## 4 Results and Discussion
It is also seen that increasing the value of the slip results in decreasing the thickness of the solutal profile boundary. Figure 6: Effects of \(kp\), \(f_{w}\), and \(S_{f}\) on \(f^{\prime}\). Figure 14 indicates the impact of \(N_{t}\) on the nano-particle volume fraction profile without the existence of nano-particles concentration slip and with the existence of nano-particles concentration slip. It is clear from the figure that in both the steady and unsteady cases, increasing values of \(N_{t}\) cause a decline in the nano-particle volume fraction profile. The impacts of \(\sigma\) and \(S_{\gamma}\) over the nano-particle volume fraction profile have been illustrated in Figure 14. It is noticed that the nano-particle volume fraction profile decreases in increments in the values of \(\sigma\) and \(S_{\gamma}\). Figures 15 and 16 show the impact of Lewis number \(Le\), unsteadiness parameter \(\sigma\), and suction parameter \(f_{w}\) on the nano-particle volume fraction profile, and interpretations about the nano-particle volume fraction profile are made. It is seen that increasing values of \(Le\) and \(f_{w}\) in the boundary layer of nano-particles causes the volume fraction profile to decline. In addition, it is clear from the figures that the nano-particle volume fraction profile decreases both with and without the existence of nano-particles concentration slip. Figure 17 shows the impact of \(M\), \(\sigma\), and \(S_{f}\) on the skin friction co-efficient and also shows that the skin friction co-efficient decreases with the increase of slip parameter, magnetic and unsteadiness parameter. In Figure 18, the skin friction coefficient increases with the increment in the thermal buoyancy, suction parameters, and solut buoyancy. Figure 19 represents the increment in the value of Nusselt number with increasing values of magnetic, radiation and thermal slip parameters. As perceive in Figure 20 that when the values of solut buoyancy and suction intensity increases with the existence and the non-existence absence of thermal buoyancy. Figure 21 demonstrates that the impact of \(Sc\), \(Sr\), and \(S_{\phi}\) on the reduced Sherwood number. Also from the Figure 22, it clear that the reduced Sherwood number decreases with increment in the values of the unsteadiness parameter \(\sigma\), magnetic parameter \(M\) and the suction parameters \(f_{w}\). Figure 11: Effects of \(Nb\), \(f_{w}\), and \(S_{\theta}\) on \(\theta\). Figure 5.0 Effects of \(M\), \(Sc\), and \(S_{\phi}\) on \(\phi\). Figure 5.1 Effects of \(Nt\), \(\sigma\), and \(S_{\xi}\) on \(\xi\). Figure 5.2 Effects of \(M\), \(\sigma\), and \(S_{f}\) on the skin friction coefficient. Figure 5.3 Effects of \(f_{w}\), \(\lambda_{1}\), and \(\lambda_{2}\) on the skin friction coefficient. Figure 5.4 Effects of \(Sc\), \(Sr\), and \(S_{\phi}\) on the reduced Sherwood number. Figure 5.5 Effects of \(M\), \(R\), and \(S_{\phi}\) on the reduced nusselt number. In Table 7 we analyze the variation of physical parameters \(M\), \(\lambda_{1},\lambda_{2},\lambda_{3},\sigma,P_{r},L_{e}\) on skin friction co-efficient \(-f^{\prime\prime}(0)\), Nusselt number \(-\theta^{\prime}(0)\), and Sherwood number \(-\xi^{\prime}(0)\). The following results are concluded from Figure 5.6  
(i) The skin-friction coefficient is increasing while reducing the local Nusselt and Sherwood numbers through improvement in the Magnetic parameter; (ii) The increment in thermal buoyancy parameters \(\lambda_{1},\lambda_{2},\lambda_{3}\) causes the skin-friction coefficient to decrease while increasing the local Nusselt number and Sherwood number; (iii) With the increasing unsteadiness parameter \(\sigma\), the skin-friction coefficient, local Nusselt, and Sherwood numbers are also increasing; (iv) The skin-friction coefficient is increasing with the increment in Prandtl number and the local Nusselt number and Sherwood number also increase; (v) The skin-friction coefficient is increasing with the increasing Lewis number and also increment in the local Nusselt number and Sherwood number.