The influence of turbulent natural convection and thermal radiation in a differentially heated square enclosure is numerically investigated. The enclosure is heated from the right wall and cooled from the left wall. The other walls are assumed to be adiabatic. The Reynolds Averaged Navier Stokes (RANS) formulation was employed for analyzing turbulent flows together with a Realizable k-epsilon model. In addition, the discrete ordinates method (DOM) was used to solve the radiative transfer equation (RTE). Influence of Rayleigh number (Ra), optical thickness (tau), Planck number (P1), scattering albedo (omega) and wall emissivity (epsilon(w)) parameters were studied numerically on square enclosure for the flow and temperature distribution. It is interesting to note that a detailed parametric study focusing on characterizing parameters in turbulent natural convection and radiation was rarely dealt with in details. Solutions were obtained for a range of Rayleigh numbers varying from 10(9) to 10(12). It was found that the radiation heat transfer alters the characteristics of flow fields in the enclosure. Increasing the optical thickness results in a decrease in combined heat transfer for a fixed Rayleigh number and the maximum of heat transfer occurred for low optical thickness with radiation presence. (Nu) over bar (t) =87.796 and 82.351 is obtained for tau=0.2 and 5, respectively (Ra=10(10), P1=0.02 and omega=0). The heat transfer increases with decreasing Planck number, and decreases with the increasing scattering albedo. (Nu) over bar (t) =445.837 and 68.100 is obtained for P1=0.001 and 10, respectively (Ra=10(10), tau=1 and omega=0). When the active walls are black and the insulated walls are reflected, (Nu) over bar (t) =85.507 is obtained for Ra=10(10), P1=0.02, tau=1 and omega=0.