Numerical Study of 3D MHD Mixed Convection and Entropy Generation in Trapezoidal Porous Enclosure Filled with a Hybrid Nanofluid: Effect of Zigzag Wall and Spinning Inner Cylinder
Abstract
:1. Introduction
2. Studied Configuration and Mathematical Formulation
2.1. Mathematical Model
The Thermophysical Properties of the Hybrid Nanoliquid
2.2. Boundary Conditions
The Total Entropy Generation
3. Mesh Sensitivity, Computation Procedure and Code Validation
3.1. Mesh Sensitivity
3.2. Computation Procedure
3.3. Code Validation
4. Results and Discussion
4.1. The Effect of Darcy Number and the Addition of Different Concentrations of Nanoparticles on Heat Transfer and Flow Behavior
4.2. The Effect of the Hartman Number on Heat Transfer and Flow Behavior
4.3. The Effect of the Rotation Velocity of the Cylinder on the Heat Transfer and the Flow Behavior
4.4. The Effect of the Zigzag Pattern of the Hot Wall on the Heat Transfer and the Flow Behavior
4.5. The Effect of Nanoparticle Amount and Darcy and Hartman Numbers on the Evolution of the Average Nusselt Number
4.6. The Effect of Cylinder Rotation Speed and Darcy and Hartman Numbers on the Evolution of the Average Nusselt Number
4.7. The Effect of Cylinder Rotation Speed, Hartman Number, and Hot Wall Zigzag Pattern on the Evolution of the Average Nusselt Number
4.8. The Effect of Darcy Number and Adding Different Concentrations of Nanoparticles on Bejan Number Development
4.9. The Effect of Darcy and Hartman Numbers on Bejan Number Development
4.10. The Effect of the Hartman Number and Cylinder Angular Velocity on Bejan Number Development
4.11. The Effect of Hot Wall Number of Undulations and Cylinder Angular Velocity on Bejan Number Development
4.12. The Effect of the Nanoparticle Concentration and Darcy and Hartman Numbers on the Development of the Average Bejan Number
4.13. The Effect of the Tube Rotation Speed and Darcy and Hartman Numbers on the Development of the Average Bejan Number
4.14. The Effect of the Tube Rotation Speed, the Hot Wall Zigzag Pattern, and the Hartman Number on the Development of the Average Bejan Number
5. Conclusions
- The fluidity of the fluid is stronger with increasing Darcy number and rotating velocity of the inner tube.
- High values of Hartman number result in a significant stagnation of flow motion.
- Increasing the concentration of nanoparticles leads to an increase in the thermal conductivity of the fluid; hence, the heat spread reaches high values.
- The maximum values of average Nusselt number were reached with high numbers of zigzag undulations in the hot wall with the lowest values of Hartman number.
- The Darcy number and the rotating speed of the inner tube positively affect Nu and heat transfer rate at high values.
- The average Nusselt number increases with greater domination of forced convection, while forced convection increases with increasing inner tube spinning rate and Darcy number when there is no magnetic field.
- The entropy generation due to fluid friction is related to fluid fluidity. It increases with both increasing Darcy number and increasing angular velocity of the inner cylinder or with both decreasing Hartman number and decreasing nanoparticle amount.
- The Bejan number decreases with both increasing Darcy number and increasing angular velocity of the inner cylinder or with decreasing Hartman number and nanoparticle amount.
- High numbers of undulations in the hot wall play an important role in reducing the irreversibility phenomenon by increasing the fluid movement inside the cavity (i.e., increasing the friction in the fluid).
