Natural convection in a thin horizontal porous annulus

Abstract

The possible modes of time-dependent natural convection in a horizontal annulus of finite length are considered. The annulus is filled with porous material and the annular thickness is assumed small in comparison with the mean radius. All boundaries are impermeable and adiabatic; heating is through a circumferentially distributed volumetric heat source. The governing equations reduce to a set of two non-linear ordinary differential equations. Steady non-linear oscillations exist for the special case of infinite Rayleigh number and symmetric heating about the vertical. For lower Rayleigh numbers, damped oscillations are obtained, the degree of damping increasing with the inclination of the line of symmetry and with decreasing Rayleigh number. Multiple stable steady states are obtained for small inclinations. Chaotic motions do not develop for non-inertial Darcy flows.