Numerical study of MHD natural convection of liquid metal with wall effects

Three-dimensional natural convection of liquid metal under a uniform magnetic field in a cubic enclosure is numerically simulated. The opposite sides of the cubic enclosure are isothermal, and the other four walls are adiabatic. The temperature gradient is perpendicular to the gravity vector. Three different magnetic field directions are applied in the computing model, respectively; namely, parallel to the temperature gradient, parallel to the gravity vector, and mutually perpendicular to them. Different wall electrical conductivities are also adopted in the simulation. Based on the Bousssinesq assumption, the numerical simulation of natural convection with Rayleigh number of 105, 25,000, and 1000, Prandtl number (physical property of Pb-17Li under 573 K) of 0.0321, and Hartmann number of 100, 50, and 10 are performed using a projection method to simulate the incompressible liquid metal flow and a consistent and conservative scheme to calculate the electromagnetic force at a nonuniform rectangular collocated grid. The influences of magnetic field directions and wall electrical conductivities on MHD flows are also studied.