# Computational Simulation and Parametric Analysis of the Effectiveness of Ternary Nano-composites in Improving Magneto-Micropolar Liquid Heat Transport Performance

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{3}O

_{4}/SiO

_{2}-polymer-based tri-hybrid nano-liquid past a heated stretching/shrinking cylindrical shape were investigated by Mahmood et al. [37]. A numerical study was carried out by Alharbi et al. [38] to analyze the heat and mass transfer of a magneto-tri-hybrid nano-liquid moving about a stretching cylinder. In their comprehensive study, Nazir et al. [39] observed the impact of the application of a magnetic field on the flow of the tri-hybrid toward a heated cylindrical object. Khan et al. [40] analyzed the flow of tri-hybrid nano-fluid characteristics around a rotating sphere in the context of trying to cool rotating spherical industrial products. Sarada et al. [41] examined the heat transport of tri-hybrid nano-liquids in motion past a curved stretching sheet, considering the non-Fourier heat flux model. In their investigation, Kumar et al. [42] provided a comparative analysis of energy transport in time-dependent MHD tri-hybrid nano-liquids, considering the conveyance of three variously shaped nano-solids. Other relevant works are included in [43,44,45,46,47].

## 2. Formulating the Governing Model

_{f}and the Nusselt number Nu can be written as the following [59]:

## 3. Numerical Approximation and Validation

## 4. Results and Discussion

_{f}, when enlarging values of mixed convection λ, micropolar K, and volume fraction ψ are the parameters. Figure 2 confirms that as the mixed convection values escalate, so do the drag forces. The skin friction increases with an increase in velocity, and previous studies confirm that for larger values of the mixed convection factor, the velocity is increased and, accordingly, there is a growth in the drag forces. Figure 3 describes that skin friction increases for micropolar factor boosting. The perceptions are that the viscosity appears to grow while the rising upsides of micropolar factor are utilized. Mathematically, Equation (22) shows that skin friction is an increasing function of the micropolar factor. As a result, the coefficient of skin friction increases. In Figure 4, it is evident that increasing the intensity of the magnetic field forces negatively affected the skin friction. This negative effect can be linked to an inhibition in the velocity of the fluid and the transport of energy, which are caused by the intensification of the magnetic field. Figure 5 is plotted to describe the tendency of skin friction when it is exposed to the volume fraction factor. Skin friction shows a positive tendency when the volume fraction factor increases, because, by increasing this factor, the thermal conductivity of the host fluid improves. In addition, looking closely at Equation (22), we find that the skin friction has a positive relationship with the nano-particle volume fraction if its values are between 0 and 1, and because this study relied on a range of volume fraction values between 0 and 0.2 (as recommended in the previous studies), the relationship will be positive, which leads to an improvement in the drag forces. The Nusselt number behaviors that result from the impacts of mixed convection, micropolar, magnetic, and volume fraction factors are captured in Figure 6, Figure 7, Figure 8 and Figure 9. Figure 6 shows how the Nusselt number behaves when the values of the mixed convection factor are escalating. The buoyant forces will undoubtedly improve as the combined convective factor values rise, and as a result, the Nusselt number value will also obviously improve. The inverse relationship between the Nusselt number and the micropolar factor is clearly visible in Figure 7. With the improvement of the micropolar factor, the resistance of the fluid to movement increases, and this means that its velocity is slowed, which causes an inhibition of energy transfer. The Nusselt number shows in Figure 8 a reverse response when exposed to a magnetic field of increasing intensity. This response is explained by the braking that occurs at the velocity of the tri-hybrid nano-fluid, which causes an inhibition of energy transfer. It is clear from Figure 9 that the Nusselt number is an increasing function of the volume fraction factor, which agrees with the fact that has been supported in several previous numerical and experimental studies, namely, that the thermal conductivity of the host fluid increases with the increase in the volume fraction factor, and accordingly, the rate of the energy transport increases.

_{2}, and graphene oxide GO is considered as a ternary hybrid nano-particle. The combination of aluminum oxide Al

_{2}O

_{3}and silver Ag is utilized as a hybrid nano-particle, whereas silver Ag is used as a mono nano-particle. All these nano-solids are suspended in ethylene glycol. It has been noticed that ternary hybrid nano-fluids have maximum local skin friction compared with hybrid fluids or mono nano-fluids. The ternary hybrid nano-fluid heat transfer performance is better than that of the hybrid nano-fluid and the mono nano-fluid. Hence, it can be concluded that the ternary hybrid nano-particles are more reliable for the development and growth of energy transfer rates. Lastly, the graphical findings for velocity, angular velocity, and temperature satisfy the considered boundary conditions.

