## 4 Results and Discussion
### Effect of Magnetic Field  
To study the impacts of uniform magnetic field, comparisons of isotherms, isoconcentrations, and projections of the flow lines in the mid (X-Y) plane are undertaken for thermally dominated (N = \(-\)0.5) and compositionally dominated (N = \(-\)2) regimes. The results for the average Nusselt and Sherwood numbers are also presented and analyzed. Figure 9 shows projections of flow lines, isotherms and isoconcentrations in the main plan Z = 0.5 for various combinations of Ra and Ha with \(\varphi\) = 4% for N = \(-\)0.5. In this case, the flow is mainly initiated by thermal volume forces so that the main flow direction is clockwise in the X-Y plane. In absence of magnetic field (Ha=0), when the Rayleigh number enhances, the convection mechanism is more noticeable. The rotation cells become larger near the isothermal and the insulated walls indicating the strength of motion of the fluid. The projections of the flow lines on the mid X-Y plane are not closed but have a spiral form. Normally, the flow structure shows with two inner vortexes at high Rayleigh number (Ra= \(10^{5}\)) but in the presence of magnetic field these two inner vortexes are initiated with lower Ra=\(10^{4}\) and are moving towards the isothermal walls as the Rayleigh number increases. When Ha = 0, an increase in Ra changes the direction of isotherms from almost vertical to the horizontal in the core and are stacked near the active walls. An isoconcentrations central zone is created and extended to the upper and lower regions of the enclosure as Ra increases. Once Ha = 40, both the thermal and solutal gradients diminish near the active walls. Furthermore, the temperature and concentration contours become inclined and parallel to each other within the core of the cavity as Ra increases and these changes in direction is an indication of weakness in convection flow due to the magnetic field. Figure 10 displays similar results as shown in Figure 9 except for N = \(-\)2. For this specific value of N, the main flow direction is reversed due to the enhancement in solutal effect. In the presence of magnetic field, the flow involves a counter-clockwise rotating main cell with two inner vortexes slightly titled to the hot wall and move towards the isothermal walls as the Rayleigh number increases. When the influence of magnetic field is negligible (Ha = 0), both isotherms and isoconcentrations became inclined and parallel to each other within the cavity center with the increase in Rayleigh number. On the contrary, as the Rayleigh number remains constant both isotherms and isoconcentrations seem to be insensitive to the magnetic field. To assess the magnetic field effect on the three-dimensional flow, the variation of the maximum of the transverse velocity versus the buoyancy ratio for two cases, Ha = 0 and Ha = 40 are illustrated in Figure 11. The presence of magnetic field causes an enhancement in the transverse velocity for both regimes regardless of the buoyancy ratio. However, its effect is more obvious for thermally-dominated zone than for the solutal-dominated one. The maximum of the transverse velocity has a minimum for N \(\approx-\)1. Figure 9: Projections of flow lines, isotherms and isoconcentrations in the main plane \(Z=0.5\) for various values Rayleigh number and Hartmann number with \(\varphi=4\%\), K = 1, N = \(-0.5\), Pr = 6.2 and Le = 1. Figure 10: Projections of flow lines, isotherms and isoconcentrations in the main plane \(Z=0.5\) for various values of Rayleigh number and Hartmann number with \(\varphi=4\%\), K = 1, N = \(-2\), Pr = 6.2 and Le = 1.