In this paper, the lattice Boltzmann method -LBM- is extended to simulate combined volumetric radiation and natural convection in a nanofluid filled the cavity with an inside heated plate. Accordingly, all of the governing equations, including the radiative equation, are solved by the LBM approach. Also, the Rayleigh theory is adopted to find the optical properties of nanofluid. The nanofluid is a mixture of Al2O3 nanoparticles suspended in pure water as a base fluid. Main efforts focus on the effects of volumetric radiation at different Rayleigh numbers -103, 104 and 105- and volumetric concentrations -0.1% and 0.3%- on the flow and temperature distribution inside the enclosure for the horizontal and vertical heated plate. The obtained results indicate that considering thermal radiation noticeably affects temperature patterns. It is also observed that the average Nusselt number is improved by reason of radiation presence, whereas it decreases with increasing volume concentration due to the increase of scattering properties of the nanofluid. The present results reveal that the used LBM for solving the radiation transport equation, instead of approximations, provides new findings that should be considered in practical applications.

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