**4. Results and Discussion**

The primary intention is to scrutinize the characteristics of generalized hybrid nanoliquid for the mixed convective flow comprising MoS2-Go nanoparticles through slender revolution bodies. The non-linear Equation (15) with boundary restrictions (Equation (16)) has been worked out numerically via Lobatto IIIa formula. The thickness of the boundary layer is considered as 30 for convergence of profiles asymptotically which is essential for this type of problem. Table 2 represents the thermo-physical characteristics of the base and nanofluids. The outcomes of the sundry parameters in the presence of the water-based fluid and the type B hybrid nanofluid on the field of velocity distribution and the skin friction have been examined in Figures 2–13. For validation, the results of the current problem have been compared with the outcomes of Ahmad et al. [34] and Saleh et al. [35] as shown in Table 3. An excellent harmony is seen. Whereas the numerical values of types B and C hybrid nanofluid for (ASSF) as well as for (OPPF) are displayed in Tables 4 and 5.


**Table 2.** Thermo-physical properties of the base fluid and hybrid nanoparticles.

**Table 3.** Comparison values of *F* <sup>00</sup>(*b*) when *m* = 1, λ = 0, ξ = −1, *R<sup>d</sup>* = φ = 0, Pr = 1 for the distinct values of *b*.


**Table 4.** Computation of the Pr−1*Pe*0.5 *<sup>x</sup> C<sup>F</sup>* for the assisting flow ξ = 1.1 utilizing the two different types of models varying φ<sup>2</sup> while the other fixed parameters are *m* = λ = 1, *b* = 0.1, *R<sup>d</sup>* = 0.5.


**Table 5.** Computation of the Pr−1*Pe*0.5 *<sup>x</sup> C<sup>F</sup>* for the opposing flow ξ = −1.1 utilizing the two different types of models varying φ<sup>2</sup> while the other fixed parameters are *m* = λ = 1, *b* = 0.1, *R<sup>d</sup>* = 0.5.


The outcomes, indicating from these tables the type B hybrid nanofluid, are superior to the type C hybrid nanofluid. Moreover, in case of the assisting flow, the skin friction increases by 0.979% for the type B hybrid nanofluid whereas the skin friction in the type C hybrid nanofluid augments by 1.001%. As the value of the nanoparticle volumetric fraction increases, the skin friction decreases continuously for both types of hybrid nanofluid. In contrast, the skin friction decreases up to 0.435% for the type B hybrid nanofluid due to the fixed value of the parameter φ<sup>2</sup> = 0.025 in the example of opposing flow while for the type C hybrid nanofluid, it is decreased by 0.446%. Due to very small negligible differences in the outcomes of both the types of hybrid nanofluid, therefore the computation throughout the paper is done only for the type B hybrid nanofluid.

Figures 2 and 7 are set to inspect the impact of the dimensionless radius of the slender body parameter *b* and the volume fraction of nanoparticle φ<sup>2</sup> on the velocity gradient against the similarity variable η for the three different phenomena such as the assisting and opposing flows, shape bodies and the normal nanofluid as well for the hybrid nanofluid. In the example of assisting flow, the velocity distribution and the momentum boundary-layer flow (MBLF) increase with increasing the dimensionless radius of the slender body parameter *b*, while in the phenomenon of the opposing flow, the behavior of the motion of the fluid behaves in the contrary direction as shown in Figure 2. It is transparent to observe from the outcomes that the gap between the curves is initially more significant in the ASSF as well as in the OPPF, while as we upsurge, the value of the dimensionless radius of the slender body parameter *b* the gap between the solution curves is reduced.

**Figure 2.** The variation of the velocity profile *F* 0 (η) for the case of assisting and opposing flow versus the similarity variable η for the distinct values of the dimensionless radius of the slender body parameter *b*.

