SST k-ω simulation of mixed convection of magnetohydrodynamic flow in a vertical duct with conducting walls

Liquid metal magnetohydrodynamic (MHD) flow has a wide range of applications in controlled nuclear fusion, metallurgy, semiconductor, and so on. The liquid metal in ducts or pipes subjected to a strong magnetic field generates Lorentz forces and causes MHD effects. The strong non-uniform thermal gradient generated by nuclear neutron heat in liquid metal blankets causes buoyancy effects. MHD mixed convection flow is a multi-physics and multi-scale coupling problem involving fluid, solid, temperature, and electromagnetic fields, considering the Lorentz force and buoyancy. In this study, mixed convection of magnetohydrodynamic flow in a vertical duct with conducting walls subjected to a non-uniform magnetic field and heat source has been numerically studied using a shear stress transport (SST) Reynolds-averaged Navier-Stokes (RANS) method developed in OpenFOAM. Effects of the Hartmann number (Ha), Reynolds number (Re), and Grashof number (Gr) on MHD mixed convection have been investigated. The results show that an increase in Ha suppresses the generation of reverse flow zones in the duct, stabilizes the flow, and improves the convective heat transfer efficiency at the hot wall. The Nusselt number (Nu) increases with the increase of the Reynolds number when it number increases to a certain extent. The influence of Gr on the velocity field is relatively small in the simulation range. Buoyancy can suppress convective heat transfer at the hot wall. Finally, there is a specific functional relationship between Nu and Gr/Ha2Re2. These findings provide valuable insights into the behavior of liquid metal flow under MHD mixed convection and have important implications for the design and optimization of liquid metal blankets in thermonuclear fusion reactors.