English abstract
Flows of viscous fluids are known to have applications in several areas. It is also well known that the Navier-Stokes equations, together with energy equation, govern the flow features of such fluids. These equations are highly non-linear partial differential ons whose analytical solutions are difficult to obtain. This project aims to discuss some viscous, incompressible flows problems; where exact or approximate solutions of the governing Navier-Stokes equations can be sought. A number of research problems have been identified from the literature and then analysed. A few extensions have also been attempted.
In the first problem, we have investigated flow in a porous channel and studied the effects of the fluid suction or injection, at the bounding porous plates, on the steady flow. A perturbation series method has been employed to obtain approximate solution of governing non-linear differential equations. The influence of wall permeability on flow variables such as velocity components and pressure has been analysed with reference to two well-defined non-dimensional parameters. Also, wall stresses have been computed both analytically and numerically for comparison..
The second problem investigated in this project deals with unsteady free convection in a viscous fluid in a vertical channel. The method of Laplace transforms has been employed to solve the coupled momentum and energy equations, assuming the constant temperature as well as uniform heat flux wall conditions. The effect of the Grashoff and Prandtl numbers on the developing temperature and velocity profiles has been discussed for a range of the values of these parameters. Solutions have been obtained for the cases corresponding to the Prandtl number being unity as well as om unity. It has been shown that solutions for these two cases have different forms.
In the last set of flow problems, we have carried out extensive investigations of coupled fluid flows in a channel bounded by porous media. It has been assumed that two immiscible fluids occupy the channel. In particular, two basic flow problems related to these immiscible fluids, namely, (a) generalized Couette flow bounded below by a porous medium, and (b) plane Poiseuille flow bounded by porous media of different permeabilities, have been considered. Both Darcy's law and Brinkman equations have been employed to model the flow within porous media. The effect of es of the bounding media on the fully developed velocity profiles in different regions of the flow and the mass flux through the channel has been investigated through a number of parameters, especially the Darcy number.
