# Trace of Chemical Reactions Accompanied with Arrhenius Energy on Ternary Hybridity Nanofluid Past a Wedge

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## Abstract

**:**

## Highlights

**What are the main findings?**

- The problem of 2-D Prandtl nanofluid past a moving wedge is investigated in detail;
- Tri-hybrid nanoparticles are considered here;
- Heat and mass transmission evaluations are conducted in the presence of endothermic/exothermic chemical reactions;
- The moving wedge is considered;

**What is the implication of the main finding?**

- LobattoIIIA scheme is implemented for the numerical solution of modeled PDEs.

## Abstract

**Purpose:**In this attempt, the effect of endothermic/exothermic chemical reactions accompanied by activation energy on a ternary hybrid nanofluid with the geometry of a wedge is taken into consideration. The mathematical form of PDEs is obtained by Navier–Stokes equations, the second law of thermodynamics, and Fick’s second law of diffusion. The geometric model is therefore described using a symmetry technique.

**Formulation:**The MATLAB built-in Lobatto III A structure is utilized to find the computational solution of the dimensionless ODEs. All computational outcomes are presented by graphs and statistical graphs in order to check the performance of various dimensionless quantities against drag force factor and Nusselt quantity.

**Finding:**the addition of tri-hybridizing nanomolecules in the standard liquid improves the thermic performance of the liquid much better in comparison to simple hybrid nanofluids. Wedge angle parameter $\alpha $ brings about a decrement in fluid velocity and augmentation in thermal conductivity $\u03f5$, thermal radiation $Rd$, thermophoresis parameter $Nt$ and endothermic/exothermic reaction $\Omega $, and fitted rate constant $n$ accelerates the heat transmission rate.

**Novelty:**The effect of tri-hybridizing nanomolecules along with endothermic/exothermic reactions on the fluid past a wedge have not been investigated before in the available literature.

## 1. Introduction

_{2}aquatic ternary hybridizing nanoliquid. The latest study regarding the development of practical correlations and viscidness and thermal conducting of H

_{2}O-Cu-SiO

_{2}-MWCNT attaching the mathematical model of ternary hybrid nanofluid by Dezfulizade et al. [7].

## 2. Mathematical Formulation

## 3. Physical Quantities

## 4. Solution Methodology

## 5. Step-By-Step Graphical Detail of the Present Problem

#### 5.1. Problem Formulation

#### 5.2. Modelling

#### 5.3. Numerical Process

#### 5.4. Numerical Results

#### 5.5. Analysis

## 6. Results and Discussions

## 7. Testing of Code

## 8. Concluding Remarks

- The addition of tri-hybrid nanomolecules in the standard liquid boosts the thermal performance of the liquid which eventually lessens the fluid viscosity;
- The amplification in the fluid parameter $B$ devalues the liquid viscidness and upsurges the liquid rapidity.
- A larger wedge $m$ brings about magnification in fluid viscosity contributing to viscous forces dominating the shear forces and depreciating the velocity field.
- Wedge angle parameter α brings about a decrement in fluid velocity. Amplification in α provides resistance to the fluid which helps the fluid to become denser and more viscous. As a result, the velocity field diminishes.
- Buoyancy forces dominate the viscous forces by virtue of magnification in the buoyancy parameter ${\gamma}_{1}$. Positive variation in buoyancy parameter ${\gamma}_{1}$ amplifies the fluid density which depreciates the Grashoff number Gr and the fluid velocity.
- Thermophoresis diffusion phenomenon ${N}_{t}$ migrates the hot fluid molecules from the warm region to the coldish zone. As a result, the temperature field increases.
- In the case of exothermic reaction $\Omega >0$, heat is released by a system that gives a reduction in the liquid temperature. Examples are fuel combustion, heat pumps, heat engines, refrigerators, etc. Heat is absorbed by the fluid in the case of exothermic reaction $\Omega <0$. Examples are absorption chillers, ammonia absorption refrigeration systems, photosynthesis, etc.
- Chemical reaction takes place which enhances the heat transfer rate and $\theta \left(\eta \right)$. Physical examples are the combustion of fuels, detonation of explosives, reaction of acids with metals, etc.
- Amplification in thermal conductivity $\u03f5$ amplifies the temperature. That is why the insertion of copper nanoparticles instead of any other sort of nanoparticles delivers more heat because they have more thermal conductivity than other metallic nanoparticles.
- Positive variation in activation energy $Q$ amplifies the fluid concentration and depreciates the thermal performance of the fluid. Enzyme reactions are a good example of activation energy.
- It is noted that an augmentation in thermal conductivity $\u03f5$, thermal radiation $Rd$, thermophoresis parameter $Nt$, endothermic/exothermic reaction $\Omega $, and fitted rate n escalate the heat transmission rate, while the opposite behavior is reported in the status of keeping factors such as Prandtl number $Pr$, ${\beta}_{1}$, Schmidt number $Sc$, Brownian parameter $Nb$, activation energy $Q$, temperature difference $\delta $.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

