This study describes a computational framework for non-Oberbeck-Boussinesq buoyancy-driven turbulent convection coupled with thermal radiation at large temperature difference. A low-Mach number (LMN) model based on the Favre-averaged (Navier-Stokes and energy) equations with the standard k-ε model is presented using unstructured finite volume method. The proposed model is used to simulate turbulent buoyancy-driven convection influenced by radiative heat transfer in a differentially heated square cavity with large temperature and density variation. The primary emphasis of the present study is to understand the non-Oberbeck-Boussinesq effects on buoyancy driven turbulent convection-radiation interaction in enclosures and its influence on overall flow dynamics and heat transfer. In this context, simulations are performed at Rayleigh numbers Ra=109,1010 and 1011 for pure natural convection and coupled convection with surface and gas radiation (τ = 0.2 and 1) at a large temperature difference. Results for Ra=1010 are discussed extensively for all the scenarios. Studies on the influence of Rayleigh number are performed for a particular case of coupled convection with gas radiation (τ=0.2). These simulations reveal that the consideration of wall and gas radiation leads to asymmetry in the flow and heat transfer. Further, the convection currents intensify, and the magnitude and extent of the turbulence effects primarily increase with the consideration of thermal radiation in the simulation. Additionally, the deviations between the proposed variable density low-Mach number model and popularly used incompressible model based on Reynolds averaged governing equations are quantified. The deviation between the two models is found to be growing with the increase in the optical thickness which invalidates the commonly used Boussinesq approximation for such flows. © 2018