| The effects of variable viscosity, porosity variation, magnetic field, radiation heat transfer, thermal conductivity and non-Darcy behaviour on some two-dimensional laminar convective boundary layer flows past a vertical flat plate embedded in a fluid-saturated porous medium have been examined theoretically and numerically in this study using the Keller-Box method and a double-shooting Runge-Kutta-Merson scheme. The thesis comprises five parts. In Part One (chapter 1) a general introduction to the fluid mechanics of convective flows in porous media is provided including the special effects of non-Darcy behaviour, magnetohydrodynamics (MHD) and radiation heat transfer. The numeric techniques employed in the study are also described. In Part Two (chapters 2 and 3) the effects of non-Darcy behaviour on some convective flows in porous media are examined. Chapter 3 employs the Darcy- Brinkman-Forscheimmer model and a viscosity ratio and porosity parameter to study the mixed convective boundary layer flow past a semi-infinite vertical flat plate in a fully-saturated porous regime. Chapter 4 considers the Darcy-Brinkman model with the supplementary effect of viscous dissipation. In Part Three (chapters 4,5) the effect of transverse magnetic field is considered using a magnetohydrodynamic body force term in the momentum equation to simulate the case of electrically-conducting fluids in porous media. The additional effect of surface transpiration is also incorporated into the momentum and thermal boundary layer equations to simulate permeability of the plate. In chapter 4 only the Keller-Box scheme is used. Chapter 5 presents solutions by both Keller's scheme and the Runge-Kutta-Merson method for Taylor expansions up to fourth order. In Part Four (chapters 6,7,8) the effect of monochromatic one-dimensional radiation on several non-Darcy convective flows in porous media has been analyzed for the special case of an optically dense viscous incompressible fluid using the classical Rosseland radiation diffusion approximation and the Runge-Kutta-Merson shooting method. In chapter 6 the effect of radiation on the convective boundary layer heat transfer from a flat permeable plate in the presence of a magnetic field is studied. Chapter 7 considers the radiation heat transfer, thermal conductivity and non-Darcy effects on steady laminar convective boundary layer flow past a flat vertical plate in a porous medium with viscosity and porosity variation. Finally chapter 8 examines the effects of radiation, porosity, viscosity and non-Darcy boundary friction and inertial drag on laminar hydromagnetic free convective porous flow. For all flow cases (chapters 2-8), the effects of the relevant thermofluid parameters, viz Reynolds number, Prandtl number, Hartmann magnetic number, Eckert number, Darcy number, Forscheimmer number, Grashof number, Rosseland number, transpiration parameter, thermal conductivity ratio, viscosity ratio and medium porosity on surface shear stress, local heat transfer, dimensionless velocity and temperature functions are presented graphically. Part 5 comprises conclusions, references and the appendices. Chapter 9 discusses general conclusions to the study and potential future extensions with respect to supplementary physical effects such as medium anisotropy, stratification, and non- Newtonian behaviour. |
