In the present study, the natural convection heat transfer inside a rectangular enclosure is investigated. The bottom and top walls are kept at constant temperatures, and the sidewalls are insulated. A single relaxation time Bhatnagar–Gross–Krook model for the lattice Boltzmann method is used. For low Rayleigh numbers, the results show that the isotherm plots are smooth and weak vortices appear only at the upper part of the cavity; whereas at high Rayleigh numbers, the isotherm plots are disordered and the vortices become strong at the bottom and top parts of the cavity. The results show that the Nusselt number increases with increasing of Rayleigh number. The average Nusselt number at turbulent regime instead of reaching steady state, it undergoes complex transitions to take periodic and chaotic behavior with time. The present numerical results have a good agreement with previous numerical and experimental results in both laminar and turbulent regimes.

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