A numerical investigation is carried out to determine the temperature and flow pat-terra of a fluid bounded by two horizontal isothermal concentric and eccentric cylinders. The inner cylinder is assumed to be at a higher temperature and rotating. The numerical method involves a mesh transformation technique coupled with the introduction of “false transient“ parameters for the steady-state solution of the problem. The parameters studied were for a Prandtl number of 0.7 and a radius ratio of 2.6 at different Rayleigh numbers, Reynolds numbers, and eccentricities. The results show that the mean Nusselt number increases with Rayleigh number. For a fixed Rayleigh number, when the inner cylinder is made to rotate, the mean Nusselt number decreases throughout the flow.