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Laminar flow in a channel filled with saturated porous media
The flow of reactive viscous fluids in porous media presents a theoretically challenging problem and has a broad range of scientific, technological and engineering applications. Real life areas where such flow systems are encountered include drying of food, geothermal energy extraction, nuclear waste disposal, the flow of heat and fluid inside human organs, insulation of buildings, groundwater movement, oil and gas production, astrophysical plasmas, magnetohydrodynamic (MHD) pumps and generators, metal extraction and granulation of metals, aerospace and ship propulsion and automobile exhaust systems. The reactions within such flow systems are inherently exothermic. It is in this view that we carry out studies of thermal effects and thermal stability criteria for unsteady flows of reactive variable viscosity non-Newtonian fluids through saturated porous media. The study focuses on non-Newtonian fluids mainly because the majority of industrial fluids exhibit non-Newtonian character. Particular focus will be on fluids of the differential type exemplified by third grade fluid. Both analytical and numerical techniques were employed to solve the nonlinear partial differential equations that were derived from the conservation principles, namely the principles of conservation of mass, momentum and energy balance. Graphical representations were adopted in trying to explain the response of solutions to various flow parameter variations. In chapter 1 we defined important terms and expressions, laid down a summary of important applications, carried out literature survey, stated the statement of the problem, the aims and objectives of the study as well as an outline of the envisaged research methodology. Chapter 2 focuses on the derivations of the fundamental equations that derive the flow system. These are the continuity equation, the momentum equation and the energy equation. In chapter 3 we computationally investigated the unsteady flow of a reactive temperature dependent viscosity third grade fluid through a porous saturated medium with asymmetric convective boundary conditions. The response of velocity and temperature fields to each of the various flow parameters was analysed and interpreted. A transient increase in both the velocity and temperature profiles with an increase in the reaction strength, viscous heating and fluid viscosity parameter was observed. On the other hand, a transient decrease in the field properties was observed with increase in non-Newtonian character and the porous medium shape parameter. The reaction was noticed to blow-up if, depending on other flow parameters, the reaction strength is not carefully controlled.