Study on the mechanisms of flow and heat transfer in natural convection of liquid metal under a horizontal magnetic field

Direct numerical simulations have been conducted to explore the mechanisms underlying flow and heat transfer in the natural convection of liquid metal within a 1:1:0.5 cavity, subjected to a transverse magnetic field oriented perpendicular to the primary circulation plane. The key computational parameters include the Prandtl number (Pr=0.025), Rayleigh number (Ra<107), and Hartmann number (Ha). Notably, the magnetic field induces a transition in the liquid metal flow from three-dimensional to two-dimensional structures with the Lorentz force serving as the key driver of this behavior. This transition is characterized by the presence of an optimal magnetic field strength (Hao) at which both the Nusselt number (Nu) and Reynolds number (Re) initially increase and subsequently decrease. Theoretical analysis not only determines this critical value but also derives the scaling relationship between Re and Ha under a strong magnetic field, which shows excellent agreement with the numerical simulation results. To fully understand the underlying physical mechanisms of flow and heat transfer, the concepts of thermal plumes and shear force are introduced. The results confirm that the efficiency of heat transfer is governed more by the intensity of thermal plumes than by their spatial extent. Therefore, at moderate magnetic field strengths, it is observed that thermal plumes significantly enhance heat flux, corresponding to a peak in heat transfer efficiency. Variations in wall shear force highlight the transport capacity of thermal plumes, underscoring their essential role in the convective heat transfer process. Additionally, for liquid metals with low Prandtl numbers, the thermal boundary layer fully encapsulates the momentum boundary layer, and its thickness exhibits a negative correlation with heat transfer efficiency, which is consistent with a classical theory.