Numerical simulations are conducted for the natural convection heat transfer in a narrow gap between two horizontal plates in air. The lower plate is an infinite plate with a circular heating zone. The upper one is the bottom of a vertical cylinder, which is placed right above the circular heated plate and kept at room temperature. A set of Navier-Stokes equations and an energy equation are analyzed for a variety of combinations of gap clearance and Rayleigh number. The calculated average heat transfer are shown to be in good agreement with the experimentally obtained ones reported in the previous paper. From the obtained isotherms, stream lines and local Nusselt numbers, it is found that two types of convection appear in the gap space according to the conditions of Rayleigh number and gap clearance : one is a simple convection due to the single renewal flow which replaces heated air with ambient air and the ether is a combined convection due to several vortex flows and the renewal flow. Furthermore, it is also found that the flow rate of each flow controls the rate of heat transfer from the limited area which is covered by each flow. From this fact, the validity of the previously proposed heat transfer correlation is briefly discussed.