Transitions of natural convection in a horizontal annulus

Transitions of natural convection in an annulus between horizontal concentric cylinders 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. It is confirmed by numerical simulations that dual stable steady solutions exist for Rayleigh numbers larger than a critical value. Bifurcation diagrams of the steady solutions are obtained by Newton–Raphsonʹs method for various values of ratio of the inner cylinder diameter to the gap width and their linear stability is investigated. The origin of the dual solutions is clarified from the bifurcation analysis.