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Purely Analytic Solutions to Some Multidimensional Viscous Flows With Heat Transfer

Thesis Info

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Author

Mehmood, Ahmer

Program

PhD

Institute

Quaid-I-Azam University

City

Islamabad

Province

Islamabad.

Country

Pakistan

Thesis Completing Year

2010

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/handle/123456789/1157

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676727045975

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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 equa- tions. 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 re- sults. 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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