included in Chapter five.
