# Significance of Bioconvective and Thermally Dissipation Flow of Viscoelastic Nanoparticles with Activation Energy Features: Novel Biofuels Significance

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## Abstract

**:**

## 1. Introduction

## 2. Mathematical Modeling

- Second-grade fluid model is used to analyze the rheological features of non-Newtonian fluid.
- The Buongiorno’s nanofluid model is utilized to report the Brownian movement and thermophoresis prospective of nanofluids.
- The energy equation can capture the effects thermal radiation, heat absorption/generation and viscous dissipation.
- The activation energy consequences are considered by using famous Arrhenius theory.

## 3. Numerical Scheme

## 4. Validation of Results

## 5. Physical Consequences of Results

## 6. Conclusions

- ❖
- The utilization of second-order slip features controls the movement of fluid particles more effectively.
- ❖
- An upsurges distribution of temperature has been noted for Hartmann number, slip parameters, thermophoresis constant, and radiation parameter.
- ❖
- A lower solute distribution is noted for Schmidt number and viscoelastic parameter.
- ❖
- The presence of viscoelastic parameter, Peclet number and bioconvection parameter decline the gyrotactic microorganism distribution.
- ❖
- The gyrotactic microorganism distribution enhanced with the presence of slip factors.

## Author Contributions

## Conflicts of Interest

## References

- Choi, S.U.S. Enhancing thermal conductivity of fluids with nanoparticles. ASME Pub. Fed.
**1995**, 231, 99–106. [Google Scholar] - Buongiorno, J. Convective transport in nanofluids. J. Heat Transf.
**2006**, 128, 240–250. [Google Scholar] [CrossRef] - Sundar, L.S.; Irurueta, G.; Ramana, E.V.; Singh, M.K.; Sousa, A. Thermal conductivity and viscosity of hybrid nanfluids prepared with magnetic nanodiamond-cobalt oxide (ND-Co3O4) nanocomposite. Case Stud. Therm. Eng.
**2016**, 7, 66–77. [Google Scholar] [CrossRef] [Green Version] - Sheikholeslami, M.; Bhatti, M. Forced convection of nanofluid in presence of constant magnetic field considering shape effects of nanoparticles. Int. J. Heat Mass Transf.
**2017**, 111, 1039–1049. [Google Scholar] [CrossRef] - Hsiao, K.-L. To promote radiation electrical MHD activation energy thermal extrusion manufacturing system efficiency by using Carreau-Nanofluid with parameters control method. Energy
**2017**, 130, 486–499. [Google Scholar] [CrossRef] - Jha, B.K.; Aina, B. Magnetohydrodynamic natural convection flow in a vertical micro-porous-channel in the presence of induced magnetic field. Commun. Nonlinear Sci. Numer. Simul.
**2018**, 64, 14–34. [Google Scholar] [CrossRef] - Mahanthesh, B.; Amala, S.; Gireesha, B.J.; Animasaun, I.L. Effectiveness of exponential heat source, nanoparticle shape factor and Hall current on mixed convective flow of nanoliquids subject to rotating frame. Multidiscip. Model. Mater. Struct.
**2019**, 15, 758–778. [Google Scholar] [CrossRef] - Siddiqui, A.A.; Turkyilmazoglu, M. A New Theoretical Approach of Wall Transpiration in the Cavity Flow of the Ferrofluids. Micromachines
**2019**, 10, 373. [Google Scholar] [CrossRef] [Green Version] - Ahmad, L.; Khan, M. Importance of activation energy in development of chemical covalent bonding in flow of Sisko magneto-nanofluids over a porous moving curved surface. Int. J. Hydrog. Energy
**2019**, 44, 10197–10206. [Google Scholar] [CrossRef] - Khan, M.I.; Alsaedi, A.; Qayyum, S.; Hayat, T.; Khan, M.I. Entropy generation optimization in flow of Prandtl–Eyring nanofluid with binary chemical reaction and Arrhenius activation energy. Colloids Surf. A Physicochem. Eng. Asp.
