## 4 Results and Discussion
In Figures 6 and 11, the graphs for the velocity under slip conditions and the corresponding velocity profile under no-slip conditions are demonstrated to analyze the relaxation parameter \(\lambda_{1}\). Viscous forces become weaker as the values of \(\lambda_{1}\) increase. Thus, it can be seen from the graphs that for both cases, the velocity profile accelerates in function of the large values of \(\lambda_{1}\). In Figures 7 and 12, the influence of the retardation parameter \(\lambda_{2}\) on the velocity field under slip conditions and in relation to the velocity profile under no-slip conditions are represented. The retardation parameter and velocity share are inversely related. It can be easily seen that both the velocity under slip conditions as well as the velocity under no-slip conditions decelerate in function of the increase in the values of \(\lambda_{2}\). From all graphs, it can be noted that similar curve trends are observed for fluid flow under slip conditions and under no-slip conditions. Furthermore, it was analyzed that for both functions \(f(t)=e^{\mu t}\) and \(f(t)=sint\), the velocity field presents the same curve pattern for all involved system parameters. Figure 2: Temperature profile using different \(Pr\) values, when \(t=0.9\) and \(t=1.5\). Figure 4: Velocity field under slip conditions as well as the velocity field under no-slip conditions for different \(Gr\) values when \(f(t)=e^{at}\), \(a=0.25\), \(t=1.5\), \(Pr=0.71\), \(\lambda_{1}=0.6\), \(\lambda_{2}=0.2\), \(M=2\). Figure 5: Velocity field under slip conditions as well as the velocity field under no-slip conditions for different \(M\) values when \(f(t)=e^{at}\), \(a=0.25\), \(t=1.5\), \(Gr=3.5\), \(\lambda_{1}=0.6\), \(\lambda_{2}=0.2\), \(Pr=0.71\). Figure 3: Velocity field under slip conditions as well as the velocity field under no-slip conditions for different \(Pr\) values when \(f(t)=e^{at}\), \(a=0.25\), \(t=1.5\), \(Gr=3.5\), \(\lambda_{1}=0.6\), \(\lambda_{2}=0.2\), \(M=2\). Figure 8: Velocity field under slip conditions as well as the velocity field under no-slip conditions for different \(Pr\) values when \(f(t)=sint\), \(t=1.5\), \(Gr=3.5\), \(\lambda_{1}=0.6\), \(\lambda_{2}=0.2\), \(M=2\). Figure 6: Velocity field under slip conditions as well as the velocity field under no-slip conditions for different \(\lambda_{1}\) values when \(f(t)=e^{at}\), \(a=0.25\), \(t=1.5\), \(Gr=3.5\), \(Pr=0.71\), \(\lambda_{2}=0.2\), \(M=2\). Figure 7: Velocity field under slip conditions as well as the velocity field under no-slip conditions for different \(\lambda_{2}\) values when \(f(t)=e^{at}\), \(a=0.25\), \(t=1.5\), \(Gr=3.5\), \(\lambda_{1}=0.6\), \(Pr=0.71\), \(M=2\). Figure 11: Velocity field under slip conditions as well as the velocity field under no-slip conditions for different \(\lambda_{1}\) values when \(f(t)=sint\), \(t=1.5\), \(Gr=3.5\), \(Pr=0.71\), \(\lambda_{2}=0.2\), \(M=2\). Figure 10: Velocity field under slip conditions as well as the velocity field under no-slip conditions for different \(M\) values when \(f(t)=sint\), \(t=1.5\), \(Gr=3.5\), \(\lambda_{1}=0.6\), \(\lambda_{2}=0.2\), \(Pr=0.71\). Figure 9: Velocity field under slip conditions as well as the velocity field under no-slip conditions for different \(Gr\) values when \(f(t)=sint\), \(t=1.5\), \(Pr=0.71\), \(\lambda_{1}=0.6\), \(\lambda_{2}=0.2\), \(M=2\).