In this work, numerical simulation of nature convection of Al ₂O ₃-H ₂O nanofluid in an inclined square porous enclosure is investigated to analyze the influence of different physical parameters on fluid flow and heat transfer via the lattice Boltzmann method. Due to stable chemical properties and low price in the dispersion system, Al ₂O ₃-H ₂O nanofluid is widely used in the field of industrial heat transfer enhancement, which is the focus of present work. When the nanofluid is transport in a porous media, the Darcy-Brinkman-Forchheimer model is usually used to describe the porous media effects on nanofluid flow. Compared with uniform thermal boundary condition, the natural convection of nanofluids with non-uniform thermal boundary condition has not received much attention. In this paper, the sinusoidal boundary condition is applied to the left side wall to analyze the heat transfer mechanism of Al ₂O ₃-H ₂O nanofluid in the inclined square porous enclosure. The effect of porosity (0.3 ≤ $\epsilon $ ≤ 0.9), Rayleigh number (10 ³≤ Ra≤ 10 ⁶), volume fraction of nanoparticle (0 ≤ ϕ≤ 0.04), tilt angle (0° ≤ γ≤ 120°) on the heat transfer performance are systematically investigated. Numerical results show that the non-uniform boundary condition can affect the heat transfer performance on Al ₂O ₃-H ₂O nanofluid with different physical quantities, which is different from the uniform boundary condition. When γ= 0° and Rais fixed, the Nu _avenumber (average Nusselt number) at the heated wall increases with porosity. When γ= 40°, 80° or 120°, the Nu _avereaches its maximum value at $\epsilon $ = 0.7. In addition, if $\epsilon $ and Raare fixed, the results show that the heat transfer performance is most efficient at γ= 40° whereas it is weakened at γ= 80°. Moreover, when different inclination angles are applied to the square cavity, the Nu _aveincreases slightly with an augmentation of ϕ. In all, compared with the uniform temperature boundary condition, the effect of volume fraction of nanoparticles on the enhanced heat transfer is not significant, therefore, to improve the heat transfer performance of nanofluids with given ϕand Ra, it is necessary to take advantage of the improvement of effective thermal conductivity for the nanofluids in porous media and the perturbation influence of inclination angles on the system together with using appropriate porosity and square cavity tilt angle to intervene the flow.