Error of labeling pages or Page 102 Not included in thesis. / <p> A semi-explicit scheme for the solution of transient multdimensional natural convection is made to study natural convection in porous media. The conservation equations are phrased in primitive form. Heat tranfer between the solid and liquid phases is modelled by representing the porous medium as an assemblage of spherical particles, and solving the conduction problem for such a system at every time step. Nusselt numbers were calculated from the temperature and velocity profiles. Numerical results for heat transfer through fluid saturated porous media heated from below are in good agreement with published experiments.</p> / Thesis / Master of Engineering (MEngr)

This thesis investigates three problems relating to thermoconvective stability in porous media. These are (i) the stability of an inclined boundary layer flow to vortex type instability, (ii) front propagation in the Darcy-B´enard problem and (iii) the onset of Prantdl-Darcy convection in a horizontal porous layer subject to a horizontal pressure gradient. The nonlinear, elliptic governing equations for the inclined boundary layer flow are discretised using finite differences and solved using an implicit, MultiGrid Full Approximation Scheme. In addition to the basic steady state three configurations are examined: (i) unforced disturbances, (ii) global forced disturbances, and (iii) leading edge forced disturbances. The unforced inclined boundary layer is shown to be convectively unstable to vortex-type instabilities. The forced vortex system is found to produce critical distances in good agreement with parabolic simulations. The speed of propagation and the pattern formed behind a propagating front in the Darcy-B´enard problem are examined using weakly nonlinear analysis and through numerical solution of the fully nonlinear governing equations for both two and three dimensional flows. The unifying theory of Ebert and van Saarloos (Ebert and van Saarloos (1998)) for pulled fronts is found to describe the behaviour well in two dimensions, but the situation in three dimensions is more complex with combinations of transverse and longitudinal rolls occurring. A linear perturbation analysis of the onset of Prandtl-Darcy convection in a horizontal porous layer subject to a horizontal pressure gradient indicates that the flow becomes more stable as the underlying flow increases, and that the wavelength of the most dangerous disturbances also increases with the strength of the underlying flow. Asymptotic analyses for small and large underlying flow and large Prandtl number are carried out and results compared to those of the linear perturbation analysis.

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