Localized magnetohydrodynamic effects on natural convection in a cubic cavity at Rayleigh number up to 107

Magnetic field control offers significant advantages for fluid flow and thermal regulation, including fast dynamics and contactless operation. However, magnetohydrodynamic systems at high Rayleigh number (Ra) present considerable challenges due to the intricate physics that render it into a stiff system, and the underlying mechanisms of complex thermal boundary flows in three-dimensional configurations remain poorly understood. In this study, the governing equations were non-dimensionalized using the buoyancy-driven scale and solved employing an established finite difference solver. The proposed scheme yields an error of only 0.55% compared to the reference solution. The effects of the Hartmann number (Ha), Ra, and thermal boundary conditions on natural convection within the cubic cavity were investigated. The interplay between variations in fluid velocity components and temperature distribution was elucidated. The results demonstrate that an increasing Ha induces a reversal in the direction of the horizontal velocity component along the cavity centerline, subsequently altering the temperature distribution. The magnetic field's suppression of flow and heat transfer is not uniform but exhibits localized enhancement in specific regions. At Ha=30 and Ra=106, the streamline center within the cavity evolves into four secondary centers. These findings underscore the complex influence of magnetic fields on flow and heat transfer in three-dimensional problems, with thermal boundary conditions playing a critical role.