Magnetothermal free convection of air in a square enclosure under a nonuniform magnetic field provided by a permanent neodymium-iron-boron magnet is numerically studied. The natural convection under the gravity field alone is also studied for comparison. The physical fields of magnetizing force, velocity, and temperature as well as the local distribution characteristic of Nusselt number are all presented in this paper. The results show that the buoyancy convection of air in the square enclosure under magnetic field is quite different from that under the gravity field. The local value of Nusselt number under the magnetic field supplied by a permanent magnet with a residual magnetic flux density of about 4.5 Tesla can reach a high value of about three times larger than the maximum local value of Nusselt number under the gravity field. Relatively uniform distributions of temperature gradient and Nusselt number can be obtained along the cold wall of the enclosure under the magnetic field. A permanent magnet with high magnetic energy product withBrreaching to 3.5 Tesla can play a comparative role on the averaged Nusselt number compared with that under the gravity environment.

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