On the other hand, the velocity distribution is enhancing the function of the shape bodies as well as for the type B hybrid nanofluid and the type A nanofluid for the higher values of *b* as shown in Figures 3 and 4, respectively. It is perceived from Figure 3 that the velocity field is superior in the flow through a cone compared to paraboloid and cylindrical type's bodies. Moreover, it is perfectly visible from the graph that the liquid flow accelerates more for the MoS2/water nanoparticle or type A nanofluid as compared to the type B hybrid nanoparticles as highlighted in Figure 4. The gap between the solution curves in the shape bodies is more when compared to the solution curves like Figure 4. Since Figure 5, it has been noticed that for the (ASSF), the velocity distribution decreases with escalating φ2, whereas for the opposing flow, it is augmented.

distribution decreases with escalating

solution curves like Figure 4. Since Figure 5, it has been noticed that for the (ASSF), the velocity

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solution curves like Figure 4. Since Figure 5, it has been noticed that for the (ASSF), the velocity

<sup>2</sup> , whereas for the opposing flow, it is augmented.

<sup>2</sup> , whereas for the opposing flow, it is augmented.

**Figure 3.** The variation of the velocity profile *F* ' for the three important cases of shape bodies such as Cone, paraboloid, and cylinder versus the similarity variable for the distinct values of the dimensionless radius of the slender body parameter *b* . **Figure 3.** The variation of the velocity profile *F* 0 (η) for the three important cases of shape bodies such as Cone, paraboloid, and cylinder versus the similarity variable η for the distinct values of the dimensionless radius of the slender body parameter *b*. such as Cone, paraboloid, and cylinder versus the similarity variable for the distinct values of the dimensionless radius of the slender body parameter *b* .

**Figure 4.** The variation of the velocity profile *F* ' for the type A normal nanofluid as well as for the type B hybrid nanofluid versus the similarity variable for the distinct values of the **Figure 4.** The variation of the velocity profile *F* 0 (η) for the type A normal nanofluid as well as for the type B hybrid nanofluid versus the similarity variable η for the distinct values of the dimensionless radius of the slender body parameter *b*.

for the type A normal nanofluid as well as for

for the distinct values of the

**Figure 4.** The variation of the velocity profile *F* '

dimensionless radius of the slender body parameter *b* .

dimensionless radius of the slender body parameter *b* .

the type B hybrid nanofluid versus the similarity variable

**Figure 5.** Shows the variation of the velocity profile *F* 0 (η) for the case of assisting and opposing flow versus the similarity variable η for the distinct values of the volume fraction of nanoparticle φ2.

Additionally, it explains that the thickness of the velocity and the (MBLF) declines with φ<sup>2</sup> for the ASSF and augments for the OPPF. The outcome of the velocity gradient in Figure 5 is showing a contrary behavior in both the cases of ASSF and OPPF as we compare with the solution curves of Figure 2. From Figure 6, it is transparent that due to the shape bodies, the velocity field is decelerated for the higher impact of φ2. In comparison, the flow of the velocity field over the cone shape body is finer than the rest of the two-shape body. Generally, the velocity upsurges due to the fact that type B hybrid nanofluid dynamic viscosity has an inverse relationship to nanoparticle volume fraction. Hence, an augmenting in φ<sup>2</sup> guides to the decline's viscosity of base liquid and therefore speeds up the motion of the liquid flow.

**Figure 6.** Shows the variation of the velocity profile *F* 0 (η) for the three important cases of shape bodies such as Cone, paraboloid, and cylinder versus the similarity variable η for the distinct values of the volume fraction of nanoparticle φ2.

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Moreover, the velocity profile reduces due to φ<sup>2</sup> for the type B hybrid nanofluid and type A nanofluid as portrayed in Figure 7. The impact between the curves is very minor for the parameter φ<sup>2</sup> while the outcome for the type B hybrid nanofluid is higher than the type A nanofluid.

**Figure 7.** The variation of the velocity profile *F* 0 (η) for the type A normal nanofluid as well as for the type B hybrid nanofluid versus the similarity variable η for the distinct values of the volume fraction of nanoparticle φ2.

