A Numerical study has been conducted to clarify the effect of the buoyancy forces on the thermal development through a horizontal annulus sector heated with constant surface temperature. The study includes the solution of governing equations for the flow and heat transfer of different sections along the channel. Theoretically these governing equations were reduced to four, which are continuity equation, radial and tangential momentum equations, axial momentum equation and vorticity equation in which the variables were the temperature, vorticity, stream function and axial velocity. These equations were reduced to dimensionless equations in which Rayleigh, Prandtl and Reynolds numbers were presented. They were numerically solved by using the marching process explicit finite difference method and Gauss elimination technique. Numerical results for annulus sector heated by constant surface temperature for different values of Rayleigh numbers and total sector angles and diameters ratio were obtained and represented by stream function contours and isotherms and circumferential distribution of local Nusselt number. Also the results include the values of friction factor and average Nusselt number for the pure forced convection. Comparisons are made between the computed results and the analytical or numerical results available in the literature, for all cases compared, satisfactory agreement is obtained. The results include a survey of annulus sector surface in many sites of channel flow, whereas it is apparent that the buoyancy force causes the secondary flow to behave non uniformly at the entrance and then the average heat transfer will increase with the increasing both of diameter ratio and total annulus sector angles. A correlation relationship is extracted to find an average change of Nusselt after the stability of the flow in the fully developed region for the studied ranges of annulus sector angles and diameters ratio.