## 5. Conclusions

- 1-
- Regardless of the influencing factors, the tri-hybrid nano-fluid, represented by GO-TiO
_{2}-Ag-ethylene glycol, produced the maximum value of the rate of energy transfer, velocity, angular velocity, skin friction, and temperature. - 2-
- Elevating the value of the mixed convection factor improves heat transport, velocity, and angular velocity.
- 3-
- The volume fraction factor of tri-hybrid nano-particles has the potential to enhance all of the physical groups investigated in this study.
- 4-
- The velocity of the tri-hybrid nano-fluids and their ability to transfer energy are significantly suppressed when the magnetic field strength is increased.
- 5-
- Greater values of the micropolar factor have the ability to improve skin friction and temperature while inhibiting velocity, angular velocity, and energy transfer.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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${(\mu )}_{thnf}=\frac{{\mu}_{f}}{{(1-{\chi}_{Ag})}^{2.5}{(1-{\chi}_{Ti{O}_{2}})}^{2.5}{(1-{\chi}_{GO})}^{2.5}}$. |

${(\rho {c}_{p})}_{thnf}=\left(1-{\chi}_{Ag}\right)\left[\left(1-{\chi}_{Ti{O}_{2}}\right)\right[\left(1-{\chi}_{GO}\right){(\rho {c}_{p})}_{f}+{\chi}_{GO}\left(\rho {c}_{p}{)}_{GO}\right]+{\chi}_{Ti{O}_{2}}\left(\rho {c}_{p}{)}_{Ti{O}_{2}}\right]+{\chi}_{Ag}{(\rho {c}_{p})}_{Ag}$ |

$\left(\rho {)}_{thnf}=\left(1-{\chi}_{Ag}\right)\left[\left(1-{\chi}_{Tzi{O}_{2}}\right)\right[\left(1-{\chi}_{GO}\right){\rho}_{f}+{\chi}_{GO}{\rho}_{GO}\right]+{\chi}_{Ti{O}_{2}}{\rho}_{Ti{O}_{2}}]+{\chi}_{Ag}{\rho}_{Ag}x$ |

${\varphi}_{thnf}=\left({\mu}_{thnf}+\kappa /2\right)j$, ${(\alpha )}_{thnf}=\frac{{k}_{thnf}}{{(\rho {c}_{p})}_{thnf}}$, |

$\frac{{k}_{thnf}}{{k}_{hnf}}=\frac{\left({k}_{GO}+2{k}_{hnf}\right)-2{\chi}_{GO}\left({k}_{hnf}-{k}_{GO}\right)}{\left({k}_{GO}+2{k}_{hnf}\right)+{\chi}_{GO}\left({k}_{hnf}-{k}_{GO}\right)}$, $\frac{{k}_{hnf}}{{k}_{nf}}=\frac{\left({k}_{Ti{O}_{2}}+2{k}_{nf}\right)-2{\chi}_{Ti{O}_{2}}\left({k}_{nf}-{k}_{Ti{O}_{2}}\right)}{\left({k}_{Ti{O}_{2}}+2{k}_{nf}\right)+{\chi}_{Ti{O}_{2}}\left({k}_{nf}-{k}_{Ti{O}_{2}}\right)}$,$\frac{{k}_{nf}}{{k}_{f}}=\frac{\left({k}_{Ag}+2{k}_{f}\right)-2{\chi}_{Ag}\left({k}_{f}-{k}_{Ag}\right)}{\left({k}_{Ag}+2{k}_{f}\right)+{\chi}_{Ag}\left({k}_{f}-{k}_{Ag}\right)}$ |

${\sigma}_{thnf}=\left[1+\frac{3\left(\left({\sigma}_{GO}/{\sigma}_{hnf}\right)-1\right){\chi}_{GO}}{\left(\left({\sigma}_{GO}/{\sigma}_{hnf}\right)+2\right)-{\chi}_{GO}\left(\left({\sigma}_{GO}/{\sigma}_{hnf}\right)-1\right)}\right]{\sigma}_{hnf}$, ${\sigma}_{hnf}=\left[1+\frac{3\left(\left({\sigma}_{Ti{O}_{2}}/{\sigma}_{nf}\right)-1\right){\chi}_{Ti{O}_{2}}}{\left(\left({\sigma}_{Ti{O}_{2}}/{\sigma}_{nf}\right)+2\right)-{\chi}_{Ti{O}_{2}}\left(\left({\sigma}_{Ti{O}_{2}}/{\sigma}_{nf}\right)-1\right)}\right]{\sigma}_{nf}$, ${\sigma}_{nf}=\left[1+\frac{3\left(\left({\sigma}_{Ag}/{\sigma}_{f}\right)-1\right){\chi}_{Ag}}{\left(\left({\sigma}_{Ag}/{\sigma}_{f}\right)+2\right)-{\chi}_{Ag}\left(\left({\sigma}_{Ag}/{\sigma}_{f}\right)-1\right)}\right]{\sigma}_{f}$ |

ζ | $\mathsf{\lambda}$ | ||||||||
---|---|---|---|---|---|---|---|---|---|

−0.85 | −0.6 | −0.4 | −0.2 | 0.0 | 0.2 | 0.34 | 0.35 | 5.0 | |

0.0 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 |

0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | |

0.2 | 0.0098 | 0.1003 | 0.1550 | 0.2044 | 0.2445 | 0.2782 | 0.3024 | 0.30227 | 0.7951 |

