Nonparallel thermal instability of natural convection flow over horizontal and inclined plates in porous media

This dissertation presents an analytical study of thermal or vortex instability of natural convection flow over heated horizontal and/or inclined flat plates embedded in fluid-saturated porous media. Both the streamwise and normal components of the buoyancy force are retained in the governing equations of the basic flow as well as the disturbance flow. An implicit finite-difference method is employed to obtain solutions of the basic flow. The linear nonparallel flow model is applied in the instability analysis, which takes into account both the streamwise and transverse variations of the disturbance amplitude functions. The resulting set of partial differential equations for the disturbance amplitude functions are converted into a system of homogeneous linear ordinary differential equations with homogeneous boundary conditions by the local non-similarity method. This results in an eigenvalue problem, which is solved by an implicit finite-difference method.; Both the Darcy's flow and the non-Darcy's flow are studied. The non-Darcy effects considered include the inertia effect, the convective effect, and the viscous effect. The numerical results obtained indicate that the nonparallel flow model predicts a more stable flow to the vortex mode of instability than the parallel flow model. It is believed that the nonparallel flow model gives rise to more accurate results than the parallel flow model which bears the assumption of a weak streamwise dependence of the disturbance amplitude functions. As compared to the Darcy's flow, the non-Darcy effects contribute to the stabilization of the basic flow.