Effects of variations in magnetic Reynolds number on magnetic field distribution in electrically conducting fluid under magnetohydrodynamic natural convection

In this study the effect of magnetic Reynolds number variation on magnetic distribution of natural convection heat transfer in an enclosure is numerically investigated. The geometry is a two dimensional enclosure which the left wall is hot, the right wall is cold and the top and bottom walls are adiabatic. Fluid is molten sodium with Pr=0.01 and natural convection heat transfer for Rayleigh number, Ra=105 , and magnetic Reynolds numbers 10-1, 10-3 and 10-5 are considered and the governing equations including continuum, momentum, energy and magnetic induction are solved together concurrent. The numerical method finite volume and simpler algorithm for coupling the velocity and pressure is used. The results show for high magnetic Reynolds number the non-dimensional magnetic field in X and Y directions approximately are constant because diffusion of magnetic Reynolds number is more than advection but as magnetic Reynolds number increases the magnetic field in enclosure is not equal to applied magnetic field and is not constant and deviation from one is increased so that for Rem=10-1 the non-dimensional magnetic field in X direction from 0.09 to 6.6 and in Y direction from -1.164 to 4.05 changes.