Figures 8 and 9 highlight the stimulus of radiation parameter *R<sup>d</sup>* on the velocity distribution against the similarity variable of the two distinct phenomena such as the assisting and opposing flows as well as for the type A nanofluid and type B hybrid nanofluid. It is clear from Figure 8 as depicted graphically that the velocity distribution augments for the ASSF and declines for the OPPF as the value of the radiation parameter *R<sup>d</sup>* upsurges. The solution behavior is similarly observed like Figure 2 while the contrary behavior of the outcomes in Figure 5 is seen for both the cases ASSF and as well as in the OPPF, while in comparison the influence between the curves is less. Additionally, *R<sup>d</sup>* is exploited to drop the molecules of liquid into hydrogen. Figure 9 displays that the velocity upsurges are owed to magnifying the radiation parameter for the type A nanofluid as well as for the type B hybrid nanofluid. The motion of the fluid flow for the type A nanofluid is superior as compare to the type B hybrid nanofluid. In addition, the solution impact in the curves for the velocity gradient is more owing to the impact of radiation parameter as compared to the significant impact of the other two parameters which is exercised in Figures 4 and 7, respectively.

**Figure 8.** Shows the variation of the velocity profile *F* 0 (η) for the case of assisting and opposing flow versus the similarity variable η for the distinct values of the radiation parameter *R<sup>d</sup>* .

**Figure 9.** The variation of the velocity profile *F* 0 (η) for the type A normal nanofluid as well as for the type B hybrid nanofluid versus the similarity variable η for the distinct values of the radiation parameter *R<sup>d</sup>* .

Figures 10–13 show the variation of the dimensionless radius of the slender body parameter *b* and the nanoparticle volume fraction φ<sup>2</sup> on the skin friction against the mixed convection parameter ξ for the two distinct cases such as the flow over the shape bodies and the corresponding type A nanofluid and the type B hybrid nanofluid. The skin friction is reduced with enhanced *b* along the horizontal axis of the range (−∞ < ξ ≤ 0) and augments in the spectrum (0 ≤ ξ < ∞) for the flow over the shape bodies as well as for the types A and B nanofluid and hybrid nanofluid as highlighted in Figures 10 and 11, respectively. The skin friction is higher in the range (0 ≤ ξ < ∞) for the flow over the cone shape body and also for the type B hybrid nanofluid as compared to the flow on the paraboloid and the cylindrical shape bodies as well as for the type A nanofluid, while the opposite trend is observed in the range (−∞ < ξ ≤ 0) as shown in Figures 10 and 11. The range in both graphs is taken from −0.5 ≤ ξ ≤ 0.5 and it is not the fixed one we can vary from this range as a real number (−∞ < ξ < ∞) but due to this

small range in the solution, the collision is more effectively significant. A similar behavior is detected (Figures 10 and 11) for the skin friction owing to the nanoparticle volume fraction φ<sup>2</sup> as described in Figures 12 and 13, respectively. Hence, in Figures 12 and 13 illustrate more transparently the impact of the curves of the flow over the shape bodies against the mixed convection parameter owing to *b* is greater compared to φ<sup>2</sup> on the skin friction while this gap for the type B hybrid nanofluid and type A nanofluid owing the parameter φ<sup>2</sup> is coarsened as compared to the dimensionless radius of the slender body parameter *b*. respectively. Hence, in Figures 12 and 13 illustrate more transparently the impact of the curves of the flow over the shape bodies against the mixed convection parameter owing to *b* is greater compared to <sup>2</sup> on the skin friction while this gap for the type B hybrid nanofluid and type A nanofluid owing the parameter <sup>2</sup> is coarsened as compared to the dimensionless radius of the slender body parameter *b* .

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compared to the flow on the paraboloid and the cylindrical shape bodies as well as for the type A

but due to this small range in the solution, the

0) as shown in Figures 10

and it is not the fixed one we can

<sup>2</sup> as described in Figures 12 and 13,

for the distinct

nanofluid, while the opposite trend is observed in the range (

and 11. The range in both graphs is taken from 0.5 0.5

vary from this range as a real number

friction owing to the nanoparticle volume fraction

**Figure 10.** Deviation of the skin friction versus the mixed convection parameter ξ for the distinct values of the dimensionless radius of the slender body parameter *b*. values of the dimensionless radius of the slender body parameter *b* .

**Figure 11.** Deviation of the skin friction versus the mixed convection parameter ξ for the distinct values of the dimensionless radius of the slender body parameter *b*.

**Figure 12.** Deviation of the skin friction versus the mixed convection parameter ξ for distinct values of the volume fraction of nanoparticle φ2.

**Figure 13.** Deviation of the skin friction versus the mixed convection parameter ξ for distinct values of the volume fraction of nanoparticle φ2.
