## 6 Analysis and Discussion of Results
It wasalso noted that the temperature distribution increased at lower value of \(\lambda=0.1\) but decreased at maximum value of \(\lambda=2.0\) in Figure 4c. Physically, it was expected because larger values of \(\lambda\) correspond to stronger buoyancy forces which lead to an increase in the acceleration of fluid flow. Due to conducting phenomena, magnetic effects are strongly observed exactly at the surface, but far from the surface, each value is zero. The good variations in each profile werenoted for each value of mix convection parameter \(\lambda\). Figure 5a-c examined the behavior of velocity \(f^{\prime}(\eta)\), temperature \(\theta(\eta)\), and magnetic field \(g^{\prime}(\eta)\) for different quantities of Prandtl number \(P_{r}=1.0,\ 4.0,\ 7.0,\ 10.0\) with some fixed parameters. It was shown that the velocity field increased at the highest value of \(P_{r}=10.0\) and decreased at \(P_{r}=1.0\) in Figure 5a. The magnetic field distribution increased at the lowest value of \(P_{r}=1.0\) but minimum value wasnoted at the highest value of \(P_{r}=10.0\) in Figure 5b. In Figure 5c, the temperature distribution wasincreased by decreasing the value of \(P_{r}=1.0\) but the temperature distribution wasdecreased by increasing the value of \(P_{r}=10.0\). This phenomenon is expected because an increase in Pr tends to increase density variation with temperature which enhances the buoyancy force.The thermal boundary layer thickness wasreduced due to increase in Pr. The prominent thermal slip with good variations are obtained in temperature graph at each value of \(P_{r}\). The good variations in each profile wereexamined for various values of Prandtl number \(P_{r}\). Figure 6a-c are demonstrated  
for velocity \(f^{\prime}(\eta)\), temperature \(\theta(\eta)\), and magnetic field \(g^{\prime}(\eta)\) for different quantities of magnetic Prandtl number \(P_{m}=0.1,\ 0.7,\ 1.5,\ 3.0\) with some fixed parameters along the surface of a vertical geometry. In Figure 6a, it wasdeduced that the fluid velocity along the surface wasincreased for the large value of \(P_{m}=3.0\) but the minimum value wasobtained at a lower value of \(P_{m}=1.0\) with good response. It was deduced that the magnetic graph increased at the large value of \(P_{m}=3.0\) but decreased at the small value of \(P_{m}=1.0\) in Figure 6b. In Figure 6c, it is depicted that the temperature distribution increased at the small value of \(P_{m}=1.0\) but the minimum value wasnoted at the large value of \(P_{m}=3.0\). It wasalso noted that temperature plots are in good form and excellent agreement for the given phenomenon. As the magnetic Prandtl number increased, viscosity of fluid increased and fluid became thicker more and consequently the boundary layer thickness decreased. Figure 7a-c are plotted for velocity, magnetic field, and fluid temperature against the various values of magnetic force parameter \(M=0.1,\ 5.0,\ 10.0,\ \text{and}\ 20.0\) with some constant parameters long the surface of the vertical geometry. In Figure 7a, it is deduced that the mixed convection effect in the velocity graph increased at the large value of \(M=20.0\) but minimum value wasobtained at the lower value of \(M=0.1\) by satisfying the given boundary conditions asymptotically. This result was expected because an increase in \(M\) means enhancement in the Lorentz forces which opposes the flow and velocity of the fluid decreases. In Figure 7b, it wasexamined that the magnetic field profile along the surface wasenhanced at the large value of \(M=20.0\) but the minimum value was obtained at small value of \(M=0.1\). Thishappens because the magnetic force parameter is the ratio of magnetic energy to kinetic energy, so with the increase in the magnetic force parameter \(P_{m}\), the magnetic energy is increased, while the kinetic energy is reduced. An excellent and favorable phenomenon is observed in magnetic field graph. In Figure 7c, it is deduced that the temperature profile decreased at the large value of \(M=20.0\) but increased at the small value of \(M=0.1\).