Exchange of instability modes for natural convection in a narrow horizontal annulus

Abstract

Instabilities and transitions of natural convection in a narrow horizontal concentric annulus are investigated theoretically by assuming two-dimensional and incompressible flow fields. It is assumed that the inner cylinder is kept at a higher temperature than the outer cylinder. Steady solutions for the natural convection are obtained numerically by Newton–Raphson’s method for various values of Prandtl number and their linear stabilities are analyzed. It is found that there are two different instability modes for the natural convection depending on the Prandtl number, which exchange at a critical value of the Prandtl number. The origins of the two instabilities are clarified from the bifurcation and linear stability analyses of the steady-state solutions.