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

•2D flow between two horizontally positioned concentric cylinders has been solved by means of spectral methods.•Boussinesq approximation has been considered.•Vast number of steady solutions have been obtained in the Pr-Ra space.•Global stability analysis has been carried out to define the stability border in the Pr-Ra map.•2 regions of multiple solutions have been found.•Stability results have been validated by means of unsteady simulations.