**2019**, 570, 117–126. [Google Scholar] [CrossRef] - Turkyilmazoglu, M. Buongiorno model in a nanofluid filled asymmetric channel fulfilling zero net particle flux at the walls. Int. J. Heat Mass Transf.
**2018**, 126, 974–979. [Google Scholar] [CrossRef] - Khan, S.U.; Shehzad, S.A. Brownian movement and thermophoretic aspects in third grade nanofluid over oscillatory moving sheet. Phys. Scr.
**2019**, 94, 095202. [Google Scholar] [CrossRef] - Malik, M.Y.; Khan, I.; Hussain, A.; Salahuddin, T. Mixed convection flow of MHD Eyring-Powell nanofluid over a stretching sheet: A numerical study. AIP Adv.
**2015**, 5, 117118. [Google Scholar] [CrossRef] - Jamalabadi, M.Y.A.; Alamian, R.; Yan, W.; Larry, K.; Li, B.; Leveneur, S.; Shadloo, M.S. Effects of Nanoparticle Enhanced Lubricant Films in Thermal Design of Plain Journal Bearings at High Reynolds Numbers. Symmetry
**2019**, 11, 1353. [Google Scholar] [CrossRef] [Green Version] - Afrand, M.; Rostami, S.; Akbari, M.; Wongwises, S.; Esfe, M.H.; Karimipour, A. Effect of induced electric field on magneto-natural convection in a vertical cylindrical annulus filled with liquid potassium. Int. J. Heat Mass Transf.
**2015**, 90, 418–426. [Google Scholar] [CrossRef] - Karimipour, A.; D’Orazio, A.; Shadloo, M.S. The effects of different nano particles of Al 2 O 3 and Ag on the MHD nano fluid flow and heat transfer in a microchannel including slip velocity and temperature jump. Phys. E Low-Dimens. Syst. Nanostruct.
**2017**, 86, 146–153. [Google Scholar] [CrossRef] - Karimipour, A.; Taghipour, A.; Malvandi, A. Developing the laminar MHD forced convection flow of water/FMWNT carbon nanotubes in a microchannel imposed the uniform heat flux. J. Magn. Magn. Mater.
**2016**, 419, 420–428. [Google Scholar] [CrossRef] - Mahmoodi, M.; Esfe, M.H.; Akbari, M.; Karimipour, A.; Afrand, M. Magneto-natural convection in square cavities with a source-sink pair on different walls. Int. J. Appl. Electromagn. Mech.
**2015**, 47, 21–32. [Google Scholar] [CrossRef] [Green Version] - Komeilibirjandi, A.; Raffiee, A.H.; Maleki, A.; Nazari, M.A.; Shadloo, M.S. Thermal conductivity prediction of nanofluids containing CuO nanoparticles by using correlation and artificial neural network. J. Therm. Anal. Calorim.
**2019**, 1–11. [Google Scholar] [CrossRef] - Abbassi, M.A.; Safaei, M.R.; Djebali, R.; Guedri, K.; Zeghmati, B.; Abdullah, A.; Alrashed, A. LBM simulation of free convection in a nanofluid filled incinerator containing a hot block. Int. J. Mech. Sci.
**2018**, 144, 172–185. [Google Scholar] [CrossRef] - Kuznetsov, A. The onset of nanofluid bioconvection in a suspension containing both nanoparticles and gyrotactic microorganisms. Int. Commun. Heat Mass Transf.
**2010**, 37, 1421–1425. [Google Scholar] [CrossRef] - Kuznetsov, A.V. Nanofluid bioconvection in water-based suspensions containing nanoparticles and oxytactic microorganisms: Oscillatory instability. Nanoscale Res. Lett.
**2011**, 6, 100. [Google Scholar] [CrossRef] [Green Version] - Bég, O.A.; Uddin, J.; Khan, W.A. Bioconvective non-newtonian nanofluid transport in porous media containing micro-organisms in a moving free stream. J. Mech. Med. Boil.
**2015**, 15, 1550071. [Google Scholar] [CrossRef] - Lu, D.; Ramzan, M.; Ullah, N.; Chung, J.D.; Farooq, U. A numerical treatment of radiative nanofluid 3D flow containing gyrotactic microorganism with anisotropic slip, binary chemical reaction and activation energy. Sci. Rep.
**2017**, 7, 17008. [Google Scholar] [CrossRef] [Green Version] - Uddin, M.; Khan, W.; Qureshi, S.; Bég, O.A. Bioconvection nanofluid slip flow past a wavy surface with applications in nano-biofuel cells. Chin. J. Phys.
