The effects of eccentricity and geometric configuration with a Newtonian fluid have been investigated numerically to determine heat transfer by natural convection between the sphere and vertical cylinder with isothermal boundary conditions. The inner sphere and outer vertical cylinder were heated and cooled in a steady change of temperature. Calculations were carried out systematically for a range of the Rayleigh numbers to determine the average Nusselt numbers which are affected by the geometric ratio (HR:RR) and eccentricity (e) parameters on the flow and temperature fields. The governing equations, in terms of vorticity, stream function and temperature are expressed in a spherical polar coordinate system. Results of the parametric study conducted further reveal that the heat and flow fields are primarily dependent on the Rayleigh number, eccentricity and geometric configuration, for a Prandtl number of 0.7, with the Rayleigh number ranging from 10 3 to 10 6 , the three eccentricities and two geometric configurations. Above all, the specification of different convective configurations has a significant effect on the average heat transfer rate across the composite annulus gap.