Hydromagnetic Flow of Micropolar Nanofluid
Abstract
:1. Introduction
2. Problem Formulation
3. Results and Discussion
4. Conclusions
- ⮚
- The temperature profile falls by improving .
- ⮚
- The Nusselt number enhances with the increase of the chemical reaction effect.
- ⮚
- The Nusselt number improves the higher the magnitude of inclination.
- ⮚
- The Sherwood number upturns by improving the inclination parameter.
- ⮚
- The Sherwood number decreases by improving the chemical reaction impact.
- ⮚
- The Sherwood number reduces the larger the value of .
- ⮚
- The skin friction decreases for higher values of .
- ⮚
- Skin friction decreases with the enhancement of the chemical reaction parameter.
Author Contributions
Acknowledgments
Conflicts of Interest
Nomenclature
Fluid concentration | Heat generation or absorption | Chemical reaction | |||
Skin friction coefficient | Thermal diffusivity | Reynolds number | |||
Ambient nanoparticle volume fraction | Lewis number | Sherwood number | |||
Surface volume fraction | Brownian motion parameter | Fluid temperature | |||
Specific heat at constant pressure | Thermophoretic parameter | Wall temperature | |||
Brownian diffusion coefficient | Nusselt number | Ambient temperature | |||
Thermophoretic diffusion coefficient | Prandtle number | wall velocity | |||
Similarity function for velocity | Gravitational acceleration | ambient velocity | |||
Volume heat capacity | Kinematic viscosity | Dynamic viscosity | |||
Dimensionless solid volume fraction | Condition at the wall | Ambient condition | |||
Local Grashof number | Thermal expansion coefficient | Concentration expansion coefficient | |||
Electric conductivity | Spin gradient viscosity | Vertex viscosity | |||
Micro inertia per unit mass | Inclination parameter | Differentiation with respect to | |||
Velocity in direction | Velocity in direction | Cartesian coordinate | |||
Dimensionless temperature | Suction or injection parameter | Thermal conductivity | |||
Fluid density | Bouncy parameter | Uniform magnetic field strength | |||
Material parameter | Similarity independent variable | ||||
Non-dimensional angular velocity | Stretching rate |
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Khan and Pop [38] | Present Results | ||||
---|---|---|---|---|---|
0.1 | 0.1 | 0.9524 | 2.1294 | 0.9524 | 2.1294 |
0.2 | 0.2 | 0.3654 | 2.5152 | 0.3654 | 2.5152 |
0.3 | 0.3 | 0.1355 | 2.6088 | 0.1355 | 2.6088 |
0.4 | 0.4 | 0.0495 | 2.6038 | 0.0495 | 2.6038 |
0.5 | 0.5 | 0.0179 | 2.5731 | 0.0179 | 2.5731 |
Nb | Nt | Pr | Le | M | K | R | λ1 | S | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0.1 | 0.1 | 7.0 | 5.0 | 0.5 | 1.0 | 1.0 | 0.1 | 0.1 | 0.9 | 0.1 | 45° | 1.1123 | 2.9146 | 1.5227 |
0.5 | 0.1 | 7.0 | 5.0 | 0.5 | 1.0 | 1.0 | 0.1 | 0.1 | 0.9 | 0.1 | 45° | 0.0978 | 3.1368 | 1.5550 |
0.1 | 0.5 | 7.0 | 5.0 | 0.5 | 1.0 | 1.0 | 0.1 | 0.1 | 0.9 | 0.1 | 45° | 0.3667 | 4.5619 | 1.4355 |
0.1 | 0.1 | 10.0 | 5.0 | 0.5 | 1.0 | 1.0 | 0.1 | 0.1 | 0.9 | 0.1 | 45° | 1.1212 | 2.9771 | 1.5206 |
0.1 | 0.1 | 7.0 | 10.0 | 0.5 | 1.0 | 1.0 | 0.1 | 0.1 | 0.9 | 0.1 | 45° | 0.9984 | 4.5817 | 1.5818 |
0.1 | 0.1 | 7.0 | 5.0 | 1.5 | 1.0 | 1.0 | 0.1 | 0.1 | 0.9 | 0.1 | 45° | 1.0760 | 2.9014 | 2.0284 |
0.1 | 0.1 | 7.0 | 5.0 | 0.5 | 3.0 | 1.0 | 0.1 | 0.1 | 0.9 | 0.1 | 45° | 1.1457 | 2.9288 | 2.0779 |
0.1 | 0.1 | 7.0 | 5.0 | 0.5 | 1.0 | 2.0 | 0.1 | 0.1 | 0.9 | 0.1 | 45° | 1.0466 | 3.8926 | 1.5556 |
0.1 | 0.1 | 7.0 | 5.0 | 0.5 | 1.0 | 1.0 | 0.5 | 0.1 | 0.9 | 0.1 | 45° | 0.3832 | 3.4477 | 1.5301 |
0.1 | 0.1 | 7.0 | 5.0 | 0.5 | 1.0 | 1.0 | 0.1 | 1.0 | 0.9 | 0.1 | 45° | 1.1218 | 2.9175 | 1.3303 |
0.1 | 0.1 | 7.0 | 5.0 | 0.5 | 1.0 | 1.0 | 0.1 | 0.1 | 2.0 | 0.1 | 45° | 1.1237 | 2.9185 | 1.2989 |
0.1 | 0.1 | 7.0 | 5.0 | 0.5 | 1.0 | 1.0 | 0.1 | 0.1 | 0.9 | 0.5 | 45° | 2.4776 | 3.0066 | 1.7661 |
0.1 | 0.1 | 7.0 | 5.0 | 0.5 | 1.0 | 1.0 | 0.1 | 0.1 | 1.0 | 0.0 | 45° | 0.8317 | 2.8251 | 1.4666 |
0.1 | 0.1 | 7.0 | 5.0 | 0.5 | 1.0 | 1.0 | 0.1 | 0.1 | 1.0 | −0.5 | 45° | −0.0228 | 1.8648 | 1.2083 |
0.1 | 0.1 | 7.0 | 5.0 | 0.5 | 1.0 | 1.0 | 0.1 | 0.1 | 1.0 | 0.1 | 60° | 1.1092 | 2.9136 | 1.5830 |
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Rafique, K.; Anwar, M.I.; Misiran, M.; Khan, I.; Baleanu, D.; Nisar, K.S.; Sherif, E.-S.M.; Seikh, A.H. Hydromagnetic Flow of Micropolar Nanofluid. Symmetry 2020, 12, 251. https://doi.org/10.3390/sym12020251
Rafique K, Anwar MI, Misiran M, Khan I, Baleanu D, Nisar KS, Sherif E-SM, Seikh AH. Hydromagnetic Flow of Micropolar Nanofluid. Symmetry. 2020; 12(2):251. https://doi.org/10.3390/sym12020251
Chicago/Turabian StyleRafique, Khuram, Muhammad Imran Anwar, Masnita Misiran, Ilyas Khan, Dumitru Baleanu, Kottakkaran Sooppy Nisar, El-Sayed M. Sherif, and Asiful H. Seikh. 2020. "Hydromagnetic Flow of Micropolar Nanofluid" Symmetry 12, no. 2: 251. https://doi.org/10.3390/sym12020251