Numerically simulate natural convection heat transfer in the slotted circle within a round in different structure sizes, and study the natural convection heat transfer and nonlinear characteristics according to the numerical results. Verified by numerical calculation, the numerical results coincide with the same working conditions experimental results of the existing literature. Studying natural convection heat transfer in the horizontal slotted round within the circle, with the increase of Ra, it is possible to obtain a stable solution, periodically oscillating solutions, non-periodic oscillation solution, ultimately chaos; on the same slotted direction, the average equivalent thermal conductivity Keqs with the increase of Ra increases, and Keqs is maximum in the vertical direction, so the convective heat transfer is the strongest. when Ra exceeds a critical value, numerical results begin to oscillate, such as the static bifurcation and periodic oscillation phenomenon, and this critical value is associated with slotted direction, The largest in vertical direction, and get the minimum in 45°. For numerical analysis of slotted circle within closed circle under the different radius ratios. The annular space pace is narrower, thermal fluid is more in slotted circle, internal isotherm closer to the horizontal, the worse of heat transfer. But once the radius ratio greater than 2.0, and then increase the radius ratio Keq is not increased too much.

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