*4.2. Entropy Optimization and Bejan Number*

Figures 24 and 25 depict the impact of Brinkman number on the total entropy profile and the Bejan number profile, respectively. The total entropy profile escalates with a higher Brinkman number, while the opposite trend is observed on the Bejan number profile. The heat rises in the fluid moving in related region heightens with greater Brinkman number. Therefore, the total entropy profile rises with the Brinkman number, and the Bejan number declines (see Figure 25). Figures 26 and 27 illustrate the change in the total entropy profile and the Bejan number profile, via greater values of the diffusion parameter. Both total entropy and the Bejan number profiles escalate with larger values of diffusion parameter. The rising diffusion parameter increases the nanoparticle's diffusion rate. Thus, both profiles escalate with a greater diffusion parameter. Figures 28 and 29 display the change in total entropy and Bejan number profiles via the magnetic parameter. The total entropy profile escalates, while the Bejan number profile deescalates with a higher magnetic parameter. According to the Lorentz force, the total entropy of the system heightens, while the Bejan number reduces with higher magnetic parameter. So, the total entropy profile escalates, while the Bejan number profile deescalates with a higher magnetic parameter. Figures 30 and 31 illustrate the change in total entropy and the Bejan number profiles via temperature difference parameters. Both profiles escalate with higher temperature difference parameters. Figures 32 and 33 show the change in total entropy and Bejan number profiles via the Weissenberg number. Increasing the Weissenberg number reduces the fluid flow viscosity. This behavior escalates both total entropy and the Bejan number profiles. Figures 34 and 35 indicate the variation the total entropy and Bejan number profiles via the Hall parameter. The total entropy profile declines, while the Bejan number profile escalates with the higher Hall parameter. The Hall parameter has a direct effect on the Lorentz force term and current density of the nanofluid. Thus, the electrical conductivity of the nanofluid heightens with the higher Hall parameter and, consequently, the total entropy profile is reduced. The opposite impact of Hall parameter on the Bejan number is displayed in Figure 35.

**Figure 25.** *Br* on *Be*(ζ).

**Figure 28.** *M* on *NG*(ζ).

**Figure 31.** θ*<sup>w</sup>* on *Be*(ζ).

**Figure 34.** *m* on *NG*(ζ).

**Figure 35.** *m* on *Be*(ζ).
