## 4 Results and Discussion  
The prime focus of this section is to graphically demystify the obtained results. The salient features of the flow and heat transfer of a Cu-Al\({}_{2}\)O\({}_{3}\)/H\({}_{2}\)O hybrid nanofluid have been examined in a rectangular channel whose walls are permeable and have a capability of dilating or squeezing. Moreover, the investigations have been carried out to see the influence of various embedded parameters such as solid volume fraction (\(0.005\leq\Phi_{2}\leq 0.06\)), deformation parameter \(\alpha\), permeation Reynold number \(\mathcal{R}\) and permeability parameter \(\mathcal{A}\) on the velocity as well as temperature profiles. Table 1 focused on the thermo-physical properties of base fluid and nanoparticles. The model employed for the effective thermal conductivity of Cu-Al\({}_{2}\)O\({}_{3}\)/H\({}_{2}\)O hybrid nanofluid has an embedded parameter '\(m_{l}=3/\psi^{\prime}\) (where \(\psi\) denotes the sphericity of different nanocomposites), which varies for  
different shapes of nanocomposites. The numerical values related to the shape factor for different non-spherical tiny sized particles can be found in Table 2. Platelet-, cylinder- and brick- shaped nanocomposites have been under consideration. Furthermore, it is important to mention that the spherical shaped Al\({}_{2}\)O\({}_{3}\) nanoparticles have been dispersed in the base fluid, therefore \(=3\). Since the hybrid nanofluid under consideration is water-based, therefore the numerical value for Prandtl number has been restricted to 6.135. To visualize the velocity behavior, Figures 2-9 are designed. Each figure holds an inset picture which give us the magnified view of the parameter's behavior within the regions \(-0.45\leq\zeta\leq-0.47\) (leftward) and \(0.45\leq\zeta\leq 0.47\) (rightward) unless specified otherwise. Figures 2 and 3 simultaneously depict the cases when the velocity behavior is influenced by channel's contraction along with suction and injection. In the first case, one can clearly observe a speedy flow nearby the wall for growing absolute values of \(\alpha\). The reason behind is the wall's contraction which suppresses the adjacent layers of fluid and force them to move forward. Suction also plays an important role to enhance the fluid's velocity nearby the wall. Instead, a retardation in the flow has been detected far away from the walls. Subsequently, Figure 3 deals with the contraction along with injection. Again, one can observe a clear enhancement in fluid's velocity close to the wall with the increased absolute values of \(\alpha\), which means that the contracted walls again play a key role to speed up the flow nearby the wall. Moreover, no considerable change has been detected in the velocity profile for various shapes of nanocomposites. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Nanocomposite Shapes** & **Aspect Ratio** & **Sphericity**\((\uppsi)\) & **Shape Factor (m)** \\ \hline
**Platelet** & 1:1/18 & 0.52 & 5.7 \\
**Cylinder** & 1:8 & 0.62 & 4.9 \\
**Brick** & 1:1:1 & 0.81 & 3.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Sphericity and shape factor of various nanocomposites [5; 9]. Figure 4: \(\mathcal{F}^{\prime}(\zeta)\) for numerous values of \(\alpha\); \(\mathcal{R}<0,\alpha>0\). Figure 8: \(\mathcal{F}^{\prime}(\zeta)\) for numerous values of \(\mathcal{R}\); \(\mathcal{R}>0,\alpha<0\). Figures 4 and 5 expose the consequences of velocity profile against the increasing \(\alpha\), i.e., the case of dilating channel coupled with suction and injection. It was observed form both the figures that depending onwhether the fluid has been injected or sucked through the walls, the channel's dilation creates a vacant space nearby the walls which is then filled by the inward motion of the adjacent fluid layers. Therefore, the flow has been decelerated in both the cases (injection/suction) which in turn causing a decline in the velocity near the wall.