*5.2. Tangential Velocity Profile*

Tangential velocity *g*(η) decreases by escalating the value of *M* because increasing magnetic field exerts a retarding force which slows the motion of the particles within the fluid. Figure 10 depicts that the tangential velocity has smaller magnitude for MWCNTs as compared to SWCNTs. Figure 11 depicts that tangential velocity decreases for increasing value of *A*<sup>1</sup> and its value is smaller for MWCNTs. Figure 12 shows that as stretching rate increases at the upper disk it causes a decrease of tangential

velocity. *g*(η) increases for incremental values of hall current parameter *m* and magnitude of tangential velocity profile is more increasing for MWCNTs as compared with SWCNTs as shown in Figure 13. Figure 14 depicts the relationship between Ω and *g*(η). It represents that the tangential velocity is an escalating function of rotation parameter. Figures 15 and 16 depict that for increasing φ the amplitude of *g*(η) increases and it decreases for increasing Reynolds number.

**Figure 10.** Tangential velocity profile for *M*.

**Figure 11.** Tangential velocity profile for *A*1.

**Figure 12.** Tangential velocity profile for γ2.

**Figure 14.** Tangential velocity profile for Ω.

**Figure 15.** Tangential velocity profile for *Re*.

**Figure 16.** Tangential velocity profile for φ.

#### *5.3. Dimensionless Temperature Distribution*

The dimensionless temperature distribution for different values of relaxation parameter is depicted for both MWCNTs and SWCNTs in Figure 17. The figure shows that higher rate of thermal relaxation parameter causes the increase in temperature profile. Results shows that temperature profile is more increasing for MWCNTs than SWCNTs. Figure 18 shows that temperature decreases by increasing nanoparticle volume fraction and temperature profile shows more decreasing behavior for MWCNTS as compared to SWCNTs. Effect of Reynolds number, Prandtl number, stratification parameter, unsteadiness parameter *A*1, stretching parameter γ<sup>1</sup> at lower disk on temperature profile is shown in Figures 19–23. Results are plotted both for MWCNTs and MWCNTs. Figure 19 shows that for positive values of *Re* there is an increase in temperature profile, and it shows that multi-walled carbon nanotubes have higher temperature distribution for increasing Reynolds number as compared to single-walled carbon nanotubes. Similarly, graph is plotted for negative values of Reynolds number. It is revealed that on decreasing the value of Reynolds number, temperature profile also decreases and shows more decreasing behavior for MWCNTs than SWCNTs. Figures 20–22 portray the variation of temperature profile which decreases for incremental values of *s*, *A*1, and γ<sup>1</sup> this decreasing behavior is observed more for SWCNTs as compared with MWCNTs. Figure 23 depicts for increasing value of Prandtl number temperature profile decreases. The decrease in temperature by augmentation of Prandtl number is consistent with the physical expectation, as by increasing Prandtl number fluid possesses lower thermal diffusivity which causes the thickness of thermal boundary layer to decrease.

**Figure 17.** Temperature profile for γ.

**Figure 20.** Temperature profile for γ1.

**Figure 23.** Temperature profile for *Pr*.

#### *5.4. Concentration Profile*

Figure 24 demonstrate the analysis of concentration profile. For various estimates of homogeneous reaction parameter *k*1 there is decay in concentration profile. Similar results are obtained for heterogeneous reaction parameter *k*2 in Figure 25. Concentration field is observed for Schmidt number in Figure 26. As it is momentum to mass diffusivity ratio, so smaller the value of mass diffusivity, stronger the value of Schmidt number, which causes the reduction of the concentration of the fluid.

**Figure 24.** Concentration profile for *k*1.

**Figure 25.** Concentration profile for *Sc*.

**Figure 26.** Concentration profile for *k*2.

Comparison of *f* --(0) and *g*- (0) with Stewartson [42] for several estimates of Ω by considering all extra terms as zero is depicted in Table 3. An excellent synchronization is achieved in this case. This substantiates our mathematical model and presented results.


**Table 3.** Comparison of *f* --(0) and *g*- (0) for numerous estimates of Ω with Stewartson [42].