Author Contributions
Funding
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclatures
Symbols | |
B | Magnetic field |
Be | Bejan number |
cp | Specific heat (J·kg−1·K−1) |
Da | Darcy number |
g | Gravitational acceleration, (m·s−2) |
Ha | Hartman number |
k | Thermal conductivity, (W·m−1·K−1) |
L | Cavity width, (m) |
Nu | Nusselt number |
p | Pressure, (Pa) |
P | Dimensionless pressure |
Pr | Prandtl number |
R | The dimensionless radius of the cylinder |
r | The radius of the cylinder |
Ra | Rayleigh number |
Re | Reynolds number |
Ri | Richardson number |
S | Entropy generation |
T | Temperature, (K) |
u, v, w | Velocities in x, y, z-directions, (m·s−1) |
U, V, W | Dimensionless velocities component in X, Y, Z-directions |
X, Y, Z | Dimensionless coordinates in x, y, and z directions |
Greek letters | |
Thermal diffusivity (m2·s−1) | |
Thermal expansion coefficient (K−1) | |
Porosity | |
Dimensionless temperature | |
Permeability (m2) | |
Dynamic viscosity (Pa.s) | |
Kinematic viscosity (m2·s−1) | |
Density (kg/m3) | |
Electrical conductivity (Ω−1·m−1) | |
Nanoparticle concentration | |
Dimensionless angular rotational velocity | |
Angular rotational velocity (rad·s−1) | |
Subscript | |
eff | Effective |
f | fluid |
ff | Fluid friction |
hnf | Hybrid nanofluid |
mf | Magnetic field |
nf | Nanofluid |
np | Nanoparticle |
s | Solid matrix |
th | Thermal |
tot | Total |
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Property | Water | MoS2 | GO |
---|---|---|---|
(kg·m−3) | 997.1 | 5060 | 1800 |
Heat capacity, Cp (J·kg−1·K−1) | 4179 | 397.21 | 717 |
(W·m−1·K−1) | 0.613 | 904.4 | 5000 |
(K−1) | 5.8 × 10−4 | 2.8424 × 10−5 | 2.84 × 10−4 |
(Ω−1·m−1) | 9.75 × 10−4 | 2.09 × 104 | 6.30 × 107 |
Dynamic viscosity, μ (Pa.s) | 0.001003 | - | - |
Property | Classical Nanofluid | Hybrid Nanofluid |
---|---|---|
Density | ||
Heat capacity | ||
Coefficient of thermal expansion | ||
Electrical conductivity | ||
Thermal conductivity | ||
Viscosity | ||
Thermal Condition | Velocity Condition | |
---|---|---|
The inclined Lift wall | Adiabatic | (no-slip) |
The inclined right wall | adiabatic | (no-slip) |
The top wall | adiabatic | (no-slip) |
The Bottom wall | adiabatic | (no-slip) |
The zigzag wall | (no-slip) | |
The front wall of the zigzag one | (no-slip) | |
The central tube wall | adiabatic |
Total Number of Elements | Average Nusselt Number | |
---|---|---|
N = 4 | 137,688 | 2.0245 |
N = 2 | 69,639 | 1.7521 |
N = 1 | 69,180 | 2.0041 |
N = 4 | 348,525 | 2.2758 |
N = 2 | 182,971 | 1.8745 |
N = 1 | 181,506 | 2.0940 |
N = 4 | 994,968 | 2.3167 |
N = 2 | 590,354 | 1.9595 |
N = 1 | 586,133 | 2.1472 |
N = 4 | 3,958,438 | 2.3174 |
N = 2 | 2,542,173 | 1.9599 |
N = 1 | 2,519,898 | 2.1502 |
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Maneengam, A.; Bouzennada, T.; Abderrahmane, A.; Ghachem, K.; Kolsi, L.; Younis, O.; Guedri, K.; Weera, W. Numerical Study of 3D MHD Mixed Convection and Entropy Generation in Trapezoidal Porous Enclosure Filled with a Hybrid Nanofluid: Effect of Zigzag Wall and Spinning Inner Cylinder. Nanomaterials 2022, 12, 1974. https://doi.org/10.3390/nano12121974
Maneengam A, Bouzennada T, Abderrahmane A, Ghachem K, Kolsi L, Younis O, Guedri K, Weera W. Numerical Study of 3D MHD Mixed Convection and Entropy Generation in Trapezoidal Porous Enclosure Filled with a Hybrid Nanofluid: Effect of Zigzag Wall and Spinning Inner Cylinder. Nanomaterials. 2022; 12(12):1974. https://doi.org/10.3390/nano12121974
Chicago/Turabian StyleManeengam, Apichit, Tarek Bouzennada, Aissa Abderrahmane, Kaouther Ghachem, Lioua Kolsi, Obai Younis, Kamel Guedri, and Wajaree Weera. 2022. "Numerical Study of 3D MHD Mixed Convection and Entropy Generation in Trapezoidal Porous Enclosure Filled with a Hybrid Nanofluid: Effect of Zigzag Wall and Spinning Inner Cylinder" Nanomaterials 12, no. 12: 1974. https://doi.org/10.3390/nano12121974