Numerical Pattern Formation on Magnetothermal Convection of Diamagnetic Liquids in a Cylindrical Vessel of Rayleigh–Benard Model: Effects of Axisymmetric Horizontal Magnetic Forces on Vertical Magnetic Forces

Abstract

We carried out three-dimensional computations of the magnetothermal convection of diamagnetic liquids (e.g., water) in a shallow cylindrical vessel of the Rayleigh–Benard model to investigate the effects of the radial components of the magnetic force (MFR) and the vertical components of the magnetic force (MFZ) on heat transfer and pattern formation. For the purpose of examining various magnitudes of radial and vertical components of the magnetic force, we used a 1800-turn coil instead of an actual conventional magnet, and a 2-turn coil as a new proposal. In the computation, the Prandtl number was constant at 6.0 (i.e., water at room temperature), and the Rayleigh number was 1.0 × 104. As a result, an axisymmetric pattern and a spokelike pattern appeared in the convection. Subsequently, we arranged all the results with a new parameter, which is the absolute ratio of the radial component of magnetic force at the vessel sidewall to the vertical resultant force at the vessel center. This parameter represents the relative contribution of MFR to the vertical resultant force (RFZ). The RFZ is the sum of the gravitational force and MFZ, and is associated with the magnetic Rayleigh number. By using this parameter, the spoke pattern convection appeared when the parameter was within 0.11 to 0.85. This result suggests that not only the MFR but also the MFZ plays an important role in determining whether the convection flow pattern transited to the axisymmetric flow or not. This parameter range is easily satisfied in a conventional superconducting magnet. We can say that the spoke pattern convection may be a common phenomenon in the magnet. On the other hand, the flow pattern had little effect on the heat transfer in convection. Thus, the effects of MFR and MFZ on the pattern formation in the magnet are much more complicated than those previously considered.