Global stability analysis of the natural convection between two horizontal concentric cylinders

Abstract

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.