*4.1. Velocities, Temperature and Concentration Fields*

Figures 3–5 exemplify the variation in velocity profiles due to the Reynolds number. Greater Reynolds number reduces the velocity profiles in axial, radial and tangential directions. The Reynolds number is associated with the inertial forces of the fluid flow. The greater the Reynolds number, the stronger the inertial forces that reduce the motion of the fluid flow. Figures 6–8 depict the change in *f*'(ζ), *g*(ζ) and θ(ζ) for greater *m*. The last terms in the principle equations of the velocity function leads us to a smaller conductivity of the fluid flow via increasing *m*. So, due to less conductivity, the damping force in fluid flow produces which intensifies the velocity components *f*'(ζ) and *g*(ζ). These phenomena reduce the thermal field of the fluid flow. Figures 9 and 10 illustrate the change in velocity components via the Weissenberg number. Greater values of the Weissenberg number heighten the velocity components. Increasing the Weissenberg number reduces the fluid flow viscosity. As the viscosity of the fluid is reduced, the motion of the fluid particles increase. Thus, the velocity

components escalate with a greater Weissenberg number. Figures 11–13 illustrate the change in *f*'(ζ), *g*(ζ) and θ(ζ) via the magnetic field parameter. A higher magnetic parameter reduces the velocity components, while a reverse impact of the magnetic parameter on the thermal field is observed. The heightening magnetic field produces higher resistive force to the flow of fluid, which drops the motion of the fluid flow. Thus, the velocity components decline. On the other hand, the higher resistive force increases the electrons collision, which produces more heat to fluid flow. Therefore, the thermal field rises with the higher values of magnetic parameter. Figures 14 and 15 exhibit the change in velocity components (*f*(ζ), *g*(ζ)) via a stretching parameter. The momentum boundary layer escalates with higher values of stretching parameter and, consequently, the velocity profile *f*(ζ) heightens. On the other hand, the velocity profile *g*(ζ) declines with a higher stretching parameter. This influence is due to the fact that the higher values of stretching parameter reduce the angular velocity of the fluid flow. Figure 16 displays the change in thermal field via Brownian motion and thermophoresis parameters. The rising values of Brownian motion and thermophoresis parameters intensify the thermal field. The rising thermophoretic force pushes the fluid particles to move form heated to cold regions and, consequently, the temperature field increases. A similar impact is also depicted against the Brownian motion parameter. Figure 17 shows the change in thermal profile via thermal relaxation parameter. Higher values of relaxation parameter decline the temperature profile. With higher values of thermal relaxation parameter, the material particles need more potential to transmit energy to its surrounding particles. Additionally, this behavior is less for the C-C model as compared to Fourier's law. Figure 18 illustrates the change in thermal field via temperature difference parameter. An escalating conduct is detected in thermal field by heightening the temperature difference parameter. By increasing the temperature difference parameter, the temperature at the wall increases, and then the ambient temperature also increases. Consequently, the temperature field heightens. Figure 19 clarifies the change in thermal field via heat generation/absorption parameter. Clearly, the increasing heat parameter increases the temperature profile. The heat generation/absorption parameter acts like a heat generator. The increasing generation/absorption increases the thermal field of the fluid flow. Figure 20 indicates the change in thermal profile via the Prandtl number. A declining impact is detected via increasing Prandtl number. Figure 21 indicates the variation in concentration field via thermophoresis parameter. As the increasing thermophoresis parameter increases the thermal field (see Figure 16), consequently, the concentration of the fluid flow also increases. The opposite impact of Brownian motion parameter is depicted against the concentration profile (see Figure 22). The change in concentration field via the Schmidt number is displayed in Figure 23. A declining impact is observed here. The concentration distribution in inversely related with the Schmidt number. The intensifying estimations of the Schmidt number reduce the thickness of the boundary layer flow. The concentration distribution therefore declines.

**Figure 3.** Re on *f*(ζ).

**Figure 6.** *m* on *f*'(ζ).

**Figure 9.** *We* on *f*(ζ).

**Figure 12.** *M* on *g*(ζ).

**Figure 15.** *A* on *g*(ζ).

**Figure 18.** θ*<sup>w</sup>* on θ(ζ).

**Figure 21.** *Nt* on ϕ(ζ).

**Figure 23.** *Sc* on ϕ(ζ).
