## 4 Results and Discussion
The decrement of velocity profile is caused due to the increment of resistive Lorentz force. It is also observed that velocity profile decreases with suction (\(f_{w}\)) and boundary layer thickness decreases when hydrodynamic slip is in fact. It is clear from the Figure 3, with the increasing values of material parameter \(K\), an increment is seen in velocity profile but velocity profile decreases with the increment in hydrodynamic slip \(S_{f}\). Physically, material constant \(K\) is the combination of the vortex and dynamic viscosity. The larger value of \(K\) means smaller dynamic viscosity \(\mu\) and hence the speed of flow becomes faster. The effect of permeability parameter \(k_{p}\) and hydrodynamic slip on velocity profile is shown in Figure 4. Decrement behavior of velocity with the rising values of \(k_{p}\) and \(S_{f}\) is noticed. It is also observed that the velocity profile decreases when \(f_{w}\) increases also boundary layer thickness decreases. The basic reason for this phenomenon is that in the porous medium the resistance becomes higher, due to this the momentum development for \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \(\mathbf{R}\) & \(\boldsymbol{Pr}\) & \(\boldsymbol{M}\) & **[PERSON] et al. [50]** & **[PERSON] [51]** & **[PERSON] et al. [52]** & **[PERSON] [53]** & **Our Results** \\ \hline
0 & 1 & 0 & 0.954783 & 0.9548 & 0.95478 & 0.9547 & 0.9546 \\
1 & 1 & 0 & 0.531730 & - & 0.53121 & 0.5312 & 0.5310 \\
0.5 & 2 & 0 & 1.073519 & 1.0735 & 1.07352 & 1.0734 & 1.0738 \\
1 & 1 & 1 & 0.450571 & 0.450571 & 0.450571 & - & 0.450571 \\
1 & 0 & 1 & - & 0.5312 & 0.5312 & 0.5312 & 0.5311 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of \(R\), \(Pr\) and \(M\). Figure 3: Influence of material and suction/injection parameter on velocity. Figure 2: Influence of magnetic and suction/injection parameter on velocity. the flow regime declines. In Figure 5, the effect of Rayleigh number \(Rb\) and \(f_{w}\) is discussed on the velocity profile. Due to this effect velocity profile shows a decrement under the action of hydrodynamic slip \(S_{f}\). Physically, the decrement occurs because buoyancy force produces resistance against the movement in the horizontal direction. From Figure 6, the effect of mixed convection parameter \(\lambda\) along with hydrodynamics slip \(S_{f}\) on angular velocity is observed. It is seen that angular velocity increases with the rising values of \(\lambda\) and \(S_{f}\). However, angular velocity profile decreases for the rising values of \(f_{w}\) (suction). Figure 7 describes the rise of material parameter \(K\) which causes a gradual increase to the angular velocity \(g(\eta)\). From these figures, it is cleared that the angular velocity is promoted along with the expanding values of \(K\) and \(f_{w}\). Because the increment in \(K\) means larger vortex viscosity and hence stronger micro-rotation. However, with the increment in the hydrodynamic slip \(S_{f}\), the profile of \(g(\eta)\) decreases. Opposite behavior of \(g(\eta)\) is shown in Figure 8, for unsteady parameter \(\delta\). It is because the larger layers after the stretch in the sheet show the overall motion of the fluid. The temperature profile is plotted in Figure 9 with the values of magnetic number \(M\) and thermal slip \(S_{\theta}\). The temperature \(\theta(\eta)\) is gradually increasing directly with the increment in the inputs of these parameters. In addition, it is observed that the thermal profile decreases with the increment in \(f_{w}\). Figure 10 shows clearly that the effect of Brownian motion parameter \(Nb\) along with thermal slip \(S_{\theta}\). It is observed that temperature rises with the rising values of \(Nb\). According to the concept of Brownian motion, nanoparticles are directly related to temperature. With the increment in temperature, an enhancement yields in the kinetic energy of these particles. Figure 4: Influence of permeability and suction/injection parameter on velocity. Figure 5: Influence of Rayleigh number and hydrodynamic slip on velocity.