Solution to natural convective motion in a vertical cylindrical annulus of large aspect ratio is examined, with the inner wall subject to a constant heat flux. Similar transformations of the appropriately simplified Navier–Stokes model of the annular flow are sought. The issue of boundary condition limitations for the considered flow is resolved in terms of acceptable error bounds for valid solutions. Results are generated for a variety of outer wall boundary conditions over various ranges of the Rayleigh number, highlighting the effects on the patterns of streamlines and “heatlines.” Correlations presented for the Nusselt number are shown to be dependent on both the boundary conditions and the geometry.