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This paper presents a numerical study of natural convection in a triangular cavity filled with water. The horizontal wall is hot, the vertical wall is cold and the inclined wall is insulated. Lattice Boltzmann method (LBM) is applied to solve the coupled equations of flow and temperature fields. This study has been carried out for the pertinent parameters in the following ranges: Rayleigh number varied from Ra = 103 to 106 and the inclination angle between Φ=0° and 315°. The effects of Rayleigh numbers and inclination angle on the streamlines, isotherms, Nusselt number are investigated. Results show that the heat transfer rate increases with the increase of Rayleigh number. In addition it is observed that the lower heat transfer rate is obtained for Φ=135°; however, the highest heat transfer is achieved at Φ=0°. The inclination angle greatly influences the heat transfer rate depending on the Rayleigh number.