Keywords (Extracted from title, table of contents and
abstract of thesis) Analytical, Solutions, Unsteady, Flows, Second, Grade,
Rate, Type, Fluids, nonNewtonian, Maxwell, graphical, illustrations 
Abstract This work presents
new results regarding the behavior of some nonNewtonian fluids into
different circumstances. After some preliminaries regarding
constitutive equations, motion equations and integral transforms,
new exact solutions for the velocity field and the shear stress
corresponding to some flows with technical relevance have been
established for ordinary second grade, OldroydB fluids and
generalized Maxwell fluids. Just as in the case of NavierStokes
fluids, it is necessary to develop a large class of exact and
approximate solutions, they serving as tests to verify numerical
schemes that are developed to study complex unsteady flow problems.
In chapter 2, by means of the Laplace transform, there are
established new exact solutions corresponding to the first problem
of Stokes for OldroydB fluids. These solutions, in accordance with
the previous results obtained using Fourier sine transform, can be
easily specialized to give similar solutions for Maxwell fluids. The
main aim of chapter 3 was to solve a very important problem, namely
to determine the required time to reach the steadystate for the
second problem of Stokes corresponding to second grade fluids. In
addition to solve this problem we also found new exact solutions for
this problem. Our solutions, unlike the solutions obtained by
Erdogan for Newtonian fluids, are written as a sum between steady
state and transient solutions.
Chapter 4 contains exact solutions for the unsteady flow of an
OldroydB fluid between two side walls perpendicular to a plate. In
the absence of side walls the obtained solutions tend to the similar
solutions for the flow over a flat plate (the first problem of
Stokes). The influence of the pertinent parameters on the velocity
of the fluid at the middle of the channel as well as on the shear
stress on the bottom is underlined by graphical illustrations. In
chapter 5, by means of Laplace and Hankel transforms, we obtained
the solutions for unsteady flow of a generalized Maxwell fluid
between two circular cylinders. These solutions, presented as a sum
of the Newtonian solutions and the nonNewtonian contributions, can
be easily specialized to give the similar solutions for ordinary
Maxwell fluids. Finally, the influence of the pertinent parameters
on the velocity of the fluid are also underlined by graphical
illustrations.
