Natural Convection in Layered Porous Media between Coaxial Cylinders

Abstract

In this thesis a mathematical model is developed to describe the onset of natural convection in a two-layer porous medium located between two coaxial cylinders, motivated by natural convection processes in geothermal systems. The cylinders are heated from below and cooled from above. We consider the top and bottom to be impermeable and perfectly heat conducting, while the sidewalls are assumed to be impermeable and insulated. At the interface between the layers, we require continuity in temperature, pressure, vertical flow and heat flow. We apply linear stability analysis to determine the criterion for onset of natural convection in the bottom layer. An investigation of the effects of permeability contrasts between the two layers on the critical Rayleigh number is performed. We present new results, as our analysis applies to a two-layer medium in cylindrical coordinates. The results are validated by comparison with similar previous studies for a single-layer medium with the same geometry, and for a layered medium within a box geometry. The model has real life applications as it may work as an indicator of the presence of natural convection in the subsurface and since the results can be applied in benchmarking of a numerical simulator.