We theoretically address the natural convection of a fluid between coaxial cylinders whose axis is horizontal, when the temperatures on the surfaces are kept constant, the inner warmer than the outer one.

We compare the outcomes of some mathematical models derived from the Oberbeck-Boussinesq approximation, having in common the existence of a steady solution different from zero for any curvature of the domain and arbitrary values of the Prandtl and Rayleigh numbers.

The basic steady solution prove to be asymptotically stable for sufficiently small Rayleigh numbers. The critical values derived by the energy method depend on the curvature and their graphs converge in the region of the parameter space where the curvature is large.

For large curvatures, we prove that the Non-Linear Stokes System exhibit a critical Rayleigh number which is mathematically well-defined and uniformly bounded from below. A numerical procedure to calculate it is suggested.