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:
- That the velocity profile provides a larger boundary layer thickness
for hybrid Nano fluids than Nano fluids.
- Multi-walled carbon nanotubes are more effective than single-walled
carbon nanotube in increasing the velocity profile.
- The SWCNT carbon nanotube, due to their premier thermal conductivity,
have a better the temperature than MWCNT carbon nanotube.
- The temperature distribution without considering the thermal slippage
parameter shows an increasing curve for Nano fluids and hybrid Nano
fluids.
- That heat transfer and surface drag force rate are enhanced linearly
for larger estimation of Nanoparticle volume fraction.
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.