Title of Thesis

Purely Analytic Solutions to some Multidimensional Viscous Flows with Heat Transfer

Author(s)

Ahmer Mehmood

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.

1

1.1 Introduction and brief history
1.2 Preliminaries

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

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

4

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

5

5.1 Introduction
5.2 Flow analysis
5.3 Heat transfer analysis
5.4 Conclusion

6

6.1 Introduction
6.2 Problemformulation
6.3 Analytic HAMsolution
6.4 Conclusion

7

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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