The unsteady numerical simulations have been presented for the laminar natural convection in a partially open compartment. Computations were performed within the domain of the compartment in order to show the thermal radiation and the partially opening effects on the flow fields and heat transfer characteristics. The results were shown for different Planck numbers(0.05~5) and opening ratios(0.25~0.75) being fixed with Ra=$10^5$ and Pr=0.71. Considering the flow which is buoyancy driven from the heated wall, and the buoyancy is not much affected by the further outside region from the opening, the numerical computations have been performed without an outer region by the particular boundary treatments on the flow velocity and temperature at the different partial openings. The confined numerical domain reduced the CPU time and the memory of computer. P-1 approximation of radiative transfer equation was employed with Marshak type boundary conditions along with the pseudo-black body approximation at the partial openings. The numerical results clearly show that the natural convective flow and heat transfer are much affected by increase of thermal radiation particularly from the initial state. When thermal radiation is not much affecting the flow ($PL{le}1$), it was found that thermal radiation effects are almost negligible.