The Instability of Natural Convection in a Fluid Layer between Co-Axial Cylinders

Abstract

The stability of natural convection in a fluid layer between co-axial cylinders is investigated theoretically. Temperatures of the two cylinders are different by 2T₀ and a uniform temperature gradient β(<0) is present in the vertical direction, and the ratio of the radii of the outer and inner cylinders is changed from 0 to 1. It is found that there exist three distinguishable instability modes and according to the values of T₀, β and the ratio of the radii, one of the three modes becomes unstable.