Keywords (Extracted from title, table of contents and abstract of thesis)
differential type fluids, analytic solutions, steady flows, newtonian fluids, nonnewtonian fluids, optimal flow, homotopy analysis method, flat porous plate, pipe flow, planar, axisymmetric flow, stretching sheet, boundary layer flow, magnetohydrodynamic pipe flow 
Abstract It has been known that Newtonian fluids are inadequate to describe nonNewtonian fluids. NonNewtonian flows arise in disparate process in engineering, science and biology for example, in polymer processing, coating, inkjet printing, microfluidics, geological flows in the earth mantle, homodynamic and many others. Modeling nonNewtonian flows is important for understanding and predicting the behaviour of processes and thus for designing optimal flow configurations and for selecting operating conditions. Several models, mainly based on empirical observations, have been suggested for nonNewtonian fluids. The rheologists have been able to provide a theoretical Foundation in the form of a constitutive equations which can in principle, have any order. For applied mathematics and computer scientists the challenge comes from a different quarter. A constitutive equation of even the simplest nonNewtonian fluids are such that the differential equation describing the motion have, in general, their order higher than those describing the motion of the Newtonian fluids, but apparently there is no corresponding increase in the number of boundary conditions. Applied mathematicians and computer scientists are thus forced with the socalled illposed boundary value problems which, in theory have a family of infinitely many solutions. The task them becomes of selecting one of them under some plausible assumption. The main objective of this thesis is to consider the problems in one class of nonNewtonian fluids namely the fluids of differential type and to develop analytic solutions for them. The explicit, totally analytic solutions for the considered problems are obtained using the homotopy analysis method (HAM). The explicit form of the series is given for the analytical solutions. The dependence of the convergence of the obtained series is discussed. The flow problems regarding the flow of second. third and fourth grade fluids are investigated for both Cartesian and Cylindrical coordinates. The considered problems involve flat porous plate, pipe flow, planar and axisymmetric flow over a linear stretching sheet. The heat transfer analysis is carried out for the stretching problems. Two heating processes namely (i) prescribed surface temperature (PST case) and (ii) prescribed heat flux (PHF case) are taken into account. The effects of the emerging nonNewtonian parameters of interest are seen and discussed. Finally, the comparison of the obtained results with the existing results in the literature is also presented.
