Analytical solutions for strong coupling MHD mixed convection with electric insulating or conducting walls

摘要: This work investigates the strong coupling effects between dynamics, electromagnetics, and heat transfer in magnetohydrodynamic mixed convection. A complete three-dimensional analytical solution and a modified quasi-two dimensional analytical solution are derived for both insulation walls and conductive walls issues. A multi parameter scaling law is established based on boundary layer approximation to quickly calculate the key pressure drop. The two types of analytical solutions presently proposed are in good agreement with previous approximate solution (Vetcha et al. 2013) and direct numerical simulation data (both reference (Abdou et al. 2020) and our own solver). These theories improves the understanding of the flow and heat transfer mechanism of liquid metals under the coupling of multiple physical fields, and are also expected to be beneficial for the design and development of new blanket for magnetic confinement fusion.