effects of variations in magnetic reynolds number on magnetic field distribution in electrically conducting fluid under magnetohydrodynamic natural convection

This study numerically investigated the effects of variations in magnetic reynolds number on magnetic field distribution in an enclosure under natural convection heat transfer. the investigated geometry was a two-dimensional enclosure with a hot left wall, a cold right wall, and adiabatic top and bottom walls. the fluid was molten sodium with pr=0.01. natural convection heat transfer at a rayleigh number of 105 and magnetic reynolds numbers (rem) of 10–1, 10–3, and 10–5 was considered in the analysis. the governing equations adopted were continuum, momentum, energy, and magnetic induction equations, which were solved concurrently using the finite volume method. for the coupling of velocity and pressure, the revised semi-implicit method for pressure linked equations algorithm was employed. results showed that under a high magnetic reynolds number, the non-dimensional magnetic fields in the x and y directions were approximately constant because the diffusion of the magnetic potential was greater than the advection of such potential. as the magnetic reynolds number increased, however, the magnetic field in the enclosure reached a magnitude unequal to that of the applied magnetic field, exhibited inconstancy, and increased to a value that deviated from 1. thus, the rem=10–1 under a non-dimensional magnetic field increased from 0.09 to 6.6 in the x direction and from –1.164 to 4.05 in y the direction.