Magneto-convective Heat Transfer Measurements in Liquid Gallium

We conduct heat transfer measurement of a liquid gallium Rayleigh-B\'enard system with a vertical magnetic field. The experiment is carried out in two cylindrical containers with diameter-to-height aspect ratio $\Gamma = 1$ and $2$ for $10^6 < Ra < 10^8$ and $0< Ch < 3\times 10^5$. Combined the results from the previous studies, our experiment shows a more complete picture of near-onset to supercritical behaviors of heat transfer in liquid metal magnetoconvection (MC) over a large range of parameter space ($10^3 < Ra < 10^9$). Moreover, we tested different critical $Ra$ predictions from Chandrasekhar(1961), Busse(2008), and Houchens et al.(2002). Our study shows that convection onsets below the predicted critical $Ra$ for an infinite fluid layer (Chandrasekhar, 1961) and MC in our finite cylindrical tanks onsets via stationary wall-attached modes. This result is in agreement with recent experiment (Z\"urner et al., 2020) where the wall-mode was found experimentally near onset. The heat transfer data also suggest that asymptotic critical $Ra$ from Busse(2008) is likely the best to describes the onset of magnetoconvection in a cylindrical confinement regardless of the different aspect ratios.