Keywords (Extracted from title, table of contents and
abstract of thesis) Asymptotic, Fractional, Equations,
Results, Fluids, Finite, Motion, Generalized, Newtonian, Cases,
General, Ordinary, New, Theory |
Abstract This thesis concerns
with the results regarding the flow behavior of some non- Newtonian
fluids under different circumstances.First of all, some concepts
regarding Newtonian and non-Newtonian fluids, constitutive
equations, equations of motion, and integral transforms have been
discussed.Then the exact solutions for the velocity field and the
shear stress corresponding to some flows with technical relevance
have been established for second grade, Maxwell, and Oldroyd-B
fluids with fractional derivatives model.
In Chapter 2, the velocity field and the adequate shear stress,
corresponding to the flow of a second grade fluid with fractional
derivatives in an annular region, due to a constant/time-dependent
shear stress, are determined by means of the Laplace and the finite
Hankel transforms.The corresponding solutions for a second grade and
Newtonian fluids, performing the same motion, are obtained from our
general solutions.
Chapter 3 deals with the motion of a Maxwell fluid with fractional
derivatives, and we studied the flow starting from rest due to the
sliding of the cylinder along its axis with a constant
acceleration.The velocity and the adequate shear stress, obtained by
means of the finite Hankel and Laplace transforms, are presented
under series form in terms of the generalized G functions.The
similar solutions for the ordinary Maxwell fluid, performing the
same motion, are obtained as special cases of our general solution.
Chapter 4 concerns with the unsteady flow of an incompressible
Oldroyd-B fluid with fractional derivatives, induced by a constantly
accelerating plate between two side walls perpendicular to the
plate.The solutions have been studied using Fourier sine and Laplace
transforms. The expressions for the velocity field and the shear
stresses, written in terms of the generalized G and R functions, are
presented as sum of the similar Newtonian solutions and the
corresponding non-Newtonian contributions. Furthermore, the
solutions for Maxwell fluid with fractional derivatives, ordinary
Oldroyd-B, Maxwell and Newtonian fluids, performing the same motion,
are also obtained as limiting cases of our general solutions. In the
absence of the side walls, namely when the distance between the two
walls tends to infinity, the solutions corresponding to the motion
over an infinite constantly accelerating plate are recovered.
Finally, the effect of the material parameters on the velocity
profile is spotlighted by means of the graphical illustrations.
Chapter 5 intends to establish exact and approximative expressions
for dissipation, the power due to the shear stress at the wall and
the boundary layer thickness corresponding to the unsteady motion of
a second grade fluid, induced by an infinite plate subject to a
shear stress.As a limiting case of our general solutions, the
similar results for Newtonian fluids performing the same motion, are
obtained. The results that have been here obtained are different of
those corresponding to the Rayleigh- Stokes problem.A series
solution for the velocity field is also determined. Its form, as it
was to be expected, is identical to that resulting from the general
solution by asymptotic approximations. |