Heat transfer rate characteristics of the magnetothermal Rayleigh–Benard convection of paramagnetic air

• Three-dimensional numerical computations for various magnetic Rayleigh numbers.
• Mechanism of the magnetothermal Rayleigh–Benard convection of air.
• Heat transfer rate of the magnetothermal Rayleigh–Benard convection of air.

We carried out complete transient three-dimensional numerical computations to clarify the heat transfer rate characteristics of magnetothermal Rayleigh–Benard convection of paramagnetic air induced by both magnetic and gravitational buoyant forces. The shallow vertical cylindrical enclosure filled with air was heated from below and cooled from above. The enclosure was assumed to be located inside the bore space of a superconducting magnet. In addition, the enclosure was fixed at the location where the magnetic force in the axial direction was more uniform in the radial direction, as was the gravitational force. The average heat transfer rates were computed for various Rayleigh numbers and magnetic strengths. The results are plotted versus both the Rayleigh number and the magnetic Rayleigh number, Ram, defined by Braithwaite et al. in comparison with experiments by Silveston. For the range 2310 < Ram ≤ 10,000, the average Nusselt numbers are found to distribute around the data by Silveston. However, in the range Ram ≤ 2310, the average Nusselt numbers are overestimated compared to those by Silveston. Probably, this is because the magnetic force approximated with a one-turn coil includes radial directional acceleration force and the convection mode differs from the unidirectional gravitational one. On the other hand, in the rage, Ram > 10,000, the overestimated Nusselt numbers may be due to a linear model.