0.0170 | 0.0917 | 0.1547 | 0.2020 | 0.2421 | 0.2778 | 0.3009 | 0.3025 | 0.7947 | |

0.4 | 0.1507 | 0.2865 | 0.3849 | 0.4624 | 0.5333 | 0.5788 | 0.5820 | 1.5605 | |

0.1456 | 0.2816 | 0.3788 | 0.4600 | 0.5319 | 0.5783 | 0.5815 | 1.5595 | ||

0.6 | 0.1174 | 0.3782 | 0.5107 | 0.6342 | 0.7450 | 0.8128 | 0.8207 | 2.2722 | |

0.1051 | 0.3550 | 0.5084 | 0.6331 | 0.7422 | 0.8121 | 0.8170 | 2.2683 | ||

0.8 | 0.3583 | 0.5753 | 0.7481 | 0.9007 | 0.9938 | 1.0016 | 2.9051 | ||

0.3475 | 0.5721 | 0.7447 | 0.8926 | 0.9866 | 0.9931 | 2.8983 | |||

1.0 | 0.2119 | 0.5518 | 0.7880 | 0.9803 | 1.1009 | 1.1036 | 3.4406 | ||

0.2097 | 0.5537 | 0.7827 | 0.9725 | 1.0912 | 1.0993 | 3.4311 | |||

1.2 | 0.4411 | 0.7507 | 1.0021 | 1.1310 | 1.1412 | 3.8587 | |||

0.4360 | 0.7410 | 0.9773 | 1.1218 | 1.1316 | 3.8535 | ||||

1.4 | 0.1976 | 0.6263 | 0.9104 | 1.1123 | 1.1238 | 4.1582 | |||

0.1585 | 0.6175 | 0.9094 | 1.0811 | 1.0927 | 4.1575 | ||||

1.6 | 0.4340 | 0.7727 | 1.0171 | 1.0225 | 4.3374 | ||||

0.4095 | 0.7774 | 0.9786 | 0.9920 | 4.3397 | |||||

1.8 | 0.0510 | 0.6402 | 0.8279 | 0.8555 | 4.1902 | ||||

0.0408 | 0.5955 | 0.8296 | 0.8448 | 4.002 | |||||

2.0 | 0.4122 | 0.7230 | 0.7581 | 4.3476 | |||||

0.3817 | 0.6544 | 0.6713 | 4.3411 |

$\mathsf{\lambda}$ | $\mathit{\theta}\left(0\right)$ | |
---|---|---|

−0.6 | 2.0547 | 2.0567 |

−0.4 | 1.9046 | 1.9088 |

−0.2 | 1.8157 | 1.8172 |

0.0 | 1.7517 | 1.7555 |

0.2 | 1.7018 | 1.7073 |

0.4 | 1.6608 | 1.6663 |

0.6 | 1.6260 | 1.6269 |

0.8 | 1.5958 | 1.5967 |

1.0 | 1.5692 | 1.5705 |

1.4 | 1.5239 | 1.5247 |

1.8 | 1.4863 | 1.4883 |

3.0 | 1.4015 | 1.4046 |

Thermo-Physical Feature | Ethylene Glycol | Ag | GO | Fe_{3}O_{4} |
---|---|---|---|---|

C_{p} (J/kg K) | 2415 | 235 | 717 | 670 |

β × 10^{−5} (K^{−1}) | 57 | 1.89 | 28 | 20.6 |

ρ (kg/m^{3}) | 1114 | 10500 | 1800 | 5180 |

K (W/m K) | 0.252 | 429 | 5000 | 80.4 |

σ (s/m) | 1.07 × 10^{−6} | 6.3 × 10^{7} | 6.3 × 10^{7} | 1.12 × 10^{5} |

Pr | 29.8 | - | - | - |

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## Share and Cite

**MDPI and ACS Style**

Alwawi, F.A.; Swalmeh, M.Z.; Hamarsheh, A.S.
Computational Simulation and Parametric Analysis of the Effectiveness of Ternary Nano-composites in Improving Magneto-Micropolar Liquid Heat Transport Performance. *Symmetry* **2023**, *15*, 429.
https://doi.org/10.3390/sym15020429

**AMA Style**

Alwawi FA, Swalmeh MZ, Hamarsheh AS.
Computational Simulation and Parametric Analysis of the Effectiveness of Ternary Nano-composites in Improving Magneto-Micropolar Liquid Heat Transport Performance. *Symmetry*. 2023; 15(2):429.
https://doi.org/10.3390/sym15020429

**Chicago/Turabian Style**

Alwawi, Firas A., Mohammed Z. Swalmeh, and Abdulkareem Saleh Hamarsheh.
2023. "Computational Simulation and Parametric Analysis of the Effectiveness of Ternary Nano-composites in Improving Magneto-Micropolar Liquid Heat Transport Performance" *Symmetry* 15, no. 2: 429.
https://doi.org/10.3390/sym15020429