Impact of the KKL Correlation Model on the Activation of Thermal Energy for the Hybrid Nanofluid (GO+ZnO+Water) Flow through Permeable Vertically Rotating Surface
Abstract
:1. Introduction
2. Mathematical Model of the Problem
- The flow is governed by the vessel wall with the stretching velocity , where and are positive constants with .
- The effective stretching rate enhances subject to an external force acting along the -axis for .
- The Reynolds number (magnetic) is considered to be much less than unity to overcome the impact of the magnetic field induced.
- The magnetic field is applied in the transverse direction to the hybrid nanofluid flow.
3. Similarity Transformations
4. Engineering Quantities of Interest and Their Calculation
5. Solution by the HAM
6. Results and Discussion
Convergence Analysis
7. Conclusions
- The skin friction augments with the rising magnetic parameter, the difference in nanomaterials’ concentrations, and the rotation parameter.
- The Nusselt number rises with the enhancing magnetic field, heat source strength, radiation parameter, and Prandtl number.
- The gradient in the fluid velocity’s horizontal component increases with the enhancing nonsteadiness parameter and has dual dependence on the augmenting magnetic field intensity.
- The horizontal component of the fluid velocity drops with the rising magnetic field and rotation parameter, whereas it rises with the increasing Grashof number.
- The vertical component of the fluid velocity rises with the increasing Grashof number and falls with the enhancing magnetic field strength.
- The hybrid nanofluid’s temperature augments with the enhancing radiation parameter and the heat source strength, while it drops with the increasing Prandtl number, Grashof number, nonsteady parameter, and nanomaterials’ concentrations.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Properties (Thermo-Physical) | |||
---|---|---|---|
GO | 5000 | 3600 | 765 |
HO | 0.613 | 997.1 | 4179 |
ZnO | 25 | 5700 | 523 |
M | ||||
---|---|---|---|---|
0.2 | 0.01 | 0.3 | 0.1 | 1.24321 |
0.4 | 1.49334 | |||
0.6 | 0.03 | 1.58438 | ||
0.06 | 1.67854 | |||
0.5 | 1.79825 | |||
0.7 | 1.98252 | |||
0.3 | 1.82112 | |||
0.5 | 1.64678 |
M | Q | |||||
---|---|---|---|---|---|---|
0.01 | 0.2 | 0.1 | 0.1 | 1 | 6.0 | 0.112530 |
0.03 | 0.223450 | |||||
0.06 | 0.4 | 0.238790 | ||||
0.6 | 0.339988 | |||||
0.3 | 0.441230 | |||||
0.6 | 0.541537 | |||||
0.3 | 0.651980 | |||||
0.6 | 0.767098 | |||||
2 | 0.889043 | |||||
3 | 0.892081 | |||||
6.3 | 0.742980 | |||||
6.6 | 0.705678 |
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Rizk, D.; Ullah, A.; Ikramullah; Elattar, S.; Alharbi, K.A.M.; Sohail, M.; Khan, R.; Khan, A.; Mlaiki, N. Impact of the KKL Correlation Model on the Activation of Thermal Energy for the Hybrid Nanofluid (GO+ZnO+Water) Flow through Permeable Vertically Rotating Surface. Energies 2022, 15, 2872. https://doi.org/10.3390/en15082872
Rizk D, Ullah A, Ikramullah, Elattar S, Alharbi KAM, Sohail M, Khan R, Khan A, Mlaiki N. Impact of the KKL Correlation Model on the Activation of Thermal Energy for the Hybrid Nanofluid (GO+ZnO+Water) Flow through Permeable Vertically Rotating Surface. Energies. 2022; 15(8):2872. https://doi.org/10.3390/en15082872
Chicago/Turabian StyleRizk, Doaa, Asad Ullah, Ikramullah, Samia Elattar, Khalid Abdulkhaliq M. Alharbi, Mohammad Sohail, Rajwali Khan, Alamzeb Khan, and Nabil Mlaiki. 2022. "Impact of the KKL Correlation Model on the Activation of Thermal Energy for the Hybrid Nanofluid (GO+ZnO+Water) Flow through Permeable Vertically Rotating Surface" Energies 15, no. 8: 2872. https://doi.org/10.3390/en15082872