Cool retention technology using permanent magnets on natural convection of air

A magnetic field was applied with permanent magnets to the natural convection of oxygen-containing air in a cubic container consisting of a pair of vertical walls maintained at different temperatures. Two-dimensional numerical simulations were performed on this configuration to investigate the change in heat transfer due to the arrangement and shape of the prismatic magnets. The governing equations were discretized using the finite volume method and solved with the SIMPLE algorithm. The accuracy of the numerical code was validated by solving a magnetic quadrupole problem, and the results showed good agreement with previous studies. The nondimensional parameters were set as Prandtl number $\mathrm{Pr}=0.71$, Rayleigh number $\mathrm{Ra}=10⁵$, and magnetic number $0\le \mathrm{Ma}\le 10$. The primary magnet shape considered was a square cross-section occupying 16 % of the container's cross-sectional area. The magnets were shifted so that their central axes varied within the ranges $0\le X_{\mathrm{pm}}\le 1.5$ or $0\le Y_{\mathrm{pm}}\le 1.5$. When the magnet was positioned near the top or right side of the container, the Nusselt number ($\mathrm{Nu}$) significantly decreased, ranging from 3.38 % to 22.3 % and from 0.781 % to 37.4 % respectively for $\mathrm{Ma}=10$. Notably, $\mathrm{Nu}$ reached its minimum when the central axis of the magnet was located at $Y_{\mathrm{pm}}=0.84$.