Enhanced Convection or Quasi-Conduction States Measured in a Super-Conducting Magnet for Air in a Vertical Cylindrical Enclosure Heated From Below and Cooled From Above in a Gravity Field

Abstract

Magnetizing force was applied for natural convection of air in a shallow cylindrical enclosure heated from below and cooled from above. The cylinder measured 45 mm in diameter and 14.8 mm in height. The convection enclosure was located 66 mm above or below the coil center in the bore of a super-conducting magnet. The average Nusselt numbers were enhanced about twice at the location +66 mm above the coil center under 3.40 Tesla and decreased to Nu=1.12∼1.28 at the location −66 mm below the coil center for the Rayleigh number from 3520 to 6980. These two locations were selected as the most effective positions for application of the magnetizing force in this super-conducting magnet. A model equation for magnetizing force was derived and numerically computed for Pr=0.7 and Ra=2100 and 7000. One turn coil was presumed as a model of thousand turns real superconductor. The magnetic strength is represented by a new parameter γ and varied from 2345 to 9124. By adjusting the location of the enclosure in the bore of the super-conducting magnet, the average Nusselt number of 1.14 at Ra=2100 varied from 1.8 to 1.0001 depending on the magnetic strength, and that of 2.02 at Ra=7000 varied from 2.6 to 1.0003. These data are plotted versus magnetic Rayleigh number Ram=Raγ∂Bz2/∂Z+1R=0,Z=0.5 at the center of the enclosure and agreed well with Silveston’s data for a classical nonmagnetic field.