**2017**, 55, 2048–2063. [Google Scholar] [CrossRef] - Sarkar, A.; Das, K.; Kundu, P.K. On the onset of bioconvection in nanofluid containing gyrotactic microorganisms and nanoparticles saturating a non-Darcian porous medium. J. Mol. Liq.
**2016**, 223, 725–733. [Google Scholar] [CrossRef] - Khan, M.I.; Waqas, M.; Hayat, T.; Alsaedi, A.; Khan, M.I. Behavior of stratification phenomenon in flow of Maxwell nanomaterial with motile gyrotactic microorganisms in the presence of magnetic field. Int. J. Mech. Sci.
**2017**, 131, 426–434. [Google Scholar] [CrossRef] - Rashad, A.; Nabwey, H.A. Gyrotactic mixed bioconvection flow of a nanofluid past a circular cylinder with convective boundary condition. J. Taiwan Inst. Chem. Eng.
**2019**, 99, 9–17. [Google Scholar] [CrossRef] - Saini, S.; Sharma, Y.D. Numerical study of nanofluid thermo-bioconvection containing gravitactic microorganisms in porous media: Effect of vertical through flow. Adv. Powder Technol.
**2018**, 29, 2725–2732. [Google Scholar] [CrossRef] - Xun, S.; Zhao, J.; Zheng, L.; Zhang, X. Bioconvection in rotating system immersed in nanofluid with temperature dependent viscosity and thermal conductivity. Int. J. Heat Mass Transf.
**2017**, 111, 1001–1006. [Google Scholar] [CrossRef] - Dhanai, R.; Rana, P.; Kumar, L. Lie group analysis for bioconvection MHD slip flow and heat transfer of nanofluid over an inclined sheet: Multiple solutions. J. Taiwan Inst. Chem. Eng.
**2016**, 66, 283–291. [Google Scholar] [CrossRef] - Mutuku, W.N.; Makinde, O.D. Hydromagnetic bioconvection of nanofluid over a permeable vertical plate due to gyrotactic microorganisms. Comput. Fluids
**2014**, 95, 88–97. [Google Scholar] [CrossRef] - Waqas, H.; Khan, S.U.; Imran, M.; Bhatti, M.M.; Waqas, S.H. Thermally developed Falkner–Skan bioconvection flow of a magnetized nanofluid in the presence of a motile gyrotactic microorganism: Buongiorno’s nanofluid model. Phys. Scr.
**2019**, 94, 115304. [Google Scholar] [CrossRef] - Jamalabadi, M.Y.A.; Ghasemi, M.; Alamian, R.; Wongwises, S.; Afrand, M.; Shadloo, M.S. Modeling of Subcooled Flow Boiling with Nanoparticles under the Influence of a Magnetic Field. Symmetry
**2019**, 11, 1275. [Google Scholar] [CrossRef] [Green Version] - Ahmadi, M.H.; Ahmadi, M.-A.; Maleki, A.; Pourfayaz, F.; Bidi, M.; Açıkkalp, E. Exergetic sustainability evaluation and multi-objective optimization of performance of an irreversible nanoscale Stirling refrigeration cycle operating with Maxwell–Boltzmann gas. Renew. Sustain. Energy Rev.
**2017**, 78, 80–92. [Google Scholar] [CrossRef] - Rashidi, M.M.; Nasiri, M.; Shadloo, M.S.; Yang, Z. Entropy generation in a circular tube heat exchanger using nanofluids: Effects of different modeling approaches. Heat Transf. Eng.
**2017**, 38, 853–866. [Google Scholar] [CrossRef] - Mabood, F.; Ibrahim, S.; Rashidi, M.; Shadloo, M.S.; Lorenzini, G. Non-uniform heat source/sink and Soret effects on MHD non-Darcian convective flow past a stretching sheet in a micropolar fluid with radiation. Int. J. Heat Mass Transf.
**2016**, 93, 674–682. [Google Scholar] [CrossRef] - Ibrahim, W. Magnetohydrodynamics (MHD) flow of a tangent hyperbolic fluid with nanoparticles past a stretching sheet with second order slip and convective boundary condition. Results Phys.
**2017**, 7, 3723–3731. [Google Scholar] [CrossRef] - Alwatban, A.M.; Khan, S.U.; Waqas, H.; Tlili, I. Interaction of Wu’s slip features in bioconvection of Eyring Powell nanoparticles with activation energy. Processes
**2019**, 7, 859. [Google Scholar] [CrossRef] [Green Version] - Khan, S.U.; Waqas, H.; Shehzad, S.A.; Imran, M. Theoretical analysis for tangent hyperbolic nanoparticles with combined electrical MHD, activation energy and Wu’s slip features: A mathematical model. Phys. Scr.
**2019**, 94, 125211. [Google Scholar] [CrossRef]

