Computational analysis is utilized to examine the effects of introducing nanoparticles to a square lid-driven cavity to enhance the hydro-magnet mixed convection. Constant temperatures are imposed along the square container’s vertical edges. Both the top and bottom surfaces are covered with insulation. The lid is thought to move in two ways: increasing or decreasing free convection. In addition, a horizontal magnetic field is applied uniformly. For various Hartmann numbers (Ha) (0:100), Richardson numbers (Ri) (0.001:10), and solid volume fractions (0:0.1), the results are reported. This research is based on a constant Grashof number (Gr) of 104. The effects of parameters, including the Richardson number, Hartmann number, solid volume percentage on the stream, isothermal lines, and local Nusselt numbers (Nu), were investigated numerically. In addition, given various parametric settings, the anticipated results for the average Nusselt (Nuavg) are shown and discussed. For all tested parameters, increasing the magnetic field makes the orientation of the lid more effective on heat and fluid movement. The magnetic field reduces heat and fluid flow. The heat transmission is aided by increasing the solid volume percentage. The effect of nanoparticles on flow and heat transmission is being studied. At Ri = 0.001, the effect of lid orientation is not significant. The highest reduction in heat transfer occurs when adding flow at Ri = 10, = 0, and Ha = 100.