*4.1. Axial Velocity Profile*

In the present study, two nanofluids namely ZnO-C2H6O<sup>2</sup> and Au-ZnO/C2H6O<sup>2</sup> are investigated whose behaviors are shown through the graphs under the effects of different parameters. In Figures 6–25, the green and magenta colors are used for ZnO-C2H6O<sup>2</sup> and Au-ZnO/C2H6O<sup>2</sup> while in Figures 24 and 25, the additional colors are also used. There are solid and dashed curves in Figures 6–23. The mechanism is that three positive increasing numerical values are given to one parameter in the HAM solution while all the remaining parameters are fixed to show the effect of that

one parameter simultaneously on the two nanofluids namely ZnO-C2H6O<sup>2</sup> and Au-ZnO/C2H6O2. When the solid lines locate below the dashed lines, then it shows the increasing effect and when the solid lines locate above the dashed lines, then it shows the decreasing effect. When the arrow head is from top to bottom, it shows the decreasing effect and when the arrow head is from bottom to top, it shows the increasing effect.

**Figure 6.** Illustration for the velocity *f*(*ζ*) and parameter *Re* = 1.00, 1.50, 2.00.

**Figure 7.** Illustration for the velocity *f*(*ζ*) and parameter *k*<sup>6</sup> = 1.00, 1.50, 2.00.

**Figure 8.** Illustration for the velocity *f*(*ζ*) and parameter *M* = 1.00, 1.50, 2.00.

**Figure 9.** Illustration for the velocity *f*(*ζ*) and parameter Ω = 1.00, 1.50, 2.00.

**Figure 10.** Illustration for the velocity *g*(*ζ*) and parameter *Re* = 1.00, 10.50, 20.00.

**Figure 11.** Illustration for the velocity *g*(*ζ*) and parameter *k*<sup>6</sup> = 1.00, 10.50, 20.00.

**Figure 12.** Illustration for the velocity *g*(*ζ*) and parameter *M* = 1.00, 10.50, 20.00.

**Figure 13.** Illustration for the velocity *g*(*ζ*) and parameter Ω = 1.00, 1.50, 2.00.

**Figure 14.** Illustration for the heat transfer *θ*(*ζ*) and parameter *Re* = 1.00, 1.50, 2.00.

**Figure 15.** Illustration for the heat transfer *θ*(*ζ*) and parameter *k*<sup>6</sup> = 1.00, 1.50, 2.00.

**Figure 16.** Illustration for the heat transfer *θ*(*ζ*) and parameter Ω = 1.00, 5.50, 10.00.

**Figure 17.** Illustration for the heat transfer *θ*(*ζ*) and parameter *Pr* = 1.00, 3.50, 6.00.

**Figure 18.** Illustration for the heat transfer *θ*(*ζ*) and parameter *M* = 1.00, 1.50, 2.00.

**Figure 19.** Illustration for the heat transfer *θ*(*ζ*) and parameter *Rd* = 1.00, 1.50, 2.00.

**Figure 20.** Illustration for the concentration *ϕ*(*ζ*) and parameter *Re* = 1.00, 1.50, 2.00.

**Figure 21.** Illustration for the concentration *ϕ*(*ζ*) and parameter *k*<sup>4</sup> = 1.00, 1.50, 2.00.

**Figure 22.** Illustration for the concentration *ϕ*(*ζ*) and parameter *k*<sup>6</sup> = 1.00, 1.50, 2.00.

**Figure 23.** Illustration for the concentration *ϕ*(*ζ*) and parameter *Sc* = 1.00, 1.50, 2.00.

**Figure 24.** Illustration for the streamlines at upper disk and parameter *Re* = 0.30.

**Figure 25.** Illustration for the streamlines for lower disks and parameter *Re* = 0.30.

Figure 6 shows that for the different values of Reynolds number *Re*, the axial velocity *f*(*ζ*) is increased. In fact, the velocity of ZnO-C2H6O<sup>2</sup> and Au-ZnO/C2H6O<sup>2</sup> increase with increasing values of Reynolds number therefore overall motion is accelerated. Figure 7 shows the prominent role of stretching parameter *k*<sup>6</sup> due to lower disk in which the axial velocity *f*(*ζ*) increases. The present motion is due to stretching so if the stretching parameter is increased, the flow of fluids is also increased. In the mean time, porosity is responsible to decrease the axial flow. It shows that motion due to different nanofluids is reduced because the permeability at the edge of the accelerating surface increases. Surely, it is noted that excess of nanoparticles concentration is involved in decelerating the motion. It is worthy of notice that the axial velocity *f*(*ζ*) decreases against the inertia. Physically it means that the absorbency of the porous medium shows an increment in the thickness of the fluid. Figure 8 shows that magnetic field parameter resists the flow since due to magnetic field, the Lorentz forces are generated which resist the motion. The curves are shrink in response to the parameter effect. Figure 9 exhibits all

the assigned values of Ω and axial velocity *f*(*ζ*) which offers opportunities to know about the rotating systems and shows that the flow of ZnO-C2H6O<sup>2</sup> and Au-ZnO/C2H6O<sup>2</sup> increase.

Some interesting results have been found in case of tangential velocity *g*(*ζ*). Figure 10 shows that as the Reynolds number Re increases, the opposite tendency has been observed in the motion of ZnO-C2H6O<sup>2</sup> and Au-ZnO/C2H6O2. The flow of mono nanofluid ZnO-C2H6O<sup>2</sup> decreases while the flow of hybrid nanofluid Au-ZnO/C2H6O<sup>2</sup> shows no prominent change for increasing the Reynolds number *Re*. In Figure 11, the tangential velocity *f*(*ζ*) tends to decreasing. Tangential velocity assumes a likely downfall so the flow is not supported by stretching due to *k*6. Figure 12 witnesses that the tangential velocity *g*(*ζ*) shifts to the effective decreasing for hybrid nanofluid Au-ZnO/C2H6O<sup>2</sup> and increases for ZnO-C2H6O<sup>2</sup> on behalf of the magnetic field parameter *M*. Figure 13 exhibits that rotation parameter Ω parameter resists the tangential flow of Au-ZnO/C2H6O<sup>2</sup> and enhances the tangential flow of ZnO-C2H6O2.
