Title of Thesis

Exact Solutions for Some Unsteady Flows of Non-Newtonian Fluids of Rate Type

Author(s)

Waseem Akhtar

Abstract
The main theme of this thesis is to establish exact solutions for certain flows of non-Newtonian fluids of rate type including Maxwell fluids, generalized Maxwell fluids and Oldroyd-B fluids. The rotational flow of a generalized Maxwell fluid in a circular cylinder, oscillating flows between two coaxial infinite cylinders for Maxwell and Oldroyd-B 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 steady-state for oscillating flows of Maxwell and Oldroyd-B 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.

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1.1 Rate Type Fluids

1.2 Constitutive Equations
1.3 Continuity Equation

1.4 Equations of Motion

1.5 Some Integral Transforms

2.1 Introduction

2.2 Governing equations

2.3 Motion between two circular cylinders one of them oscillating

2.4 Motion within an infinite oscillating circular cylinder

2.5 Limiting case → 0 (Newtonian fluids)

2.6 Numerical results and conclusions

3.1 Introduction

3.2 Governing equations
3.3 Solution of the problem
3.4 The special case → 0 (Newtonian fluids)
3.5 Limiting case h → ∞ (Flow over a flat plate)

3.6 Conclusions and numerical results

4.1 Introduction

4.2 Governing equations

4.3 Rotating flow in an infinite circular cylinder

4.4 Limiting cases

4.5 Conclusions

5.1 Introduction

5.2 Governing equations
5.3 Wording of the problem

5.4 Solution of the problem

5.5 Limiting cases

5.6 Conclusions and numerical results

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