A numerical simulation on the combined natural convection and radiation is carried out in a partially open rectangular enclosure with a heater by using the finite volume and the S-8 discrete ordinate methods. The fluid inside the enclosure is considered as an absorbing, emitting and anisotropic scattering media. The heater causes a natural circulation of the fluid (10$^{5}$ <Ra<10$^{9}$ ) which results in significant in-flow of the ambient cold fluid through the partially open wall. Comparing the results of pure convection with those of the combined convection- radiation, the combined heat transfer results with small Planck numbers (P$_{l}$ <1.0) show much stronger circulation than those of the pure convection, and the fluid circulation is more evident for larger Rayleigh numbers. When one of three radiative properties - the medium absorption coefficient, the wall reflectivity, and the scattering albedo - increases, the fluid circulation and the heat transfer in the enclosure are reduced. The location of the heater and the open ratio of the right wall are also shown to affect the fluid circulation and heat transfer significantly. However, the anisotropy of the scattering phase function is shown to be unimportant for the fluid circulation and heat transfer within the enclosure considered in this study.