# Irreversibility Analysis of Hybrid Nanofluid Flow over a Thin Needle with Effects of Energy Dissipation

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## Abstract

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## 1. Introduction

_{2}H

_{6}O

_{2}) bio fluids, engine oil, polymeric solutions, blends of water and glycol, and other basic fluids are utilized as coolants. To enhance the thermal conductivity of liquid coolants, several researchers played an important role in the past two decades. Choi et al. [15] introduced the idea of boosting the thermal conductivity of working fluids by insertion of nanoparticles. Nanofluids are basically the amalgamation of solid nanoparticles and liquid coolants. This new type of coolant revolutionized the modern industrial world. The nanoparticles have amazing capabilities to increase the heat transfer phenomenon and the thermal conductivity of the working fluid. After the seminal work of Choi et al. [15], several researchers investigated the effects by adding different solid nanoparticles into the various working fluids (base fluids) [16,17,18,19,20,21,22,23,24,25,26]. Recently, an advanced version of nanofluid known as hybrid nanofluid was introduced. Hybrid nanofluid is colloidal suspensions of two distinct nanoparticles in the base fluid. Hybrid nanofluid has numerous applications in medical, lubrication, solar heating, refrigeration, microfluids, electronic cooling, nuclear system cooling, welding, vehicle thermal management, and generator cooling. The hybrid nanofluid works more efficiently as a cooling agent compared to regular nanofluid. Recently, Devi and Devi [27] reported the influences of mass suction on heat transfer in hybrid nanofluid flow over an elastic permeable stretching surface. Afridi et al. [28] compared the flow and heat transfer in two different base fluids and two different hybrid fluid flows by utilizing the three-stage Lobatto IIIA formula. Farooq et al. [29] reported the transpiration effects on entropy generation in hybrid nanofluid flow with energy dissipation. Some recent innovative research on hybrid nanofluid is mentioned in [30,31,32,33,34].

## 2. Mathematical Formulation

## 3. Irreversibility Analysis

## 4. Numerical Solution

- Convert Equations $\left(10\right)$ and $\left(11\right)$ to a set of first order initial value problems.
- The shooting technique is used to determine the missing initial conditions such that the conditions at $\xi \to \infty $ are satisfied.
- Finally, the Fehlberg fourth order Runge-Kutta method (initial value problem method) is utilized to get the required numerical solutions.

## 5. Results and Discussion

## 6. Conclusions

- The temperature and the entropy generation were found to decrease with needle size decrement.
- The velocity profile was reduced with the increment in the size of the needle.
- The velocity of the hybrid nanofluid $Cu-A{l}_{2}{O}_{3}-{H}_{2}O$ was observed to be lower than the regular nanofluid $A{l}_{2}{O}_{3}-{H}_{2}O$, whereas the rate of heat transfer was greater in the hybrid nanofluid as compared to the regular nanofluid.
- A reduction in entropy generation $Ns$ was found by raising the values of $\omega $.
- It was perceived that $Ns$ and temperature distribution were directly proportional to Eckert number $Ec$ and $\varphi $.
- High entropy generation was found in the hybrid nanofluid as compared to the regular one.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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Properties. | Base Fluid (Water) | Al_{2} O_{3} (Aluminum Oxide) | Cu (Copper) |
---|---|---|---|

${c}_{p}\left(J/kgK\right)$ | 4179 | 765 | 385 |

$k\left(W/mK\right)$ | 0.613 | 40 | 401 |

$\rho \left(kg/{m}^{3}\right)$ | 997.1 | 3970 | 8933 |

$\mathrm{Pr}$ | 6.8 | - | - |

**Table 2.**Numerical values of ${g}^{\u2033}(a)$ when ${\varphi}_{1}={\varphi}_{2}=0$ and $\epsilon =0$.

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**MDPI and ACS Style**

Afridi, M.I.; Tlili, I.; Goodarzi, M.; Osman, M.; Khan, N.A.
Irreversibility Analysis of Hybrid Nanofluid Flow over a Thin Needle with Effects of Energy Dissipation. *Symmetry* **2019**, *11*, 663.
https://doi.org/10.3390/sym11050663

**AMA Style**

Afridi MI, Tlili I, Goodarzi M, Osman M, Khan NA.
Irreversibility Analysis of Hybrid Nanofluid Flow over a Thin Needle with Effects of Energy Dissipation. *Symmetry*. 2019; 11(5):663.
https://doi.org/10.3390/sym11050663

**Chicago/Turabian Style**

Afridi, Muhammad Idrees, I. Tlili, Marjan Goodarzi, M. Osman, and Najeeb Alam Khan.
2019. "Irreversibility Analysis of Hybrid Nanofluid Flow over a Thin Needle with Effects of Energy Dissipation" *Symmetry* 11, no. 5: 663.
https://doi.org/10.3390/sym11050663