Natural convective nanofluid flows immersed in oscillating magnetic fields are simulated with a sub-continuous nondimensional lattice Boltzmann model. The effective electrical conductivity model is built including coupled effects of nanoparticle concentrations and two Knudsen numbers. Effects of directions, frequencies, and strength amplitudes of the magnetic fields are studied in wide ranges of Hartmann numbers () and Rayleigh numbers (). To achieve higher values of cycle averaged Nusselt numbers , optimal magnetic directions are along or opposite from the gravity directions. Effects of the magnetic frequency are negligible, in the conduction dominating lower Rayleigh number regime of . In the convection dominating regime, increase with in orders of and for vertical and horizontal magnetic directions, respectively, and maximum values of appear at the optimal magnetic frequency of for all magnetic directions. With as high as , the oscillating amplitudes of the transient wall mean Nusselt numbers increase with increasing , but the cycle averaged Nusselt numbers decrease from 9.35 to 1.42 with increasing in the transient regime of . Meanwhile, heat transfer patterns transit back from convection to conduction dominating patterns with increasing , as illustrated by transient streamlines and isotherms.