A numerical investigation for three-dimensional natural convection inside horizontal concentric annulus with open ends and conditions of either adiabatic or isothermal outer cylinder surface is made by a zonal grid approach, which extends the outlet boundary from the open end of the annuli to a far enough outside position that can be reasonably specified with the ambient flow properties. Computational result reveals that the maximum inner cylinder surface temperature occurs right at the top of the inner cylinder. It is also found that the inner cylinder surface temperatures decrease towards the outlet plane for the adiabatic case, while remains relatively constant for the isothermal case. The variation of the inner cylinder surface temperatures is smaller for the isothermal case as compared to the adiabatic case.