Study of natural convection in a heated cavity with magnetic fields normal to the main circulation

•Both 3D and Q2D numerical simulations are conducted to study the magneto-convection.•The physical mechanism of heat transfer enhancement with lower magnetic fields has been analyzed in detail.•The results confirm that the damping velocity and kinetic energy of main convection are scaled as Gr/Ha.•The average Nusselt number can be correlated as a function of Ha/Gr3/4.