Enhanced heat transfer rates caused by magnetic field for natural convection of air in an inclined cubic enclosure

Enhancement of heat transfer rates of natural convection of air was considered in a cubic enclosure heated from one vertical wall and cooled from an opposing wall with one magnetic coil placed on a plane with the top wall. With electric current in this coil, the magnetic field is induced in the enclosure to effect the natural convection of air. Magnetizing (or magnetic) force has been known to be proportional to the magnetic susceptibility and the gradient of a square of magnetic induction. In the momentum equation, this magnetizing force was considered. The magnetic induction was computed from Biot-Savart's law. Characteristic dimensionless values are the Rayleigh number, the Prandtl number, and gamma, which represents the strength of the magnetizing force. Sample computations were carried out for the parameter ranges Pr = 0.71, Ra = 10(5), and gamma = 0-100. When the enclosure was kept horizontal, the average Nusselt number at Ra = 10(5) was 4.48 at gamma = 0 without a magnetic field. Then it became 3.97 at gamma = 1, 5.16 at gamma = 10, and 12.5 at gamma = 100. When the enclosure was turned upside down, it became 4.89 at gamma = 1, 6.97 at gamma = 10, and 13.0 at gamma = 100. The effect of inclination of the enclosure was further considered by keeping the hot and cold walls in a vertical gravitational direction.