

Title of Thesis
Some New Results in the Theory of NonNewtonian Fluids. Exact
Solutions and Energetic Balance 
Author(s)
AMIR MAHMOOD 
Institute/University/Department
Details Abdus Salam School of Mathematical Sciences / GC
University, Lahore 
Session 2009 
Subject Mathematics 
Number of Pages 86 
Keywords (Extracted from title, table of contents and
abstract of thesis) Results, Theory,
NonNewtonian, Fluids, Exact, Solutions, Energetic, Balance,
Motions, Derivatives, Integer, Order 
Abstract The main aim of this
thesis is to present some new and recent results from the theory of
nonNewtonian fluids. Such results refer to different motions of
generalized second grade and OldroydB fluids and ordinary Maxwell
fluids. Generally, the constitutive equations for generalized
nonNewtonian fluids are obtained from those for nonNewtonian
fluids by replacing the time derivatives of an integer order by the
so called RiemanLiouville fractional operators.
In chapter 2, it is studied the rotational flow of a generalized
second grade fluid between two infinite coaxial cylinders. The
velocity field !(r, t) and the shear stress (r, t), obtained by
means of Laplace and Hankel transforms, are presented under series
form in terms of generalized G functions. The obtained solutions can
be specialized to give the similar solutions for ordinary second
grade and Newtonian fluids performing the same motion. Chapter 3
deals with the study of helical flow of generalized OldroydB fluids
in a single circular cylinder. The components of velocity field and
their associated shear stresses have been found in terms of
generalized G and R functions and are presented as sum of two terms,
one of them is the similar solution for the Newtonian fluid. Chapter
4 contains some remarkable results regarding the energetic balance
for the flow of Maxwell fluid due to a constantly accelerating
plate. We have determined the dissipation, the power due to the
shear stress at the wall and boundary layer thickness for this
motion. The corresponding results for the similar flow of a
Newtonian fluid are also recovered as special case. The specific
features of both fluids are compared and discussed.

