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Title of Thesis

Purely Analytic Solutions to some Multidimensional Viscous Flows with Heat Transfer

Author(s)

Ahmer Mehmood

Institute/University/Department Details
Department Of Mathematics / Quaid-i-azam University, Islamabad
Session
2010
Subject
Mathematics
Number of Pages
180
Keywords (Extracted from title, table of contents and abstract of thesis)
Analytic, Heat, Transfer, Solution, Equations, Situations, Flows, Purely, Viscous, Multidimensional, Comparison, Flow, Calculating

Abstract
Exact solution of Navier-Stokes equations is possible only for very simple flow situations such as unidirectional flows.Due to the nonlinear nature of these equations their analytic solutions are rare and the situation gets worse in the case of unsteady and multidimensional flow problems.
In this thesis we report highly accurate and purely analytic solutions to some steady/unsteady multidimensional viscous flows over flat surface. Heat transfer analysis has also been carried out where the flat surface is considered as a stretching sheet.In each case the skin friction and the rate of heat transfer has been reported.The issue of cooling of stretching sheet in the presence of viscous dissipation has been discussed in detail.
We have considered multidimensional flows of viscous fluid over a flat plate in different flow situations such as flow over an impulsively started moving plate; flow over a stretching sheet, viscous flow in a channel of lower stretching wall, and the channel flow with lower wall as a stretching sheet in a rotating frame. In all the above mentioned flow situations similarity transformations have been used in order to normalize the problem.The reduced governing equations are then solved analytically.
We have used homotopy analysis method to solve the governing nonlinear differential equations.The results are purely analytic and highly accurate.The accuracy of results has been proved by calculating the residual errors and (or) giving the comparison with the existing results.For unsteady flows it is worthy to mention here that our analytic solutions are uniformly valid for all time in the whole spatial domain.

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18,668 KB
S. No. Chapter Title of the Chapters Page Size (KB)
1 0 CONTENTS

 

2
43 KB
2

1

INTRODUCTION

1.1 Introduction and brief history
1.2 Preliminaries

5
202 KB
3 2 UNSTEADY BOUNDARY-LAYER FLOW OVER AN IMPULSIVELY STARTED SURFACE

2.1 Introduction
2.2 Unsteady flowpast amoving rigid plate
2.3 Unsteady flowpast an impulsively started porous plate
2.4 Conclusion

26
270 KB
4 3 UNSTEADY BOUNDARY-LAYER FLOW OVER AN IMPULSIVELY STRETCHING SURFACE WITH HEAT AND MASS TRANSFER

3.1 Introduction
3.2 Mathematical description of the problem
3.3 Solution by homotopy analysismethod
3.4 Conclusion

52
190 KB
5

4

GENERALIZED 3D VISCOUS FLOW AND HEAT TRANSFER OVER A STRETCHING PLANE WALL

4.1 Introduction
4.2 Flow analysis
4.3 Heat transfer analysis
4.4 Discussion on results
4.5 Conclusion

67
232 KB
6

5

HEAT TRANSFER ANALYSIS OF 3D VISCOUS FLOW IN A CHANNEL OF LOWER STRETCHING WALL

5.1 Introduction
5.2 Flow analysis
5.3 Heat transfer analysis
5.4 Conclusion

87
328 KB
7

6

UNSTEADY 3DMHD BOUNDARY-LAYER FLOW OVER IMPULSIVELY STARTED STRETCHING SHEET

6.1 Introduction
6.2 Problemformulation
6.3 Analytic HAMsolution
6.4 Conclusion

115
214 KB
8

7

ROTATINGFLOW IN A CHANNEL OF LOWER STRETCHING WALL WITH HEAT TRANSFER

7.1 A generalized Ostrowski type inequality for a random variable whose probability density function belongs to L1[a; b]
7.2 A generalized Ostrowski type inequality for a random variable whose probability density function belongs to Lp[a; b]; p > 1
7.3 Conclusion

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9

8

CONCLUSION

 

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9

BIBLIOGRAPHY

 

160
118 KB