## 3 Numerical Approach: SHAM
\[A_{23}=DfPrD^{2},\ \ A_{31}=c_{1}+c_{3}D,\ \ A_{32}=ScSrD^{2},\ \ A_{33}=D^{2}+c_{2}D+c_{4}\]5 Effect of magnetic parameter M on (**a**) velocity, (**b**) temperature, and (**c**) concentration profiles. Figure 5 represents the contribution of the viscous/energy term (i.e., Eckert) on temperature and velocity, as well as concentration distributions. The viscous/energy dissipation represents the relationship existing between the kinetic energy of fluid movement and the enthalpy. It is obvious from Figure 5a,b that as the Eckert number increases, elevation in the velocity and temperature of the fluid is observed. \[A_{23}=DfPrD^{2},\ \ A_{31}=c_{1}+c_{3}D,\ \ A_{32}=ScSrD^{2},\ \ A_{33}=D^{2}+c_{2}D+c_{4}\]6 Effect of Prandtl number Pr on (**a**) velocity, (**b**) temperature, and (**c**) concentration profiles. Figure 6 exhibits the velocity, concentration, and temperature plots for distinct numbers of Schmidt (Sc). Sc defined the quotient of momentum over mass diffusivity. Thus, in Figure 6c, a decrease in the concentration distribution is observed when Sc is increased. In fact, it shows that larger values of Sc are equivalent to very small mass diffusivity. In Figure 6a, a degeneration in the fluid velocity is noted when Sc is increased. \[A_{23}=DfPrD^{2},\ \ A_{31}=c_{1}+c_{3}D,\ \ A_{32}=ScSrD^{2},\ \ A_{33}=D^{2}+c_{2}D+c_{4}\]7 Effect of Eckert number E on (**a**) velocity, (**b**) temperature, and (**c**) concentration profiles. The influence of suction velocity (Sw) is explored in \[A_{23}=DfPrD^{2},\ \ A_{31}=c_{1}+c_{3}D,\ \ A_{32}=ScSrD^{2},\ \ A_{33}=D^{2}+c_{2}D+c_{4}\]8 It is noticeable that acceleration in the suction velocity causes an elevation in the velocity, as well as temperature at the plate, but decreases when it is further from the plate as shown in Figure 7a,b. Moreover, from Figure 7c, an elevation in the concentration can be observed when the suction velocity is higher. \[A_{23}=DfPrD^{2},\ \ A_{31}=c_{1}+c_{3}D,\ \ A_{32}=ScSrD^{2},\ \ A_{33}=D^{2}+c_{2}D+c_{4}\]9 Effect of Schmidt number Sc on (**a**) velocity, (**b**) temperature, and (**c**) concentration profiles. The contribution of Dufour and Soret is explained separately for thorough investigations. We plotted the contribution of Dufour on the velocity, concentration, and temperature graphs in \[F_{L}=[f_{l}(\xi_{0},\ldots),f_{l}(\xi_{N}),\theta_{l}(\xi_{0},\ldots),\theta_ {l}(\xi_{N}),\theta_{l}(\xi_{0}),\ldots,\phi_{l}(\xi_{N})]^{T}\]0 It is noticed that the Dufour or diffusion thermal parameter alters the temperature. From Figure 8a, as the Dufour parameter is intensified, the fluid velocity increases, whereas Figure 8b shows that a higher value of the Dufour term produces an acceleration in the fluid temperature. In the same vein, the effect of Dufour on the fluid concentration is very minimal, as shown in Figure 8c. \[F_{L}=[f_{l}(\xi_{0},\ldots),f_{l}(\xi_{N}),\theta_{l}(\xi_{0},\ldots),\theta_ {l}(\xi_{N}),\theta_{l}(\xi_{0}),\ldots,\phi_{l}(\xi_{N})]^{T}\]1 Effect of suction velocity Sw on (**a**) velocity, (**b**) temperature, and (**c**) concentration profiles. Figure 9 represents the consideration of a distinct Soret number in the concentration, velocity, and temperature plots. Figure 9c shows that an increment in the Soret term produces an acceleration in the concentration plot, as expected. In Figure 9a, an increase in the velocity graph is detected with a higher value of the Soret term. We observed that the contribution of the Soret term (Sr) and Dufour parameter (Df) on the temperature and concentration plot is opposite. \[F_{L}=[f_{l}(\xi_{0},\ldots),f_{l}(\xi_{N}),\theta_{l}(\xi_{0},\ldots),\theta_ {l}(\xi_{N}),\theta_{l}(\xi_{0}),\ldots,\phi_{l}(\xi_{N})]^{T}\]2 Effect of Dufour parameter Df on (**a**) velocity, (**b**) temperature, and (**c**) concentration profiles.