Flow and heat transfer mechanism of wall mode in Rayleigh-Bénard convection under strong magnetic fields

Direct numerical simulations have been performed to investigate the quasistatic magnetoconvection of a low Prandtl number fluid (Pr = 0.025) within a rectangular cell of varying aspect ratios under the influence of a vertical magnetic field. The Hartmann number (Ha) is fixed at Ha = 200 and Ha = 1000, while the Rayleigh number (Ra) ranges from 2 x 105 to 1 x 107, encompassing the entire region of the wall mode. Under a strong magnetic field, sidewall instability triggers convection onset, leading to wall mode states with enhanced heat transfer. As Ra increases, wall mode expands towards the cell center, increasing heat transfer intensity, as indicated by the Nusselt number (Nu). Reducing the aspect ratio and increasing the magnetic field both improve global Nu by enlarging the wall-mode region and intensifying heat transfer within it. This study introduces a root-mean-square velocity-based method for characterizing the wall mode, revealing significant circulation in the bulk. It also analyzes the double-layer structure of the wall mode, where the core and reverse flows are driven by buoyancy with an anomalous weakening of the Lorentz force in the core. A thermal boundary layer is observed in the impact zone, correlating inversely with heat transfer intensity.