$Q$ | activation energy | $\delta $ | temperature difference |

$n$ | power law indicator | $Nt$ | thermophoretic diffusion |

$Nb$ | Brownian diffusion | $B$ | elastic parameter |

${\gamma}_{1}$ | buoyancy parameter | $Gr$ | Grashof quantity |

$\u03f5$ | thermal conductivity | $C{f}_{x}$ | Frictional force |

${\beta}_{1}$ | reaction rate | $Rd$ | radiative variable |

$Pr$ | Prandtl number | ${q}_{r}$ | radiant heat fluxing |

$N$ | Sustentation factor | $A$ | Prandtl fluid parameter |

$\lambda $ | buoyancy ratio parameter | ${\alpha}_{thnf}$ | thermal diffusion |

${\rho}_{thnf}$ | consistency | ${k}_{thnf}$ | thermal conducting |

${C}_{p}$ | specific heat | ${\kappa}^{*}$ | absorbed factor |

${\sigma}^{*}$ | Stefan-Boltzmann value |

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**Figure 3.**(

**a**). Novel effects. (

**b**). Transformation step. (

**c**). Numerical process. (

**d**). Computed quantities.

Properties | Ethylene Glycol (EG) | Al_{2}O_{3} | TiO_{2} | SiO_{2} |
---|---|---|---|---|

$\rho $ | 1115 | 6310 | 4250 | 2270 |

${C}_{p}$ | 4179 | 773 | 690 | 765 |

$k$ | 0.253 | 32.9 | 8.953 | 1.4013 |

**Table 2.**Comparison analysis of the obtained results with existing literature for the case of ${f}^{\u2033}\left(0\right)$ for various values of $m$.

$\mathit{m}$ | Ref. [38] | Ref. [39] | Ref. [40] | Present Results |
---|---|---|---|---|

