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The study of the effect of periodic boundary condition is of primary interest to understand the maximum temperature of the wall and avoid overheating phenomena. Available computational fluid dynamic studies provide information on the effect of the local heat flux or local temperature. This study aims to understand the temperature and fluid flow distribution inside the cavity under such periodic thermal boundary conditions to avoid overheating phenomena. This study reports the numerical results of the natural convection inside an air-filled cavity with its horizontal walls insulated and its vertical walls at different thermal boundary conditions. The heat flux of the left wall and the temperature of the right wall are varied sinusoidally. The Lattice Boltzmann Method (LBM) is used to solve the governing equations with the related boundary conditions. The maximum temperature of the wall under the heat flux and the maximum stream function inside the cavity are investigated. Also, the effect of oscillation period on the maximum temperature of the left wall is studied. The results show that the maximum temperature of the left wall corresponds to the heat flux wavelength of 0.8. Moreover, the stream function value increases intensively by increasing the Rayleigh number.

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