LBM simulation for combined thermal radiation and natural convection in 2D enclosure with multiple solid blocks

A numerical investigation of conjugate natural convection in a 2D square enclosure with multiple solid blocks, considering the impact of volumetric thermal radiation, was conducted using the lattice Boltzmann method (LBM). The effect of Planck number 0.01 <= Pl <= 1, wall surface emissivity 0 <=epsilon w <= 1, extinction coefficient 0.1 <=beta <= 5, solid-to-fluid volume fraction 15%<=chi <= 60%, and the number of solid blocks 1 <= N <= 64, on the fluid-structure and heat transfer within the enclosure were analyzed. The numerical model was validated using benchmark problems from the literature, showing good agreement. The results revealed that at Pl=0.01 and N=16, increasing wall surface emissivity significantly increased the Nusselt number, ranging from approximately 51-116% for different wall emissivity values, as compared to scenarios without surface radiation (epsilon w). On the other hand, reducing chi, Pl, and beta improved the heat transfer rate. The results also demonstrated that subdividing the initial block reduced the heat transfer rate depending on the number of blocks and the value of the Planck number. For instance, when 64 solid blocks were present in the cavity and Pl=0.01, the Nusselt number decreased by 59.36% compared to the case with a lower solid-to-fluid volume fraction (chi = 15%). The parametric analysis provided useful insights for engineering design in the modern construction industry, with possible applications in building block design and energy efficiency enhancements.