Experimental Heat Transfer Rates of Natural Convection of Molten Gallium Suppressed Under an External Magnetic Field in Either the X, Y, or Z Direction

The heat transfer rates of natural convection of molten gallium were measured under various strengths of heating rates and three coordinate directional magnetic fields. Molten gallium (Pr = 0.024) was filled in a cubic enclosure of 30 mm × 30 mm × 30 mm whose one vertical wall was uniformly heated and an opposing wall was isothermally cooled, with otherwise insulated walls. An external magnetic field was impressed either perpendicular and horizontal to the heated wall (x direction) or in parallel and horizontal to the heated wall (y direction) of the enclosure or in a vertical direction (z direction). For the modified Grashof number, based on the heat flux, less than 4.24 × 106 and the Hartmann number less than 461, the average Nusselt numbers were measured. These results proved that our previous three-dimensional numerical analyses for an isothermal hot wall boundary were in good qualitative agreement. A much higher suppression effect is given in the x- and z-directional magnetic fields than that in the y-directional one. The measured heat transfer rates were correlated as follows: NuB−1Nu0−1=1−[1+(aGr1/3/Ha)b]−1/nMagneticfield¯a¯b¯c¯x-directional0.573.191.76y-directional4.192.071.45z-directional0.522.721.44