Mixed Convection and Entropy Generation of an Ag-Water Nanofluid in an Inclined L-Shaped Channel
Abstract
:1. Introduction
2. Mathematical Modelling
- At solid walls: U = V = 0;
- Inlet port: U = 0, V = 1, and ;
- Outlet port: V = 0, , ;
- At heat source: ;
- At the others solid walls: , where n is a normal vector.
Nanofluid Relations
3. Numerical Solutions
3.1. Methodology
3.2. Validations
4. Results and Discussion
4.1. Effect of the Reynolds Number
4.2. Effect of the Richardson Number
4.3. Effect of the Aspect Ratio
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Nomenclature
AR | aspect ratio (H/L) |
g | gravitational field (m s−2) |
H | inner side of the channel (m) |
k | thermal conductivity (W m−1 K−1) |
L | outer side of the channel (m) |
Nu | average Nusselt number |
Ri | Richardson number |
Re | Reynolds number |
Sl | entropy generation rate (WK−1·m−3) |
Sgen,m | total entropy generation rate |
T | temperature (K) |
P | pressure (Nm−2) |
u, U | velocity component in x-axis (m·s−1, dimensionless) |
v, V | velocity component in y-axis (m·s−1, dimensionless) |
x, y | Cartesian coordinates (m) |
X, Y | Cartesian coordinates (dimensionless) |
Greek symbols | |
α | thermal diffusivity (m2·s−1) |
β | coefficient of thermal expansion t (K−1) |
ε | performance criterion () |
φ | volume fraction |
λ | inclination of the channel (30°) |
µ | dynamic viscosity (N·s·m−2) |
θ | temperature (dimensionless) |
ρ | density (kg·m−3) |
Ψ | stream function (dimensionless) |
Subscripts | |
c | cold |
f | fluid |
h | hot |
l | local |
m | mean |
nf | nanofluid |
s | solid nanoparticles |
Superscripts | |
* | dimensionless |
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Thermo-Physical Properties | Ag-Nanoparticle | Water (Base Fluid) |
---|---|---|
ρ (kg·m−3) | 10,500 | 997.1 |
Cp (J·kg−1·K−1) | 235 | 4179 |
k (W·m−1·K−1) | 430 | 0.613 |
Β × 10−5 (K−1) | 5.1 | 21 |
µ × 10−4 (kg·m−1·s−1) | - | 8.9 |
α × 10−6 (m−1·s−1) | 149 | 0.14 |
Number of Grids | 40 × 40 | 60 × 60 | 80 × 80 | 100 × 100 | 120 × 120 | 140 × 140 | 160 × 160 |
---|---|---|---|---|---|---|---|
Re = 50 | 10.953 | 11.134 | 11.228 | 11.285 | 11.331 | 11.331 | 11.331 |
Re = 200 | 14.847 | 13.372 | 12.760 | 12.475 | 12.324 | 12.324 | 12.324 |
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Armaghani, T.; Ismael, M.A.; Chamkha, A.J.; Pop, I. Mixed Convection and Entropy Generation of an Ag-Water Nanofluid in an Inclined L-Shaped Channel. Energies 2019, 12, 1150. https://doi.org/10.3390/en12061150
Armaghani T, Ismael MA, Chamkha AJ, Pop I. Mixed Convection and Entropy Generation of an Ag-Water Nanofluid in an Inclined L-Shaped Channel. Energies. 2019; 12(6):1150. https://doi.org/10.3390/en12061150
Chicago/Turabian StyleArmaghani, Taher, Muneer A. Ismael, Ali J. Chamkha, and Ioan Pop. 2019. "Mixed Convection and Entropy Generation of an Ag-Water Nanofluid in an Inclined L-Shaped Channel" Energies 12, no. 6: 1150. https://doi.org/10.3390/en12061150