

Title of Thesis
Exact Solutions for Some Unsteady Flows of NonNewtonian Fluids
of Rate Type 
Author(s)
Waseem Akhtar 
Institute/University/Department
Details Abdus Salam School of Mathematical Sciences / GC
University, Lahore 
Session 2009 
Subject Mathematics 
Number of Pages 92 
Keywords (Extracted from title, table of contents and
abstract of thesis) Exact, Solutions, Unsteady, Flows,
NonNewtonian, Fluids, Rate, Type, Hankel, transform, tangential,
stresses, permissible 
Abstract The main theme of
this thesis is to establish exact solutions for certain flows of
nonNewtonian fluids of rate type including Maxwell fluids,
generalized Maxwell fluids and OldroydB fluids. The rotational flow
of a generalized Maxwell fluid in a circular cylinder, oscillating
flows between two coaxial infinite cylinders for Maxwell and OldroydB
fluids, as well as the flow induced in Maxwell fluids by a
constantly accelerating plate between two side walls perpendicular
to the plate have been discussed here. The mathematical formulation
of these problems leads to partial differential equations which are
solved by different mathematical techniques like Laplace transform,
Fourier sine transform and Hankel transform. The associated
tangential stresses are also determined. By means of graphical
illustrations, the required time to reach the steadystate for
oscillating flows of Maxwell and OldroydB fluids are also obtained.
The solutions that have been obtained satisfy both the governing
equations and all imposed initial and boundary conditions, the
differentiating term by term into infinite sums being clearly
permissible. Finally, the corresponding solutions for Newtonian
fluids are also obtained as limiting cases.