0.0 | 0.46960 | 0.46960 | 0.46961 | 0.46970 |

0.1 | 0.65510 | 0.65511 | 0.65509 | 0.65510 |

0.2 | 0.80210 | 0.80210 | 0.80211 | 0.80221 |

0.3 | 0.92760 | 0.92760 | 0.92771 | 0.92780 |

0.5 | 1.03850 | 1.03860 | 1.03892 | 1.03911 |

1.0 | 1.13250 | 1.23260 | 1.23261 | 1.23282 |

Parameters | Skin Friction |
---|---|

${\gamma}_{1}=0.2$ | 6.03433 |

${\gamma}_{1}=0.4$ | 6.03418 |

${\gamma}_{1}=0.4$ | 6.03406 |

$\lambda =-0.2$ | 6.17675 |

$\lambda =0.0$ | 7.33591 |

$\lambda =0.2$ | 8.26719 |

$N=0.2$ | 7.89913 |

$N=0.4$ | 9.66534 |

$N=0.6$ | 11.45915 |

${\beta}_{1}=1.0$ | 7.28419 |

${\beta}_{1}=2.0$ | 7.35732 |

${\beta}_{1}=3.0$ | 7.68177 |

$\mathit{\u03f5}$ | $\mathit{R}\mathit{d}$ | $\mathit{P}\mathit{r}$ | $\mathit{N}\mathit{b}$ | $\mathit{N}\mathit{t}$ | $\mathit{\Omega}$ | ${\mathit{\beta}}_{1}$ | $\mathit{\delta}$ | $\mathit{n}$ | $\mathit{Q}$ | $\mathit{S}\mathit{c}$ | $\mathit{N}{\mathit{u}}_{\mathit{x}}\mathit{R}{\mathit{e}}_{\mathit{x}}^{1/2}$ | $\mathit{S}{\mathit{h}}_{\mathit{x}}\mathit{R}{\mathit{e}}_{\mathit{x}}^{1/2}$ |
---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 1 | 1.7 | 1 | 0.5 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | 0.5 | 4.9383 | 2.3428 |

2 | 5.9218 | 2.3437 | ||||||||||

3 | 6.9050 | 2.3448 | ||||||||||

4 | 7.8888 | 2.3458 | ||||||||||

2 | 4.1025 | 3.3490 | ||||||||||

3 | 5.7546 | 3.3534 | ||||||||||

4 | 6.3993 | 3.3967 | ||||||||||

3 | 3.0691 | 2.3342 | ||||||||||

4 | 3.5236 | 1.9310 | ||||||||||

5 | 4.1573 | 1.3294 | ||||||||||

2 | 4.8302 | 3.3665 | ||||||||||

3 | 5.7312 | 2.3740 | ||||||||||

4 | 6.6413 | 1.3774 | ||||||||||

1 | 3.8959 | 2.3150 | ||||||||||

1.5 | 2.8556 | 1.9948 | ||||||||||

2 | 1.8173 | 1.2814 | ||||||||||

0.3 | 2.9229 | 2.3443 | ||||||||||

0.5 | 1.9074 | 2.3459 | ||||||||||

0.7 | 0.8920 | 2.3475 | ||||||||||

0.3 | 3.9246 | 2.3110 | ||||||||||

0.5 | 2.9114 | 2.2779 | ||||||||||

0.7 | 1.8987 | 2.2496 | ||||||||||

0.3 | 3.9387 | 2.3437 | ||||||||||

0.5 | 2.9391 | 3.3545 | ||||||||||

0.7 | 1.9395 | 4.4454 | ||||||||||

0.3 | 4.9384 | 3.3460 | ||||||||||

0.5 | 3.9400 | 2.3528 | ||||||||||

0.7 | 2.9596 | 1.3776 | ||||||||||

0.3 | 6.9396 | 3.3457 | ||||||||||

0.5 | 5.9406 | 4.3480 | ||||||||||

0.7 | 4.9415 | 5.3500 | ||||||||||

1 | 2.9262 | 4.4540 | ||||||||||

1.5 | 2.8827 | 3.5228 | ||||||||||

2 | 2.7218 | 2.5726 |

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**MDPI and ACS Style**

Sajid, T.; Ayub, A.; Shah, S.Z.H.; Jamshed, W.; Eid, M.R.; El Din, E.S.M.T.; Irfan, R.; Hussain, S.M.
Trace of Chemical Reactions Accompanied with Arrhenius Energy on Ternary Hybridity Nanofluid Past a Wedge. *Symmetry* **2022**, *14*, 1850.
https://doi.org/10.3390/sym14091850

**AMA Style**

Sajid T, Ayub A, Shah SZH, Jamshed W, Eid MR, El Din ESMT, Irfan R, Hussain SM.
Trace of Chemical Reactions Accompanied with Arrhenius Energy on Ternary Hybridity Nanofluid Past a Wedge. *Symmetry*. 2022; 14(9):1850.
https://doi.org/10.3390/sym14091850

**Chicago/Turabian Style**

Sajid, Tanveer, Assad Ayub, Syed Zahir Hussain Shah, Wasim Jamshed, Mohamed R. Eid, El Sayed M. Tag El Din, Rida Irfan, and Syed M. Hussain.
2022. "Trace of Chemical Reactions Accompanied with Arrhenius Energy on Ternary Hybridity Nanofluid Past a Wedge" *Symmetry* 14, no. 9: 1850.
https://doi.org/10.3390/sym14091850