MHD Heat Transfer in W-Shaped Inclined Cavity Containing a Porous Medium Saturated with Ag/Al2O3 Hybrid Nanofluid in the Presence of Uniform Heat Generation/Absorption
Abstract
:1. Introduction
2. Numerical Model
2.1. Simplifying Assumptions
- A thermal equilibrium is supposed between the water base fluid and the nanoparticles;
- The nanofluid is supposed to be Newtonian and incompressible;
- The flow is assumed to be steady and laminar;
- The radiation, the dissipation and Joule heating effects, the displacement currents and the induced magnetic field are neglected.
2.2. Boundary Conditions
2.3. Non-Dimensional Governing Equations
2.4. Nusselt Number Calculation
2.5. Solution Procedure and Grid Sensitivity Test
3. Results and Discussion
3.1. Validation
3.2. Effect of Rayleigh and Hartmann Numbers
3.3. Effect of Darcy Number
3.4. Effect of the Aspect Ratio of the W-Shaped Enclosure
3.5. Effect of the Inclination of the W-Shaped Cavity
3.6. Effect of the Fraction of Ag in the Volumetric Fraction of Nanoparticles
4. Conclusions
- The increase of the Rayleigh and Darcy numbers leads to the intensification of the hydrodynamic flow near the boundary heated walls and improves the convection heat transfer performance inside the cavity.
- The increase of the Hartmann number attenuates the convection heat transfer inside the cavity; this effect is insignificant for the case of an aspect ratio of AR = 0.7.
- The augmentation of the aspect ratio intensifies the hydrodynamic field and ameliorates the heat convection heat transfer performance. The convection heat transfer reaches a maximum for AR = 0.7.
- The average Nusselt number reaches its maximum for an angle of inclination and a minimum for ; the effect of the inclination angle is negligible for an aspect ratio of AR = 0.7.
- The convection heat transfer performance is ameliorated with the addition of composite nanoparticles. This effect is proportional to the increase of Rayleigh and Darcy numbers, the aspect ratios and the fraction of Ag in the volumetric fraction of nanoparticles.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Nomenclature
AR | Aspect ratio, H/L |
Magnetic field strength | |
Bf | Length of baffle |
Cp | Specific heat, |
Da | Darcy number |
Fr | Fraction of Ag in the volumetric fraction of nanoparticles |
g | Gravitational acceleration, |
Grashof number | |
H | Width of corrugation of cavity (m) |
Ha | Hartmann number |
K | Permeability of porous medium, |
k | Thermal conductivity, |
L | Length of cavity, (m) |
Nu | Nusselt number |
p | Fluid pressure, |
p* | Dimensionless pressure |
Pr | Prandtl number |
q* | Dimensionless heat generation or absorption |
Ra | Rayleigh number |
T | Temperature, |
T* | Dimensionless temperature |
u, v, | Velocity components in x, and y directions |
u*, v* | Dimensionless velocity components |
x, y, | Cartesian coordinates |
x*, y* | Dimensionless coordinates |
Greek symbols | |
α | Thermal diffusivity |
σ | Electrical conductivity, |
Solid volume fraction of Ag nanoparticles | |
Solid volume fraction of nanoparticles | |
β | Expansion coefficient, |
ρ | Local density, |
Temperature difference, | |
μ | Dynamic viscosity, |
ν | Cinematic viscosity, |
Angle of inclination | |
Subscripts | |
c | Cold wall |
h | Hot wall |
Hybrid nanofluid | |
f | Fluid |
l | Local |
m | Average |
p | Nanoparticle |
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Border | Condition On u* | Condition On v* | Condition On T* |
---|---|---|---|
1 | 0 | 0 | 1 |
2 | 0 | 0 | 0 |
3 | 0 | 0 | 0 |
4 | 0 | 0 | 0 |
5 | 0 | 0 | 0 |
6 | 0 | 0 | |
7 | 0 | 0 |
Basic Fluid and Nanoparticles | Pr | Cp (J/kg·K) | k (W/m·K) | |||
---|---|---|---|---|---|---|
Ethylene Glycol | 151 | 1109 | 2400 | 0.26 | 65 | 0.0163 |
Al2O3 | 3970 | 765 | 40 | 0.85 | - | |
Ag | 10,500 | 535.6 | 429 | 0.85 | - |
Predefined Mesh Size | Mesh Elements | CPU Time (s) | |
---|---|---|---|
Extremely coarse | 1846 | 4.6897 | 4.63 |
Extra coarse | 2210 | 4.6924 | 5.589 |
Coarser | 3092 | 4.6976 | 7.56 |
Coarse | 3654 | 4.6974 | 9.072 |
Normal | 4608 | 4.6980 | 11.475 |
Fine | 4710 | 4.6980 | 12.796 |
Finer | 5784 | 4.6984 | 14.901 |
Extra fine | 9182 | 4.6980 | 20.765 |
Extremely fine | 28,368 | 4.6981 | 108.848 |
Ha | [17] | |
---|---|---|
0 | 7.4103 | 7.4019 |
10 | 7.1514 | 7.1315 |
20 | 6.5125 | 6.5059 |
30 | 5.8725 | 5.8709 |
40 | 5.17 | 5.1612 |
50 | 4.5505 | 4.5483 |
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Dhia Massoudi, M.; Ben Hamida, M.B.; Mohammed, H.A.; Almeshaal, M.A. MHD Heat Transfer in W-Shaped Inclined Cavity Containing a Porous Medium Saturated with Ag/Al2O3 Hybrid Nanofluid in the Presence of Uniform Heat Generation/Absorption. Energies 2020, 13, 3457. https://doi.org/10.3390/en13133457
Dhia Massoudi M, Ben Hamida MB, Mohammed HA, Almeshaal MA. MHD Heat Transfer in W-Shaped Inclined Cavity Containing a Porous Medium Saturated with Ag/Al2O3 Hybrid Nanofluid in the Presence of Uniform Heat Generation/Absorption. Energies. 2020; 13(13):3457. https://doi.org/10.3390/en13133457
Chicago/Turabian StyleDhia Massoudi, Mohamed, Mohamed Bechir Ben Hamida, Hussein A. Mohammed, and Mohammed A. Almeshaal. 2020. "MHD Heat Transfer in W-Shaped Inclined Cavity Containing a Porous Medium Saturated with Ag/Al2O3 Hybrid Nanofluid in the Presence of Uniform Heat Generation/Absorption" Energies 13, no. 13: 3457. https://doi.org/10.3390/en13133457