A numerical study for steady laminar double-diffusive natural convection within a vertical closed annulus is examined with constant temperature and mass species (concentration) differences imposed across the vertical walls. The annulus has an aspect ratio of 1 and a curvature ratio of 2, while the fluid Prandtl number is 7. In this paper the problem is defined and the numerical solution procedure is validated. Moreover, the effect of buoyancy ratio on the flow structure and rite resulting heal and mass transfer rates is presented. It is determined that buoyancy ratio is the primary factor that defines flow structure, including concentration—dominated (buoyancy force) opposing flow, transitional flow, thermal-dominated flow, or concentration-dominated aiding flow. The relationship for buoyancy ratios, in the range -10 ≤ n ≤ 10, and the average NusseU and Sherwood numbers have been obtained for a thermal Rayleigh number of 50,000 and a Lewis number of 5. Future papers wilt include the effect of thermal Rayleigh number, Lewis number, and various geometric parameters on the flow structure and heat and nusi transfer.