This study numerically investigates the effect of a magnetic field on the natural convective heat transfer of silver nanoparticle-water nanofluid within a square cavity. The cavity is heated from below, with its vertical side walls kept at a constant lower temperature, while the top surface is adiabatic and a constant magnetic field is applied to the left vertical surface. The effects of Rayleigh number (103 to 106), Hartmann number (0 to 20), and nanoparticle volume fraction (2% to 8%) on heat transfer and fluid flow characteristics are analyzed. The results show that increasing the nanoparticle concentration significantly increases the heat transfer in the enclosure at higher values of Rayleigh number. Contrary, increasing Hartmann number, reduces the fluid velocities and average Nusselt number due to the effect of Lorentz forces. This dual influence highlights the potential for optimized thermal management in diverse applications. The novelty of this work lies in investigating the silver-water nanofluids under varying magnetic field and buoyancy forces in enclosed geometries offering new insights into engineering applications.