Results and discussions:
The differential systems consisting of Eqs. (9) - (11) have been solved via analytical manner (Homotopy Perturbation Method (HPM)) in Matlab-14 software. Graphical analysis of the impressive parameters like: Prandtl number (Pr), Thermal slip parameter (δ), CNTs volume fraction (ϕ) is precisely checked on the profiles of velocity and temperature for disparate carbon nano-tubes (MWCNT - SWCNT). (See Figures 5-8). In order to achieve more accurate outputs in line with the objectives of this paper and to validate the results in the simulation section, a precise comparison has been made in this research. The comparison between the analytical (HPM) and numerical (4th-5th-order Runge–Kutta–Fehlberg) methods for base fluids (C2H6O2, H2O and Engine oil) and various carbon nanotubes in this essay shows the high accuracy of the present simulation and the discussed results. (See figures 2-4) Likewise, in order to survey the perspicuity of the present probe, we evaluate HPM solution with the output of prior essay published by Ref (Dinarvand et al. [30]) for titanium dioxide and Cu-H2O Nano liquid. The comparisons are tested in Table 2. The low mistake in this table displays the high punctuality of the present simulation.
The choice of base liquid has a significant impact on the graphs of velocity and temperature. This research shows that the highest graphs of velocity and temperature is for Engine oil base fluid. Also, the lowest graphs of velocity and temperature is for water base fluid. (See figure 5). Figure 6(a-d) shows the mutations in the velocity profile (f’(η)) along the x axis for diverse amounts of the nanoparticles’ volume fraction parameter (ϕ). This figure actually depicts the behavior of the hybrid Nano liquid and Nano liquid flow for different carbon nanotubes (SWCNT-MWCNT) at saddle points and nodal points. Based on observations, it was determined that the profile f’(η) is a decreasing function of ϕ at both dots. In addition, it should be noted that the velocity profile f’(η) provides a larger boundary layer thickness for hybrid Nano fluids than Nano fluids. Furthermore, multi-walled carbon nanotubes are more effective than single-walled nanotubes in increasing the velocity profile. The impact of the nanoparticles’ volume fraction (ϕ) on the velocity of the Nano fluids and hybrid Nano fluids along the Y axis is shown in Figure 7(a-d). In these figures, a diverse behaviour is observed for the velocity profile at saddle and nodal dots. It is as well as clear that the velocity graph along the Y axis is, similarly to f’(η), a decreasing function of ϕ at both points, but with the difference that the velocity profile at the saddle point has first an increasing tend up to the point ηm. In fact, ηm is the intersection dot of the velocity graph for several values of ϕ. In addition, it can be seen from these figures that the velocity profile G’(η) has a lower boundary layer thickness than the velocity profile along the x axis (f’(η)). It is noteworthy that the velocity graph G’(η) provides a lower boundary layer thickness at the saddle point for hybrid Nano fluids than Nano fluids. The impact of the nanoparticles’ volume fraction parameter ϕ on the temperature profile Θ(η) for various carbon nanotubes (SWCNT-MWCNT) is shown in Figure 8(a-d). As expected, the straight relevance between ϕ and thermal conductivity growths the thickness of the heat and temperature layer at both saddle and nodal points. Furthermore, due to the higher thermal conductivity of the SWCNT nano-particles, the growth in temperature in these nano-particles is more than MWCNT. It is noteworthy that the temperature profile Θ (η) provides a larger thermal boundary layer thickness at both points for hybrid Nano fluids than Nano fluids. The temperature distribution without considering the thermal slippage parameter shows an increasing curve for Nano fluids and hybrid Nano fluids. (See Figure 8 b-c). For better visualization, the effect of the thermal slippage parameter is evident in Figure 7(e). It is deduced from this form that high temperature decreases with increasing thermal slippage parameter. In addition, the behaviour of the Pr number on the profile Θ(η) implies that Θ(η) declines for a major Pr number. Indeed, enhancing the Pr number corresponds to a diminution in the thermal permeability coefficient (α), which declines the temperature. (See Figure 8 f). Changes in skin friction and Nusselt number for diverse volume fractions of nanoparticles ϕ for Nano fluids containing carbon nanotubes (SWCNT-MWCNT) are depicted in Tables (2-4). Our outcome demonstrate that heat transfer and surface drag force rate are enhanced linearly for larger estimation of Nanoparticle volume fraction. Additionally, the comparison between (SWCNT-MWCNT) Nano liquids in the actual simulation displays that MWCNT nano-particles have higher crust friction coefficient (Cf) than SWCNT nano-particles.
Conclusions:
In this research the specification of 3-dimensional flow stagnation dot of hybrid Nano liquids passing through circular cylinder with sinusoidal radius is analyzed. Plus, the influence of the impressive parameters is precisely studied on the graphs of velocity and temperature for diverse carbon nanotubes (SWCNT-MWCNT). Outcomes displayed that:
In the long run, it will be beheld that the nano-particle kind and Nano liquid base is an significant factor in the heating and cooling activities.