## 6 Analysis and Discussion of Results
This given mechanism is performed with good agreement. Figure 3: (**a–c**) The geometric profiles of \(f^{\prime}(\eta),\ \ g^{\prime}(\eta)\), and \(\theta(\eta)\) against \(St\). Figure 4: (**a–c**) The geometric profiles of \(f^{\prime}(\eta)\), \(g^{\prime}(\eta)\), and \(\theta(\eta)\) against \(\lambda\). From Table 1, it is concluded that the skin friction \(f^{\prime\prime}(0)\) increased at \(m=0.5\) but the minimum skin friction wasobtained at small \(m=0.0\) in the presence of buoyancy forces. It should be noted that \(m=0\) corresponds to the case of a small temperature difference between the surface and fluid, i.e., the buoyancy approximation becomes valid for this particular case, whereas for a high temperature difference, a considerable enhancement in the numerical values of the skin friction and heat transfer rate wasinspected and can be clearly seen in Table 1. It wasdeduced that the magnetic intensity \(-g^{\prime\prime}(0)\) wasmaximum at larger \(m=0.5\) but the smaller quantity of magnetic intensity wasexamined at smaller \(m=0.0\) in the presence of strong magnetic field. 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. It was also expected because as magnetic Prandtl number increases, the viscosity of fluid increases and fluid becomes thicker and consequently the boundary layer thickness decreases. It is also depicted that the heat transfer wasincreased at maximum \(m=0.5\) but the lower quantity of heat transfer is depicted at minimum \(m=0.0\) in the presence of magnetic force \(M\). With the increase in value of \(M\), the magnetic field became stronger along the surface which is a clear indication that the Lorentz force is more effective in this case. In Table 2, the influence of stratification \(St\) number with various values along a vertical plate is shown to check the behavior of physical properties of the rate of skin friction, the rate of magnetic intensity, and the rate of heat transfer. From Table 2, it is computed that the skin friction is maximum at smaller value of \(St=0.1\) but the minimum quantity of skin friction is depicted at a large value of \(St=0.4\) in the presence of Prandtl number \(P_{r}=7.0\). Physically, it is possible because thermal conductivity decreases as Pr increases, which has a lower magnitude of frictional forces between the viscous layers. It is depicted that the magnetic intensity is decreased at larger \(St=0.4\) but the maximum value of magnetic intensity is explored at small \(St=0.1\) in the presence of \(\lambda=6.5\). However, due to the strong buoyancy number \(\lambda\) which acts like a pressure gradient and dominated over the resistance, skin friction is increased and slight changes in heatmap magnetic intensitynet noted. It is also mentioned that the heat transfer \(-\theta^{\prime}(0)\) wasmaximum at the lower value of \(St=0.1\) but the minimum quantity of heat transfer wasnoticed at larger \(St=0.4\) in the presence of magnetic Prandtl number \(P_{m}=8.3\). The reason behind this is that increasing the value of \(P_{m}\) is equivalent to decreasing magnetic diffusivity and consequently the strength of magnetic field becomes loose. Figure 7: (**a–c**) The geometric profiles of \(f^{\prime}(\eta)\), \(g^{\prime}(\eta)\), and \(\theta(\eta)\) against \(M\).