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Title of Thesis

Analytical Solutions for Some Unsteady Flows of Second Grade and Rate Type Fluids

Author(s)

MUDASSAR NAZAR

Institute/University/Department Details
Abdus Salam School of Mathematical Sciences / GC University, Lahore
Session
2009
Subject
Mathematics
Number of Pages
91
Keywords (Extracted from title, table of contents and abstract of thesis)
Analytical, Solutions, Unsteady, Flows, Second, Grade, Rate, Type, Fluids, non-Newtonian, Maxwell, graphical, illustrations

Abstract
This work presents new results regarding the behavior of some non-Newtonian fluids into different circumstances. After some preliminaries regarding constitutive equations, motion equations and integral transforms, new exact solutions for the velocity field and the shear stress corresponding to some flows with technical relevance have been established for ordinary second grade, Oldroyd-B fluids and generalized Maxwell fluids. Just as in the case of Navier-Stokes fluids, it is necessary to develop a large class of exact and approximate solutions, they serving as tests to verify numerical schemes that are developed to study complex unsteady flow problems.
In chapter 2, by means of the Laplace transform, there are established new exact solutions corresponding to the first problem of Stokes for Oldroyd-B fluids. These solutions, in accordance with the previous results obtained using Fourier sine transform, can be easily specialized to give similar solutions for Maxwell fluids. The main aim of chapter 3 was to solve a very important problem, namely to determine the required time to reach the steady-state for the second problem of Stokes corresponding to second grade fluids. In addition to solve this problem we also found new exact solutions for this problem. Our solutions, unlike the solutions obtained by Erdogan for Newtonian fluids, are written as a sum between steady state and transient solutions.
Chapter 4 contains exact solutions for the unsteady flow of an Oldroyd-B fluid between two side walls perpendicular to a plate. In the absence of side walls the obtained solutions tend to the similar solutions for the flow over a flat plate (the first problem of Stokes). The influence of the pertinent parameters on the velocity of the fluid at the middle of the channel as well as on the shear stress on the bottom is underlined by graphical illustrations. In chapter 5, by means of Laplace and Hankel transforms, we obtained the solutions for unsteady flow of a generalized Maxwell fluid between two circular cylinders. These solutions, presented as a sum of the Newtonian solutions and the non-Newtonian contributions, can be easily specialized to give the similar solutions for ordinary Maxwell fluids. Finally, the influence of the pertinent parameters on the velocity of the fluid are also underlined by graphical illustrations.

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788 KB
S. No. Chapter Title of the Chapters Page Size (KB)
1 0 CONTENTS

 

v
27 KB
2

1

PRELIMINARIES

1.1 Rate Type Fluids

1.2 Differential Type Fluids
1.3 Constitutive Equations
1.4 Equations of Motion
1.5 Some Integral Transforms

6
84 KB
3 2 NEW EXACT SOLUTIONS CORRESPONDING TO THE FIRST PROBLEM OF STOKES FOR OLDROYD-B FLUIDS

2.1 Governing equations

2.2 Solution of the problem

2.3 Limiting cases

2.4 Numerical results and conclusions

14
161 KB
4 3 NEW EXACT SOLUTIONS CORRESPONDING TO THE SECOND PROBLEM OF STOKES FOR SECOND GRADE FLUIDS

3.1 Governing equations

3.2 Solution of the problem
3.3 Conclusions

26
169 KB
5 4 UNSTEADY FLOW OF AN OLDROYD-B FLUID GENERATED BY A CONSTANTLY ACCELERATING PLATE BETWEEN TWO SIDE WALLS PERPENDICULAR TO THE PLATE

4.1 Governing equations

4.2 Solution of the problem
4.3 Limiting cases
4.4 Flow over a flat plate
4.5 Discussion and numerical results
4.6 Concluding remarks

38
496 KB
6 5 UNSTEADY FLOW OF A GENERALIZED MAXWELL FLUID BETWEEN TWO CIRCULAR CYLINDERS

5.1 Governing equations

5.2 The analytic solutions
5.3 Limiting case
5.4 Conclusions and numerical results

59
189 KB
7 6 BIBLIOGRAPHY

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