In this investigation, the 2D flow between two horizontally positioned concentric cylinders (gravity per-
pendicular to the axis of the cylinders), where the inner cylinder is kept at constant temperature Ti higher
than the outer border temperature To, is analyzed. Buoyancy forces initiate the movement of the fluid and
the generated flow is studied in a fixed geometry for values of Prandtl numbers (Pr) between 0.01 and 1,
and Rayleigh numbers (Ra) between 102 and 5 · 106 . To solve the problem, a Chebyshev-Fourier spectral
code is developed in polar coordinates (r, θ ) respectively, and a complete map of steady-state solutions
is obtained where regions with multiple solutions are identified. Later, a global stability study of the ob-
tained stationary solutions is carried out, providing a transition curve to unstable areas as a function of
the control parameters of the problem (Pr, Ra). Finally, to check the stability results, temporal evolution
simulations are accomplished for several cases where dual solutions are presented, finding intermediate
almost stationary solutions, and demonstrating that there exist typically single oscillating plume or dou-
ble oscillating plume solutions (depending on the parameter space), where some of them have higher
heat transfer coefficients, which may be interesting alternatives to improve heat exchange systems by
means of passive control techniques.
