## 4 Results and Discussion
### Physical Parameters  
This section delves into the investigation of various physical parameters concerning temperature and velocity distributions within a system comprising a rotating disk and cone, a setup critical to the overall inquiry.  
Figure 5 examines in its upper left part the influence of the magnetic number (\(M\)) on the axial velocity profile (\(F(\zeta)\)). A rise in \(M\) leads to a decrease in fluid velocity for both copper (\(Cu\)) and aluminum oxide (\(Al_{2}O_{3}\)) hybrid nanoliquids due to the Lorentz force impeding fluid velocity. In its upper right and lower left parts, Figure 5 depicts the effect of volume fraction factors, specifically \(\phi_{Al_{2}O_{3}}\) and \(\phi_{Cu}\), on the axial velocity profile. An increase in volume fraction parameters enhances the boundary layer thickness, resulting in a decline in the velocity profile. Finally, in its lower right part, the figure explores the impact of the magnetic parameter (\(M\)) on the radial velocity profile, \(G(\zeta)\), showing similar behavior to the axial velocity discussed earlier.  
Figure 4: (**a,c**): Plots of \(Re_{\omega}\) and \(Re_{\Omega}\) for \(G(\zeta)\). (**b,d**): Plots for solving \(M\) for \(\theta(\zeta)\).  
Figure 5: (**Up-left**): Impact of \(M\) on \(F(\zeta)\). (**Up-right**) Impact of \(\phi_{Al_{2}O_{3}}\) on \(F(\zeta)\). (**Down-left**): Impact of \(\phi_{Cu}\) on \(F(\zeta)\). (**Down-right**): Influence of \(M\) on \(G(\zeta)\).  
Figure 6 investigates first the influence of volume fraction factors of iron oxide on the radial velocity profile, with changes in \(\phi_{Al_{2}O_{3}}\) exhibiting analogous behavior to the axial velocity. Then, the figure examines the influence of the copper volume fraction parameter (\(\phi_{Cu}\)) on the radial velocity profile, \(G(\zeta)\), indicating similar variations as observed in the axial velocity. A brief discussion of four instances of disk and cone angular motion is later presented in Figure 6. Case (1) describes the scenario where the cone is spinning and the disk is at rest, leading to the highest flow intensity near the cone's vicinity, influencing the radial profile, \(G(\zeta)\), positively through the cone's angular velocity variation, \(Re_{\Omega}\). Case (2) shows the opposite trend, with the disk moving while the cone is stationary, resulting in resistance at the cone wall due to the no-slip condition. Scenario (3) demonstrates the dominance of the flow field over \(Re_{\Omega}\) and \(Re_{\omega}\), respectively, as there is minimal resistance to both cone and disk rotating in the same direction. In contrast, the figure finally illustrates the reduction in fluid velocity due to the counter-rotation of the disk and cone, leading to the highest resistance, as demonstrated by Case (4).  
Figure 7 first describes the type of temperature distribution, \(\theta(\zeta)\), vs magnetic strength, \(M\), where the Lorentz force impedes fluid motion, gradually raising the fluid temperature, \(\theta(\zeta)\). The addition of \(\phi_{Al_{2}O_{3}}\) and \(\phi_{Cu}\) nanoparticles to the carrier fluid increases its viscosity and heat absorption capacity, as evidenced later in Figure 7. The figure then showcases the dominance of the Prandtl number, Pr, over temperature distribution, where fluids with high Prandtl numbers exhibit lower thermal diffusivity, and vice versa.  
Figure 6: (**Up-left**): Influence of \(M\) on \(G(\zeta)\). (**Up-right**): Influence of \(\phi_{Al_{2}O_{3}}\) on \(G(\zeta)\). (**Middle-left**): Case (1) influence over \(G(\zeta)\). (**Middle-right**): Case (2) influence over \(G(\zeta)\). (**Down-left**): Case (3) influence on \(G(\zeta)\). (**Down-right**): Case (3) influence on \(G(\zeta)\).