Linear Instability Analysis of Natural Convection in a Heated Vertical Porous Annulus

The stability analysis of non-isothermal annular parallel flow through a highly permeable porous medium is studied. The flow is governed by the buoyancy force induced due to the different temperature conditions on the surface of inner and outer cylinders. A linear stability analysis subjected to normal mode analysis has been considered to investigate the influence of gap between cylinders (defined by the curvature parameter, C), Darcy number (Da, which is defined in terms of permeability of the porous medium) as well as Prandtl number (Pr) on the flow instability characteristics. The existence of the inflection point in the laminar base flow profile is checked. Depending on the value of controlling parameters (C, Pr, and Da), the least stable disturbance is found to be axisymmetric for smaller gap and non-axisymmetric for a larger gap between cylinders. The physical mechanism of the flow instability has been examined through kinetic energy analysis.