Investigations of instability mechanisms of buoyant flow in a vertical porous layer

Abstract

The present work aims to investigate the stability of buoyant flow in a vertical layer of fluidsaturated newlineporous medium by employing Darcy and non-Darcy models under the regimes of newlinelocal thermal equilibrium and nonequilibrium. In the investigation, several issues have been newlinetackled, in particular, volumetric internal heating, viscosity variation with temperature, solute newlineconcentration field, and maximum density. A combination of analytical and numerical newlinemethods such as the Chebyshev collocation method and/or the Galerkin method is employed newlineto examine a wide range of physical parameters, yielding significant insights on the stability newlinecharacteristics of the system. To address this, the probe incorporates linear stability theory, newlinewhich allows for the determination of criteria for the onset of stationary and/or travellingwave newlinemode instability. The intricate interaction between a uniform volumetric heat source newlineand the Prandtl-Darcy number has revealed the possibility of inducing instability in the base newlineflow. The influence of linear temperature-dependent viscosity on the stability of the system is newlinediscussed and established that the base flow remains stable for all infinitesimal disturbances. newlineThe study of solute concentration field on the Gill-Rees problem has explored some novel newlinefindings not found hitherto in the studies of double-diffusive convection in a vertical porous newlinelayer under the local thermal equilibrium regime and also in non-porous layers. Later, the newlineimplementation of the Brinkman porous medium with quadratic density law on the stability of newlinebase flow is examined. Lastly, potential future research directions related to the problems newlineaddressed in this thesis are discussed. newline