Natural convection of multi-wall carbon nanotubes-Iron Oxide nanoparticles/water hybrid nanofluid (MWCNT-Fe3O4/water hybrid nanofluid) inside a perpendicular to shaped enclosure has been numerically investigated using Lattice Boltzmann Method. Numerical in-house code has been developed to study the effects of different parameters including the nanoparticles volume fraction, the Rayleigh number, the cavity obstruction ratio, the heat source position, and the heat source aspect ratio on the hydrodynamic and thermal characteristics. In order to validate the developed numerical code, the results have been compared with previous works and have shown a good concordance. The results indicate that Nusselt number degrades respect to the cavity obstruction ratio because of development of the thermal boundary layer thickness. In addition, an increment of the heat source aspect ratio results in better cooling condition due to decreasing in the boundary layer thickness.