الملخص الإنجليزي
The simultaneous flow of a viscous fluid in an open space and in an adjoining porous medium is an example of a coupled flow due to apparent interaction between flows in the two regions. Because of numerous industrial and engineering applications, the theoretical studies of such flows have received a good deal of attention in the literature during the last four decades or so. This project is concerned with analytical and numerical investigations of some coupled flows of viscous incompressible fluids in the presence of bounding porous media which are assumed to be isotropic, fully saturated and with constant properties. Three basic flow problems from the literature have been analyzed in detail. The first problem (Chapter 2), comprising two parts, deals with generalized Couette flow, including heat transfer, of two immiscible fluids in a straight channel bounded below by a porous medium of finite thickness. Using the Brinkman equation to model the flow in the porous medium and assuming the presence of a heat source in the upper fluid of the clear region, exact solutions for velocity and temperature variables, in all three regions of flow, have been obtained subject to a host of matching and boundary conditions. The variation of velocity and temperature profiles in each region has been discussed graphically in relation to a number of non-dimensional parameters. In the next part, we have extended this problem by introducing another heat source term in the clear region. In the second problem (Chapter 3) of this project, the classical Stokes layer has been extended to the case when an infinite extent of viscous fluid is bounded below by an oscillating permeable medium. Using the Darcy law to model the flow in the porous region, in conjunction with the Beavers- Joseph slip condition at the porous interface, both steady state and transient solutions, including boundary layer thickness, have been obtained. The effect of two key parameters on the flow, has been analyzed by plotting unsteady velocity profiles in the clear region for a range of values of these parameters. The third and final flow problem (Chapter 4) considered in this project deals with the steady viscous flow between two infinite circular disks, rotating with constant but different angular velocities about their common axis. It is assumed that the lower disk, made of a porous material of low permeability, is rotating like a rigid body. We have used the continuity and momentum equations for both clear and porous regions in the cylindrical coordinate system to analyze this coupled flow. Using similarity solutions, the governing partial differential equations and the associated matching and boundary conditions have been transformed to a system of coupled non-linear ordinary differential equations for the similarity functions. A numerical method has been used to solve this system. Plots of various velocity components have been presented in two cases to illustrate the effects of rotation and permeability parameters.
