Magnetic Field Effect on the Double Diffusive Natural Convection in Three-Dimensional Cavity Filled with Micropolar Nanofluid
Abstract
:1. Introduction
2. Mathematical Formulation
3. Numerical Approach and Benchmarking of the Code
- :
- : dimensionless coefficient
- : source term
4. Results and Discussion
4.1. Comparison between the Micropolar Nanofluid and Nanofluid Models
4.2. Effect of Magnetic Field
5. Conclusions
- -
- For a micropolar nanofluid model, both heat and mass transfer rates are smaller than those of a pure nanofluid model.
- -
- Taking in to account particle microrotation, the three-dimensional flow character is weakened.
- -
- For a fixed value of nanoparticle volume fraction with a wide range Rayleigh number, the heat and mass transfer rates are reduced due to increase in the Hartman number.
- -
- For various Rayleigh numbers, the maximum of the transverse velocity enhances for Hartmann numbers lower than a critical value and diminishes as the Hartmann number increases. This critical value moves towards the highest value of the Ha number as increasing the Ra number.
- -
- In the absence of magnetic field, the increase in nanoparticles volume fraction deteriorates the heat and mass transfer. However, for Ha greater than 30, the enhancement of nanoparticle volume fraction increases the heat and mass transfer rates.
- -
- During non-existence of a magnetic field, an increase in vortex viscosity parameter diminishes the average heat and mass transfer rates and is more pronounced when the magnetic field is enforced. However, for Ha greater than 30, the enhancement of nanoparticle volume fraction increases heat and mass transfer rates.
Author Contributions
Funding
Conflicts of Interest
Nomenclature
B0 | Magnetic field strength, N·m−1·A−1 |
C | Dimensionless species concentration, |
D | Species diffusivity, m2/s |
g | Acceleration of gravity, m/s2 |
Dimensionless microrotation vector | |
The microrotation vector, m/s | |
Ha | Hartmann number, dimensionless |
K | Micropolar vortex parameter |
k | Vortex viscosity, kg. m−1·s−1 |
L | Enclosure height, m |
Le | Lewis number, |
N | Buoyancy ratio, |
Average Nusselt number | |
Pr | Prandtl number, |
Ra | Thermal Rayleigh number, |
Average Sherwood number | |
t | Dimensionless time, |
T | Dimensionless temperature, |
Dimensionless velocity | |
x, y, z | Dimensionless Cartesian coordinates, x = x’/L, y = y’/L, z = z’/L |
Greek symbols | |
Thermal diffusivity, m2s−1 | |
βC | Coefficient of compositional expansion, m3kg−1 |
βT | Coefficient of thermal expansion, K−1 |
φ | Solid volume fraction |
λ | Thermal conductivity, Wm−1K−1 |
μ | Dynamic viscosity of the fluid, kg m−1 s−1 |
υ | Kinematic viscosity, m2s−1 |
ρ | Density, kgm−3 |
σ | Electrical conductivity, Ω−1m−1 |
Dimensionless vorticity, | |
Dimensionless vector potential of velocity, | |
Subscripts | |
c | cold |
f | fluid |
h | hot |
l | low |
nf | Al2O3/water nanofluid |
s | solid |
Superscript | |
‘ | dimensional variables |
1 | x-component |
2 | y-component |
3 | z-component |
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Pure Water | Alumina (Al2O3) | |
---|---|---|
Pr | 6.2 | |
ρ (kg/m3) | 997.1 | 8933 |
Cp (J/kg·K) | 4179 | 385 |
k (W/m.K) | 0.613 | 401 |
β (K−1) | 21.10−5 | 1.67.10−5 |
σ (Ω·m)−1 | 0.05 | 1.10−10 |
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Abidi, A.; Raizah, Z.; Madiouli, J. Magnetic Field Effect on the Double Diffusive Natural Convection in Three-Dimensional Cavity Filled with Micropolar Nanofluid. Appl. Sci. 2018, 8, 2342. https://doi.org/10.3390/app8122342
Abidi A, Raizah Z, Madiouli J. Magnetic Field Effect on the Double Diffusive Natural Convection in Three-Dimensional Cavity Filled with Micropolar Nanofluid. Applied Sciences. 2018; 8(12):2342. https://doi.org/10.3390/app8122342
Chicago/Turabian StyleAbidi, Awatef, Zehba Raizah, and Jamel Madiouli. 2018. "Magnetic Field Effect on the Double Diffusive Natural Convection in Three-Dimensional Cavity Filled with Micropolar Nanofluid" Applied Sciences 8, no. 12: 2342. https://doi.org/10.3390/app8122342
APA StyleAbidi, A., Raizah, Z., & Madiouli, J. (2018). Magnetic Field Effect on the Double Diffusive Natural Convection in Three-Dimensional Cavity Filled with Micropolar Nanofluid. Applied Sciences, 8(12), 2342. https://doi.org/10.3390/app8122342