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 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.
