## 3 Problem Formulation
From these figures, it can be concluded that the proposed scheme is more accurate than the forward Euler scheme, because it produced the lowest absolute error. Figure 5 shows the impact of porosity parameter \(\lambda\) on the velocity profile. The velocity profile decreases as the porosity parameter increases because the fluid's viscosity rises. Figure 6 shows the influence of the inertia coefficient on the velocity profile. From Figure 6, it can be observed that the velocity profile decreases as the inertia coefficient increases, which can be considered a consequence of the elevated drag force that produces resistance in the flow as the values of the inertia coefficient rise. Figure 7 depicts the velocity profile according to variations in the coupling parameter. The velocity profile displays dual behavior. It grows slightly near the plate and decreases as the coupling parameter increases. This boosted velocity profile is a result of the enhanced viscosity of the fluid due the rising coupling parameter values. Therefore, the velocity of the flow escalates in that region. Figure 8 shows the impact of the coupling parameter on the angular velocity. The angular velocity displays dual behavior as the coupling parameter increases. The angular velocity escalates near the plate and then de-escalates as the coupling parameter rises. The effect of the microrotation parameter on the angular velocity is depicted in Figure 9, which also displays the dual behavior of the angular velocity as the values of the microrotation parameter increase. The escalation of the microrotation parameter leads to an increase in the microrotation constant and a decay in the kinematic viscosity of the fluid. Since the flow velocity is at its maximum near the plate, the angular velocity decreases, and the flow velocity decreases away from the plate. Due to the increasing values of the microrotation constant, the angular velocity escalates in the region near the edge of the boundary layer. The effect of the Biot number on the temperature profile is depicted in \[+\overline{h}^{2}\{c_{1}\Bigl{(}2\overline{f}_{1,i}\overline{f}_ {2,i}(1+F_{r})-\overline{f}_{1,i}\overline{f}_{2,i}-\overline{f}_{i}\overline {f}_{2,i}^{2}-\overline{f}_{i}\overline{f}_{2,i}-K_{b}\overline{H}_{1,i}+ \lambda\overline{f}_{1,i}+F_{r}\overline{f}_{1,i}^{2}\Bigr{)}-\frac{\kappa_{b}} {\overline{c}}\Bigl{(}2\overline{H}_{i}+\overline{f}_{2,i}\Bigr{)}\]0 The temperature profile rises as the Biot number increases. This is the case when the convective heat transfer rises due to a reduction in the conductive heat transfer, which is a consequence of the decreasing thermal conductivity of the plate and leads to growth in the temperature profile. The temperature profile increases as the heat source parameter increases, which is shown in \[+\overline{h}^{2}\{c_{1}\Bigl{(}2\overline{f}_{1,i}\overline{f}_ {2,i}(1+F_{r})-\overline{f}_{1,i}\overline{f}_{2,i}-\overline{f}_{i}\overline {f}_{2,i}^{2}-\overline{f}_{i}\overline{f}_{2,i}-K_{b}\overline{H}_{1,i}+ \lambda\overline{f}_{1,i}+F_{r}\overline{f}_{1,i}^{2}\Bigr{)}-\frac{\kappa_{b}} {\overline{c}}\Bigl{(}2\overline{H}_{i}+\overline{f}_{2,i}\Bigr{)}\]1 The rise in the heat source parameter increases the heat flux of the fluid due to incoming radiation from the heating process that boosts the temperature profile. The changes in the concentration profiles of species \(A\) and \(B\) according to variations in the Schmidt number are shown in \[+\overline{h}^{2}\{c_{1}\Bigl{(}2\overline{f}_{1,i}\overline{f}_ {2,i}(1+F_{r})-\overline{f}_{1,i}\overline{f}_{2,i}-\overline{f}_{i}\overline {f}_{2,i}^{2}-\overline{f}_{i}\overline{f}_{2,i}-K_{b}\overline{H}_{1,i}+ \lambda\overline{f}_{1,i}+F_{r}\overline{f}_{1,i}^{2}\Bigr{)}-\frac{\kappa_{b}} {\overline{c}}\Bigl{(}2\overline{H}_{i}+\overline{f}_{2,i}\Bigr{)}\]2 The concentration profile of species \(A\) grows as the values of the Schmidt number rise, whereas the concentration profile of species \(B\) decreases as consequence of the reduction in the mass diffusivity.