**Table 1.**Comparison of solution for ${f}^{\u2033}\left(0\right)$ with various values of $M$ when $\alpha =Nr=Nc=Rc=\Gamma =\lambda =0$.

$\mathit{M}$ | Wubshet Ibrahim [38] | Present Results |
---|---|---|

0.0 | 1.0000 | 1.0000 |

1.0 | 1.4142 | 1.4142 |

5.0 | 2.4495 | 2.4496 |

**Table 2.**Variation in $-{f}^{\u2033}\left(0\right)$ for $M,$ $Nr,$ $Nc,$ $\alpha ,$ $\lambda $ and $\Gamma .$

$\mathit{M}$ | $\mathit{N}\mathit{r}$ | $\mathit{N}\mathit{c}$ | $\mathit{\alpha}$ | $\mathit{\lambda}$ | $\mathbf{\Gamma}$ | $-{\mathit{f}}^{\u2033}\left(0\right)$ |
---|---|---|---|---|---|---|

0.1 | 0.5 | 0.5 | 0.1 | 1.0 | −1.0 | 0.3355 |

0.2 | 0.3359 | |||||

0.3 | 0.3361 | |||||

0.1 | 0.3349 | |||||

0.7 | 0.3366 | |||||

1.2 | 0.3381 | |||||

0.1 | 0.3328 | |||||

0.7 | 0.3377 | |||||

1.4 | 0.3434 | |||||

0.2 | 0.3346 | |||||

0.4 | 0.3339 | |||||

0.8 | 0.3335 | |||||

2.0 | 0.2507 | |||||

3.0 | 0.2005 | |||||

4.0 | 0.167 | |||||

−2.0 | 0.2552 | |||||

−3.0 | 0.2077 | |||||

−4.0 | 0.1756 |

**Table 3.**Variation in $-{\theta}^{\prime}\left(0\right)$ for $M,$ $Nr,$ $Nc,$ $\alpha ,$ $\lambda ,$ $\Gamma ,$ $\mathrm{Pr},$ $Nb,$ $Nt$ and $Bi.$

$\mathit{M}$ | $\mathit{N}\mathit{r}$ | $\mathit{N}\mathit{c}$ | $\mathit{\alpha}$ | $\mathit{\lambda}$ | $\mathit{\Gamma}$ | $\mathbf{Pr}$ | $\mathit{N}\mathit{b}$ | $\mathit{N}\mathit{t}$ | $\mathit{B}\mathit{i}$ | $-{\mathit{\theta}}^{\prime}\left(0\right)$ |
---|---|---|---|---|---|---|---|---|---|---|

0.1 | 0.5 | 0.5 | 0.1 | 1.0 | −1.0 | 2.0 | 0.2 | 0.3 | 2.0 | 0.5514 |

0.2 | 0.5433 | |||||||||

0.3 | 0.5360 | |||||||||

0.1 | 0.5254 | |||||||||

0.7 | 0.5218 | |||||||||

1.2 | 0.5188 | |||||||||

0.1 | 0.5310 | |||||||||

0.7 | 0.5189 | |||||||||

1.4 | 0.5037 | |||||||||

0.2 | 0.5258 | |||||||||

0.4 | 0.5278 | |||||||||

0.8 | 0.5300 | |||||||||

2.0 | 0.4759 | |||||||||

3.0 | 0.4436 | |||||||||

4.0 | 0.4207 | |||||||||

−2.0 | 0.4787 | |||||||||

−3.0 | 0.4483 | |||||||||

−4.0 | 0.4267 | |||||||||

1.0 | 0.4318 | |||||||||

3.0 | 0.6012 | |||||||||

5.0 | 0.7149 | |||||||||

0.1 | 0.5246 | |||||||||

0.4 | 0.5264 | |||||||||

0.7 | 0.5267 | |||||||||

0.1 | 0.5318 | |||||||||

0.4 | 0.5229 | |||||||||

0.7 | 0.5142 | |||||||||

1 | 0.4234 | |||||||||

1.4 | 0.4765 | |||||||||

1.8 | 0.5121 |

**Table 4.**Variation in $-{\varphi}^{\prime}\left(0\right)$ for $M,$ $\Lambda ,$ $Nr,$ $Nc,$ $\alpha ,$ $\lambda ,$ $\Gamma ,$ $Nt,$ $Le$ and $Bi.$

$\mathit{M}$ | $\mathit{\Lambda}$ | $\mathit{N}\mathit{r}$ | $\mathit{N}\mathit{c}$ | $\mathit{\alpha}$ | $\mathit{\lambda}$ | $\mathit{\Gamma}$ | $\mathit{N}\mathit{t}$ | $\mathit{L}\mathit{e}$ | $-{\mathit{\varphi}}^{\prime}(0)$ |
---|---|---|---|---|---|---|---|---|---|

