## 4 Results and Discussion
### Comparison between the Micropolar Nanofluid and Nanofluid Models  
Comparison between micropolar and non-micropolar nanofluid models are made in terms of \(\overline{\text{Nu}}\), \(\overline{\text{Sh}}\) and U\({}_{3\text{max}}\) as per the buoyancy ratio illustrated in Figure 5. It can be observed for a micropolar nanofluid model that all of \(\overline{\text{Nu}}\), \(\overline{\text{Sh}}\) and U\({}_{3\text{max}}\) are smaller than that of a pure nanofluid model regardless the value of N considered. This gap is minimized adjacent to the transition value of N = \(-1\) and the disparity is more significant for the thermal buoyancy-dominated zone.  
Variation of \(\overline{\text{Nu}}\) and \(\overline{\text{Sh}}\) against the Rayleigh is shown in Figure 6. Both micropolar and non-micropolar nanofluid models are considered with N = 0.5 in the thermal buoyancy-dominated regime and N = 2 in the solutal buoyancy-dominated regime. Both \(\overline{\text{Nu}}\) and \(\overline{\text{Sh}}\) are smaller than when considering the micropolar theory regardless of the value of Ra for both values of buoyancy ratio. However, the gap is more prominent when the Rayleigh numbers are enhanced. The current observations are in good agreement with the results of [PERSON] and [PERSON] [PERSON] and [PERSON] (2018) for two-dimensional flow by considering only the thermal gradient.  
Figure 5: Variation of \(\overline{\text{Nu}}\), \(\overline{\text{Sh}}\) and U\({}_{3\text{max}}\) with buoyancy ratio for both micropolar and non-micropolar nanofluid models for Ra = \(10^{5}\), \(\varphi\) = 0.04, Pr = 6.2 and Le = 1.  
Figure 7 elucidates the variations of the horizontal and vertical velocity components at the Z = 0.5 plane according to the Rayleigh numbers for N = \(-\)0.5 and N = \(-\)2. Regardless of the modelconsidered, it is noticed that with increase in Rayleigh numbers, the flow regime is intensified and the magnitude of each component of velocity is increased. However, their magnitudes are higher in the case of ordinary nanofluid than in that of micropolar nanofluid. This difference becomes more significant for Ra up to \(10^{4}\) and implies that the insertion of the vortex viscosity parameter decelerates the principal flow strength for both regimes.  
Figure 8 shows the maximum of the transverse velocity for various Rayleigh number applying the micropolar and non-micropolar nanofluid models in the absence microrotation for N = \(-\)0.5 and N = \(-\)2. For both cases, U\({}_{3\max}\) is smaller without considering the micropolar theory and the gap is more noticeable when Ra outdoes \(10^{4}\). Hence, the consideration of micropolar material parameter weakens the three-dimensional character of the flow.  
Figure 6: Variation of \(\overline{\mathrm{Nu}}\) and \(\overline{\mathrm{Sh}}\) with Rayleigh number for micropolar and non-micropolar nanofluid models for N = \(-\)0.5 and N = \(-\)2.  
Figure 8: Variations of U\({}_{3\max}\) versus Rayleigh number for both micropolar and non-micropolar nanofluid models for N = \(-\)0.5 and N = \(-\)2.  
Figure 7: Variations of the horizontal and vertical velocity components at Z = 0.5 plan according to the Rayleigh number for both micropolar and non-micropolar nanofluid models for \(\varphi\) = 4%, for N = \(-\)0.5 (Top) and N = \(-\)2 (Bottom).