A numerical study of MHD natural convection in an upright porous cylindrical annulus filled with magnetized nanomaterial is made by using the specificity of nanoliquids to improve the phenomenon of heat transport. The upper and lower walls are thermally insulated, whereas the outer wall is kept at a lesser temperature. The finite volume method is used to treat the governing equations via computer code with Fortran programming. The results obtained are given for the values of the Rayleigh number between 103 and 106, aspect ratio Ar = 2, radii ratio λ = 2, Hartmann number (0 ≤ Ha ≤ 80), Darcy number (10−5 ≤ Da ≤ 10−2), porosity ratio (0.1 ≤ ε ≤0.9), and the nanoparticles volume fraction (0 ≤ φ ≤ 0.1). The transferred thermal flux, in laminar natural convection, increases with the growth of the nanoparticle concentration, the Darcy number, the porosity, the Rayleigh number and, the length of the source.