Detailed numerical analysis is presented for natural convection heat transfer in internally finned horizontal annuli. Governing equations are discretized using the finite volume method, and solved using SIMPLE algorithm with Quick scheme. The results show that the flow and heat transfer can reach steady state when the Rayleigh number is below 2×10⁴. When the Rayleigh number is greater than 3×10⁴, two different types of numerical solutions under the same parameters can be obtained for different initial conditions. The critical Rayleigh numbers with two different initial conditions are different from steady to unsteady solutions. The oscillatory flow undergoes several bifurcations and ultimately evolves to a chaotic flow as the Rayleigh numbers increase.