Applied heat transfer modeling in conventional hybrid (Al2O3-CuO)/C2H6O2 and modified-hybrid nanofluids (Al2O3-CuO-Fe3O4)/C2H6O2 between slippery channel by using least square method (LSM)

Adnan; Khalid Abdulkhaliq M. Alharbi; Waqas Ashraf; Sayed M. Eldin; Mansour F. Yassen; Wasim Jamshed; Adnan; Khalid Abdulkhaliq M. Alharbi; Waqas Ashraf; Sayed M. Eldin; Mansour F. Yassen; Wasim Jamshed

doi:10.3934/math.2023215

AIMS Mathematics

2023, Volume 8, Issue 2: 4321-4341. doi: 10.3934/math.2023215

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Applied heat transfer modeling in conventional hybrid (Al₂O₃-CuO)/C₂H₆O₂ and modified-hybrid nanofluids (Al₂O₃-CuO-Fe₃O₄)/C₂H₆O₂ between slippery channel by using least square method (LSM)

1.
Department of Mathematics, Mohi-ud-Din Islamic University, Nerian Sharif 12080, AJ & K, Pakistan
2.
Mechanical Engineering Department, College of Engineering, Umm Al-Qura University, Makkah, 24382, Saudi Arabia
3.
Department of Applied Mathematics and Statistics (AM & S), Institute of Space Technology (IST), 44000 Islamabad, Pakistan
4.
Center of Research, Faculty of Engineering, Future University in Egypt, New Cairo 11835, Egypt
5.
Department of Mathematics, College of Science and Humanities in Al-Aflaj, Prince Sattam Bin Abdulaziz University, Al-Aflaj 11912, Saudi Arabia
6.
Department of Mathematics, Faculty of Science, Damietta University, New Damietta 34517 Damietta, Egypt
7.
Department of Mathematics, Capital University of Science and Technology, Islamabad, Pakistan

Received: 02 October 2022 Revised: 25 November 2022 Accepted: 28 November 2022 Published: 05 December 2022
MSC : 47H09, 47H10

In this research, a new heat transfer model for ternary nanofluid (Al₂O₃-CuO-Fe₃O₄)/C₂H₆O₂ inside slippery converging/diverging channel is reported with innovative effects of dissipation function. This flow situation described by a coupled set of PDEs which reduced to ODEs via similarity and effective ternary nanofluid properties. Then, LSM is successfully coded for the model and achieved the desired results influenced by $ \alpha ,Re,{\gamma }_{1} $ and $ Ec $. It is examined that the fluid movement increases for $ Re $ in the physical range of 30–180 and it drops for diverging channel ($ \alpha > 0 $) when the slippery wall approaches to $ \alpha = {60}^{o} $. The fluid movement is very slow for increasing concentration factor $ {\varphi }_{i} $ for $ i = \mathrm{1,2},3 $ up to 10%. Further, ternary nanofluid temperature boosts rapidly due to inclusion of trinanoparticles thermal conductivity and dissipation factor ($ Ec = \mathrm{0.1,0.2,0.3,0.4,0.6} $) also contributes significantly. Moreover, the temperature is maximum about the center of the channel ($ \eta = 0 $) and slip effects ($ {\gamma }_{1} = \mathrm{0.1,0.2,0.3,0.4,0.5,0.6} $) on the channel walls lead to decrement in the temperature $ \beta \left(\eta \right) $.
- heat transfer,
- hybrid nanofluids,
- modified hybrid nanofluids,
- (Al₂O₃,
- CuO,
- Fe₃O₄) nanoparticles,
- converging/diverging channel,
- least square method
Citation: Adnan, Khalid Abdulkhaliq M. Alharbi, Waqas Ashraf, Sayed M. Eldin, Mansour F. Yassen, Wasim Jamshed. Applied heat transfer modeling in conventional hybrid (Al2O3-CuO)/C2H6O2 and modified-hybrid nanofluids (Al2O3-CuO-Fe3O4)/C2H6O2 between slippery channel by using least square method (LSM)[J]. AIMS Mathematics, 2023, 8(2): 4321-4341. doi: 10.3934/math.2023215

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Abstract

In this research, a new heat transfer model for ternary nanofluid (Al₂O₃-CuO-Fe₃O₄)/C₂H₆O₂ inside slippery converging/diverging channel is reported with innovative effects of dissipation function. This flow situation described by a coupled set of PDEs which reduced to ODEs via similarity and effective ternary nanofluid properties. Then, LSM is successfully coded for the model and achieved the desired results influenced by $ \alpha ,Re,{\gamma }_{1} $ and $ Ec $. It is examined that the fluid movement increases for $ Re $ in the physical range of 30–180 and it drops for diverging channel ($ \alpha > 0 $) when the slippery wall approaches to $ \alpha = {60}^{o} $. The fluid movement is very slow for increasing concentration factor $ {\varphi }_{i} $ for $ i = \mathrm{1,2},3 $ up to 10%. Further, ternary nanofluid temperature boosts rapidly due to inclusion of trinanoparticles thermal conductivity and dissipation factor ($ Ec = \mathrm{0.1,0.2,0.3,0.4,0.6} $) also contributes significantly. Moreover, the temperature is maximum about the center of the channel ($ \eta = 0 $) and slip effects ($ {\gamma }_{1} = \mathrm{0.1,0.2,0.3,0.4,0.5,0.6} $) on the channel walls lead to decrement in the temperature $ \beta \left(\eta \right) $.

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