Title of Thesis
Advancements in the Theory of Generalized
Abdus Salam School of Mathematical Sciences / GC
|Number of Pages|
|Keywords (Extracted from title, table of contents and
abstract of thesis)|
Unsteady, Derivatives, Solutions,
Laplace, Transforms, Newtonian, Advancements, Perpendicular,
Cylinder, Fractional, Generalized, Theory, Fluids, Solutions
In this work I have
presented the exact solution of some non-Newtonian fluids in
different situation after some preliminaries regarding continuity
equation, constitutive equation, equation of motion and integral
transforms, the newly exact solutions for second grade fluid with
fractional derivatives, Maxwell fluid with fractional derivatives
and ordinary Oldroyd-B fluid have been found in which we have
calculated the velocity and shear stress.
In chapter 2, we established exact solutions for the velocity field
and shear stress corresponding to the flow of a second grade fluid
with fractional derivatives (SGFFD) between two infinite circular
cylinders due to an azimuthal constant/time-dependent shear stress
on the surface of the inner cylinder. The solutions that have been
determined using Laplace and finite Hankel transforms, are presented
under integral and series form in terms of the generalized Ga; b;
c(: ; :) functions.
In chapter 3, we present exact solutions for the unsteady flow of a
Maxwell fluid with fractional derivatives (MFFD) due to a constantly
accelerating plate. The velocity field and the adequate shear stress
corresponding to the unsteady flow of a MFFD are determined using
Fourier sine and Laplace transforms. They are presented as a sum of
the Newtonian solutions and the corresponding non-Newtonian
contributions. Graphical illustrations show that the velocity
profiles corresponding to a MFFD are going to that for an ordinary
Maxwell fluid if → 1.
In chapter 4, we succeeded to provide exact solutions for the
unsteady flow of a MFFD between two side walls perpendicular to a
plate. The motion is produced by the infinite plate that at time t =
0+ begins to slide into its plane with a constant acceleration A.
The exact solutions for the velocity field and the adequate shear
stresses, obtained by means of Fourier sine and Laplace transforms,
are presented in terms of the generalized Mittag-Leffler functions.
In the absence of the side walls, all solutions that have been
obtained reduce to the solutions corresponding to the motion over an
infinite constantly accelerating plate.
Chapter 5 deals with the study of unsteady rotational flow of an
Oldroyd-B fluid in an annular pipe. The motion of the fluid is
produced by the inner cylinder that, at the initial moment, is
subject to a time dependent couple per unit length. The exact
solutions, obtained by means of Laplace and finite Hankel
transforms, satisfy all imposed initial and boundary
conditions.Finally, the influence of the material constants on the
velocity and shear stress is underlined by graphical illustrations.