## 5 Results and Discussion
Figure 3 display the effect of different slip parameters on the skin friction coefficient \(f^{\prime\prime}\left(0\right)\) and heat transfer coefficient \(-\theta^{\prime}(0)\) with stretching/shrinking parameter \(\varepsilon\) in a Copper water nanofluid. Based on the figures, dual solutions exist when \(\varepsilon_{c}\leq\varepsilon\), while no solution could be reported for \(\varepsilon<\varepsilon_{c}\). It can also be observed that as the slip effect becomes higher, the range of solutions is consequently expanded, also decreasing the skin friction coefficient \(f^{\prime\prime}\left(0\right)\) for the first solution, but increasing it for the second solution within the range \(\varepsilon<1\). The heat transfer coefficient \(-\theta^{\prime}(0)\) showed an uptrend for the first solution and downward one for the second, as the velocity slip \(\sigma\) increases. In addition, the skin friction coefficient for the shrinking surface was found higher than \(f^{\prime\prime}\left(0\right)\) for the stretching surface. It can be observed that the heat transfer coefficient \(-\theta^{\prime}(0)\) for the shrinking surface is slightly decreased compared to that of the stretching surface. Hence, the friction between the nanofluid and the surface is larger when the surface is shrunk compared to the stretched surface. Meanwhile, based on Figure 3b, the heat transfer rate at the surface was found to be faster for a stretching surface than a shrinking surface; thus, the cooling process becomes better when the surface is in stretched state. Figure 2: (**a**) Skin friction coefficient and (**b**) Local Nusselt number for different \(\varphi\) in Copper-water nanofluid with \(\varepsilon\) when \(s=2\), \(\sigma=0.1\) and \(A=0.1\). Variations of the skin friction coefficient \(f^{\sigma}\left(0\right)\) and heat transfer coefficient \(-\theta^{\prime}(0)\) due to the effect of unsteadiness of parameter \(A\) with stretching/shrinking surfaces, are shown in Figure 4. In the range of \(\varepsilon_{c}\leq\varepsilon\), dual solutions can be found, while no solution may be obtained when \(\varepsilon_{c}\leq\varepsilon\). According to these figures, the unsteadiness parameter \(A\) only expanded the range of solutions slightly compared to the effects of the nanoparticle volume fraction \(\varphi\) and the velocity slip parameter \(\sigma\). Increasing the unsteadiness parameter \(A\) increases the skin friction coefficient for the first solution, and decreases if for the second. In addition, as \(A\) increases, the heat transfer rate at the surface for the first solution is also increased, but the second solution shows the opposite behavior. The skin friction coefficient \(f^{\sigma}(0)\) was shown to decrease when the value of \(\varepsilon\) increases, which indicates that the skin friction over a shrinking surface is higher than that over a stretching surface. In the meantime, the heat transfer coefficient \(-\theta^{\prime}(0)\) increases slightly when \(\varepsilon\) increases, which shows that the heat transfer rate for the shrinking surface is higher than that of the stretching surface. Figure 3: (**a**) Skin friction coefficient and (**b**) Local Nusselt number for different \(\sigma\) with \(\varepsilon\) in Copper-water nanofluid when \(s=2\), \(\sigma=0.1\) and \(A=0.1\). Figure 5 is presented in order to show the effect of the \(\varepsilon\) parameter with the suction/injection parameter on the skin friction coefficient as \(f^{\alpha}\left(0\right)\), and the heat transfer coefficient \(-\theta^{\prime}(0)\) where the dual solutions are obtained for a permeable surface \(\left(s>0\text{ and }s<0\right)\) and an impermeable surface \(\left(s=0\right)\). Figure 5a shows the decreasing skin friction coefficient for the first and second solutions when the value of \(\varepsilon\) is increased. This indicates that the resulting skin friction coefficient for the shrinking case is higher than that of the skin friction coefficient, which is caused in the stretching case by either a permeable or an impermeable surface.