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• Topology optimization of natural convection process using metal foam is studied. • The adjoint model based on the lattice Boltzmann method is derived in detail. • The level-set based optimization method is validated by the pipe bend problem. • Passive heat sink designs under different parameters are obtained and analyzed. • Three-dimensional performance examination of the optimized designs are given. In this work, the level-set based topology optimization (TO) method for optimizing the distribution of porous metal foam in the fully-coupled natural convection system is developed. The respective adjoint lattice Boltzmann (LB) model and the sensitivity expression are derived. The forward LB model is validated by natural convection in cavity partially filled with porous medium and the TO method is validated by the pipe bend optimization problem. The validated TO method is utilized to design the two-dimensional passive heat sink made up of metal foam. It is found that the optimized design can approach the heat transfer enhancement of the conventional design with 100% filling while using only 40% material. For the base case, the average Nusselt number can be increased by 3.96∼6.74 times with the optimized designs mounted on the heating element when the Grashof number ranges from 15.7 to 2.8 × 104. Effects of increasing the Darcy number, decreasing the thermal conductivity ratio and decreasing the maximum foam volume fraction on the optimized designs and the heat transfer performance are discussed in detail. The two-dimensional TO structures are further stretched to three-dimension for further verification, and a 13.1%∼41.4% lower temperature than the conventional design is achieved by the optimized designs, indicating the superiority of the TO method. [ABSTRACT FROM AUTHOR]