In heat exchangers and heated solenoids, the annular structure is widely used and it often transfers heat through natural convection. So, the heat-transfer characteristics of the annular structure are numerically studied in the range of 10≤Ra≤5×105 in this paper. The chimney effect and the air-heating effect are investigated. When the combined effect of two is the strongest, the ratio of the average Nusselt number of the annulus to that of the cylinder reaches the maximum value of 1.019 and the thermal boundary layer is tangent to each other. By the research, the heat exchange efficiency is the worst in the position of θ=0° due to the air-heating effect when 10≤Ra≤102 meanwhile in the position of 278°≤θ≤285° for 103≤Ra≤5×105. At last, the Nusselt number correlation has been fitted: Nu¯=0.6398×Ra0.2205. The specific study of the heat transfer characteristics on the outer flow of the annulus and the correlating equation can provide guidance for the design of heat exchangers, solenoids, and enrich the basic research content of natural convection.