Numerical Simulation and Mathematical Modeling of Electro-Osmotic Couette–Poiseuille Flow of MHD Power-Law Nanofluid with Entropy Generation
Abstract
:1. Introduction
2. Problem Design
2.1. Physical Considerations
2.2. Electrical Potential Distribution
2.3. Power Law Model
2.4. Governing Equations
2.5. Thermophysical Relations
2.6. Heat Transfer Rate
2.7. Entropy Generation
3. Discussion of Results
3.1. Analytic Solution
3.2. Convergence Inspection
3.3. Graphical Illustration
4. Conclusions
- When the magnetic parameter and nanoparticle volume fraction are increased, then the velocity of the nanofluid decreases whereas the temperature profile is increased.
- Velocity profile is increased for increasing PVC while a decrease in temperature is detected.
- Temperature and velocity demonstrate similar behavior for increasing values of and the ratio between and .
- It is observed that increases at the heated wall against higher Brinkman number and volume fraction while the reverse behavior is noted for the increasing ratio between and . The same phenomena are observed for the cases of electro-osmotic and magnetic factors.
- Skin friction is improved with increasing values of and the ratio between and , whereas it decreases with the increase in Brinkman number, volume fraction and the magnetic parameter.
- The Nusselt number escalates for a snowballing magnetic parameter but de-escalates with the increasing ratio between and , volume fraction, Brinkman number and electro-osmotic factors.
- The entropy generation increases with an increase of volumetric volume expansion , magnetic field and , while it decreases with an increase of and Brinkman number.
- A dual behavior of entropy generation is noted for decreasing and increasing values of .
- The Bejan number escalates by snowballing values of both and magnetic elements in direct relation with each other and is depicted for both of them.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Appendix A
References
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Properties | (J kg−1 K−1) | (K−1) | (kg m−3) | (W m−1 K−1) | (Ns m−2) | |
---|---|---|---|---|---|---|
Al2O3 | 765 | 8.5 × 10−1 | 3970 | 40 | ----- | |
PVC | 2% | 4117.56 | 21.9 | 1006.24 | 0.586 | 0.0015 |
3% | 4085.34 | 21.8 | 1010.25 | 0.579 | 0.00107 | |
4% | 4053.12 | 21.8 | 1014.27 | 0.572 | 0.00114 | |
5% | 4020.9 | 21.8 | 1018.29 | 0.718 | 0.00114 | |
6% | 3988.68 | 21.8 | 1022.31 | 0.559 | 0.00116 | |
7% | 3956.46 | 21.7 | 1026.33 | 0.552 | 0.00119 |
PVC (%) | Consistency Index | Power Index | Shear Stress |
---|---|---|---|
2 | 0.00494 | 0.790 | |
3 | 0.00925 | 0.764 | |
4 | 0.01557 | 0.734 | |
5 | 0.02170 | 0.718 | |
6 | 0.02616 | 0.691 | |
7 | 0.03033 | 0.663 |
Order of Approximation | Time | ||
---|---|---|---|
05 | 8.2651 | 9.8020 × 10−3 | 9.8561 × 10−3 |
10 | 29.3761 | 9.3023 × 10−3 | 7.6511 × 10−3 |
15 | 62.4216 | 2.3452 × 10−3 | 2.2438 × 10−3 |
20 | 100.0125 | 1.0411 × 10−3 | 1.9624 × 10−3 |
0.1 | 0.1 | 0.0 | 0.00317506 | 0.00388072 |
0.2 | 0.00317497 | 0.00388079 | ||
0.3 | 0.00317489 | 0.00388087 | ||
0.4 | 0.00317481 | 0.00388095 | ||
0.0 | 0.00317423 | 0.00388169 | ||
0.5 | 0.00317428 | 0.00388157 | ||
1.0 | 0.00317443 | 0.00388152 | ||
1.5 | 0.00317468 | 0.00388148 | ||
0.0 | 0.00317506 | 0.00388072 | ||
1.0 | 0.00317512 | 0.00388066 | ||
2.0 | 0.00317518 | 0.00388060 | ||
3.0 | 0.00317524 | 0.00388054 |
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Ellahi, R.; Sait, S.M.; Shehzad, N.; Mobin, N. Numerical Simulation and Mathematical Modeling of Electro-Osmotic Couette–Poiseuille Flow of MHD Power-Law Nanofluid with Entropy Generation. Symmetry 2019, 11, 1038. https://doi.org/10.3390/sym11081038
Ellahi R, Sait SM, Shehzad N, Mobin N. Numerical Simulation and Mathematical Modeling of Electro-Osmotic Couette–Poiseuille Flow of MHD Power-Law Nanofluid with Entropy Generation. Symmetry. 2019; 11(8):1038. https://doi.org/10.3390/sym11081038
Chicago/Turabian StyleEllahi, Rahmat, Sadiq M. Sait, N. Shehzad, and N. Mobin. 2019. "Numerical Simulation and Mathematical Modeling of Electro-Osmotic Couette–Poiseuille Flow of MHD Power-Law Nanofluid with Entropy Generation" Symmetry 11, no. 8: 1038. https://doi.org/10.3390/sym11081038
APA StyleEllahi, R., Sait, S. M., Shehzad, N., & Mobin, N. (2019). Numerical Simulation and Mathematical Modeling of Electro-Osmotic Couette–Poiseuille Flow of MHD Power-Law Nanofluid with Entropy Generation. Symmetry, 11(8), 1038. https://doi.org/10.3390/sym11081038