Numerical computation for Rayleigh-Benard convection of water in a magnetic field

摘要

The derivation process for the model equation is shown for the natural convection of water (diamagnetic) under both gravity and magnetizing force fields and numerically solved for the Rayleigh-Benard convection in a shallow cylinder heated from below and cooled from above. The cylindrical enclosure was located at two levels in the bore of a super-conducting magnet, where the radial component of the magnetizing force is minimal and its axial component prevails. The cylindrical enclosure was assumed to be located coaxially with the bore of the magnet, and a two-dimensional model equation was presumed. Sample computations were carried out without or with a gravity force for various strengths of Rayleigh number and magnetic induction. When the enclosure was placed above the coil center, where the magnetizing force is opposed to the gravitational force, the average Nusselt number decreased with increasing strength of the magnetic field. When the enclosure was placed below the coil center, where the magnetizing force is parallel to gravity, the average Nusselt number increased above unity even at Ra = 1000 and 1500. All of the data agreed favorably with the classical experimental data of Silveston when plotted against the magnetic Rayleigh number proposed by Braithwaite et al.