In this paper, the Taguchi method was performed to determine the optimum values of the design parameters of the combined volumetric radiation and natural convection heat transfer in a square cavity with a horizontal fin on the hot wall. The radiative equation, like flow and energy equations, of the physical model containing participating medium, is solved by separate distribution functions in the novel lattice Boltzmann method (LBM). The effects of the five design parameters such as Rayleigh number, extinction coefficient, scattering albedo, fin length and height are investigated. In the Taguchi design method, the total Nusselt number on the cold wall is considered as a performance parameter. The levels of each parameter were set as 3 levels and the L27 orthogonal array was used for optimization. The results of the LBM-Taguchi combined method showed that the optimal condition was achieved at the maximum Rayleigh number, extinction coefficient, fin length and height, and minimum scattering albedo in the range of design factors. However the most important parameter affecting the total Nusselt number was the Rayleigh number, while the fin length and height had a minor effect.

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