## 4 Results and Discussion
Thus, to preserve the momentum, the velocity of the fluid speeds up in the central half of the channel for increasing values of \(\alpha\). Again, velocity profile seems to be least affected by the nanoparticles shape. To check the flow behavior, when the suction or injection takes place at the walls along with embracing or parting motion, Figures 6-9 are plotted. The graphs are sketched for the growing absolute values of the permeation Reynolds number \(\mathcal{R}\). Figure 6 elucidates the case when the walls simultaneously experience the squeezing motion and suction. The absolute rise of \(\mathcal{R}\) produces a decline in velocity which has been detected in the region below the central line of the channel. The permeability parameter \(\mathcal{A}=\overline{\mathcal{V}}_{l}/\overline{\mathcal{V}}_{u}\) might be a reason behind this behaviour. Thus, the value \(\mathcal{A}=-0.1\) implies that the suction dominates in the region above the central line of the channel and as a result a speedy flow has been perceived in this region. Figure 7 has been decorated for the case when the dilation along with suction takes place at the same time. An almost similar velocity behaviour has been detected with a clear deviation. From Figures 8 and 9, one can clearly notice a reverse behaviour in the velocity as compared to Figures 6 and 7, when the phenomena of injection simultaneously combined with dilation and contraction. In all the above-mentioned cases, the velocity profiles remain unchanged for different shapes of Cu nanocomposites. Our next goal is to investigate the temperature behaviors under the influence of various involved parameters. Over here, we only consider the cases when the injection combined with embracing or parting motion, just to maintain the length of the article. Since, Al\({}_{2}\)O\({}_{3}\) has been considered as a nanofluid in which Cu nanocomposites have been latterly dispersed, therefore, the proportion of Al\({}_{2}\)O\({}_{3}\) nanoparticles within the base fluid (water) remains fixed (i.e., \(\Phi_{1}=0.1\)). Figures 10 and 11 helps to visualize the impact of permeability parameter \(\mathcal{A}\) simultaneously coupled with the cases of injection/dilation and injection/squeezing on the temperature profile. An increment in temperature has been recorded with the increasing absolute \(\mathcal{A}\). Since the temperature of the wall at the top is less than the bottom one, therefore a minimum temperature was observed in the region close to the upper wall. The fluid injected from the lower side of the channel bears a high thermal energy, therefore it significantly raises the temperature of the fluid in the region close to the bottom wall. As the fluid moves onward, it gradually experiencing a loss in energy and hence leaves the region adjacent to the upper wall with the minimum temperature. This phenomenon is more prominently observed in Figure 11, when injection is accompanied by dilation. In first case, platelet shaped nanocomposites possess higher temperature values, while, in the second case, the platelet shaped nanostructures prominently found in the region away from the bottom wall. Figure 12 has been painted with the nanoparticle volume fraction \(\Phi_{2}\) as a varying parameter to discuss the similar case as in Figure 10. A definite rise in temperature has been recorded in the lower half of the channel. The temperature's pattern seems to be dominant for the platelet shaped nanoparticles as compared to the cylindrical or brick shaped nanoparticles. Figure 13 deals with the case when the injection has been considered along with dilation. The readers can clearly observe a drop in the temperature in the earlier (lower) half of the channel while a rise has been perceived in the upper half of the channel. Moreover, the platelet shaped nanocomposites shows its dominancy in the upper region of the channel. To check the impacts of various embedded parameters on the local Nusselt number, Figures 14-19 are plotted. The horizontal axis has been decorated with the numerous values of \(\Phi_{2}\).