The present study explores nanofluid magnetohydrodynamics (MHD) natural convection in an incinerator shaped enclosure including a rectangular hot block situated on the bottom wall. A parametric investigation is conducted to explore the effect of different parameters such as nanoparticles volume fraction (ϕ = 0–4%), Rayleigh number (Ra = 103–105), external magnetic field intensity (Ha = 0–100), incinerator tilting angle (γ = 0–360°) and hot block's height (0.1–0.5), width (0.1–0.8) and position on heat transfer, nanofluid flow, and entropy generation inside the incinerator. The top and bottom horizontal walls of enclosure are adiabatic; the right, left vertical and inclined walls are supposed to have cold temperature whereas the hot block is maintained at a hot temperature. The Brownian motion was also considered in calculating the effective nanofluid thermal conductivity and viscosity using Koo–Kleinstreuer–Li (KKL) correlation. The lattice-Boltzmann method is used with a D2Q9-D2Q9 double population's model as utilized CFD approach. The mesh independency study and the validation of proposed model are accomplished in several cases and very good agreement is found between present results and former experimental and numerical findings. The results showed that entropy generation is augmented by increasing height and width of heater, nanoparticles volume fraction and Rayleigh number but it is reduced by enhacing Hartmann number. However, increasing the magnetic field does not have notable influence on heat transfer, compared to other parameters. The optimum incinerator inclination angles to maximize heat transfer and minimize entropy generation are 90° and 270°.