0.1 | 0.1 | 0.5 | 0.5 | 0.1 | 1.0 | −1.0 | 0.3 | 2.0 | 0.8271 |

0.2 | 0.8150 | ||||||||

0.3 | 0.8039 | ||||||||

0.1 | 0.6654 | ||||||||

0.2 | 0.5969 | ||||||||

0.3 | 0.5767 | ||||||||

0.1 | 0.7880 | ||||||||

0.7 | 0.7827 | ||||||||

1.2 | 0.7781 | ||||||||

0.1 | 0.7964 | ||||||||

0.7 | 0.7784 | ||||||||

1.4 | 0.7555 | ||||||||

0.2 | 0.7888 | ||||||||

0.4 | 0.7917 | ||||||||

0.8 | 0.7950 | ||||||||

2 | 0.7139 | ||||||||

3 | 0.6653 | ||||||||

4 | 0.6311 | ||||||||

−2 | 0.7181 | ||||||||

−3 | 0.6725 | ||||||||

−4 | 0.6401 | ||||||||

0.1 | 0.2659 | ||||||||

0.4 | 1.0458 | ||||||||

0.7 | 1.7996 | ||||||||

1.0 | 0.7915 | ||||||||

1.4 | 0.7903 | ||||||||

1.8 | 0.7892 |

**Table 5.**Of $-{\chi}^{\prime}\left(0\right)$ for $\alpha ,$ $M,$ $\Lambda ,$ $Nc,$ $Nr,$ $\lambda ,$ $\Gamma ,$ $Pe$ and $Lb.$

$\mathit{M}$ | $\mathit{\Lambda}$ | $\mathit{N}\mathit{r}$ | $\mathit{N}\mathit{c}$ | $\mathit{\alpha}$ | $\mathit{\lambda}$ | $\mathit{\Gamma}$ | $\mathit{P}\mathit{e}$ | $\mathit{L}\mathit{b}$ | $-{\mathit{\chi}}^{\prime}(0)$ |
---|---|---|---|---|---|---|---|---|---|

0.1 | 0.1 | 0.5 | 0.5 | 0.1 | 1.0 | −1.0 | 0.1 | 1.0 | 0.3904 |

0.2 | 0.3777 | ||||||||

0.3 | 0.3665 | ||||||||

0.1 | 0.2170 | ||||||||

0.2 | 0.1795 | ||||||||

0.3 | 0.1708 | ||||||||

0.1 | 0.3510 | ||||||||

0.7 | 0.3453 | ||||||||

1.2 | 0.3403 | ||||||||

0.1 | 0.3602 | ||||||||

0.7 | 0.3404 | ||||||||

1.4 | 0.3146 | ||||||||

0.2 | 0.3518 | ||||||||

0.4 | 0.3542 | ||||||||

0.8 | 0.3556 | ||||||||

2.0 | 0.3000 | ||||||||

3.0 | 0.2669 | ||||||||

4.0 | 0.2441 | ||||||||

−2.0 | 0.3029 | ||||||||

−3.0 | 0.2717 | ||||||||

−4.0 | 0.2500 | ||||||||

0.2 | 0.4310 | ||||||||

0.4 | 0.5902 | ||||||||

0.8 | 0.9119 | ||||||||

1.2 | 0.4070 | ||||||||

1.4 | 0.4603 | ||||||||

1.8 | 0.5611 |

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## Share and Cite

**MDPI and ACS Style**

Waqas, H.; Khan, S.U.; Tlili, I.; Awais, M.; Shadloo, M.S.
Significance of Bioconvective and Thermally Dissipation Flow of Viscoelastic Nanoparticles with Activation Energy Features: Novel Biofuels Significance. *Symmetry* **2020**, *12*, 214.
https://doi.org/10.3390/sym12020214

**AMA Style**

Waqas H, Khan SU, Tlili I, Awais M, Shadloo MS.
Significance of Bioconvective and Thermally Dissipation Flow of Viscoelastic Nanoparticles with Activation Energy Features: Novel Biofuels Significance. *Symmetry*. 2020; 12(2):214.
https://doi.org/10.3390/sym12020214

**Chicago/Turabian Style**

Waqas, Hassan, Sami Ullah Khan, Iskander Tlili, Muhammad Awais, and Mostafa S. Shadloo.
2020. "Significance of Bioconvective and Thermally Dissipation Flow of Viscoelastic Nanoparticles with Activation Energy Features: Novel Biofuels Significance" *Symmetry* 12, no. 2: 214.
https://doi.org/10.3390/sym12020214