Numerical Study of Laminar Flow and Convective Heat Transfer Utilizing Nanofluids in Equilateral Triangular Ducts with Constant Heat Flux
Abstract
:1. Introduction
2. Mathematical Modeling
2.1. Assumptions and Governing Equations
2.2. Physical Properties of the Nanofluid
2.2.1. Density and Heat Capacity
2.2.2. Viscosity
2.2.3. Thermal Conductivity
2.3. Boundary Conditions
2.4. Solver
- Guess the pressure p*.
- Solve the momentum equations to obtain u*, v*, w*. Notice that unless the correct pressure field is employed, the resulting velocity field will not satisfy the continuity equation. Such an imperfect field based on a guessed pressure field p* will be denoted by u*, v*, w*.
- Solve p′ equation. p′ is the pressure correction.
- Calculate corrected pressure p (p = p* + p′).
- Calculate corrected velocity components u, v, w (u= u* + u′, v = v* + v′, w = w* + w′). u′, v′, and w′ are the velocity corrections for u, v, and w, respectively.
- Solve other variables (such as T).
- Treat the corrected pressure p as a new guessed pressure p*.
3. Results and Discussion
3.1. Grid-Independence Analysis
3.2. Validation
3.3. Effects of Peclet Number and Particle Volume Concentrations
4. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
Nomenclature
Surface area of square cross-section duct (m2) | |
C | Specific heat (kJ·kg−1·K−1) |
Dh | Hydraulic diameter (m) |
Experimental average nanofluid heat transfer coefficient (W·m−2·K−1) | |
Simulated average nanofluid heat transfer coefficient (W·m−2·K−1) | |
k | Thermal conductivity (W·m−1·K−1) |
L | Duct length (m) |
Average nanofluid Nusselt number obtained from experiments | |
Average nanofluid Nusselt number calculated from CFD analysis | |
Pe | Peclet number |
Pr | Prandtl number |
q | Heat flux (W/m2) |
Re | Reynolds number |
Tb | Bulk temperature (K) |
Tw | Duct wall temperature (K) |
Average fluid velocity (m·s−1) | |
u | The x-component of the velocity (m−1·s−1) |
v | The y-component of the velocity (m−1·s−1) |
w | The z-component of the velocity (m−1·s−1) |
Greek Symbols | |
γ | Ratio of the nano-layer thickness to original particle radius |
μ | Viscosity (Pa s) |
μwnf | Nanofluid viscosity at duct wall temperature (Pa s) |
Nanoparticle volume fraction (%) | |
Density (kg·m−3) | |
Subscripts | |
bf | Base fluid |
i | Inlet |
nf | Nanofluid |
o | Outlet |
p | Solid nanoparticles |
w | Wall |
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Property | Basic Fluid (Water) | γ-Al2O3 | CuO |
---|---|---|---|
Specific heat (J/kg K) | 4182 | 880 | 535.6 |
Density (kg/m3) | 998.2 | 3890 | 6350 |
Thermal conductivity (W/m K) | 0.597 | 46 | 69 |
Viscosity (kg/ms) | 9.93 × 10−4 | - | - |
Nanoparticle | (%) | ||||
---|---|---|---|---|---|
Al2O3 | 0.1 | 1.0029 | 0.9968 | 1.0843 | 1.0031 |
0.5 | 1.0145 | 0.9844 | 1.1557 | 1.0157 | |
1.0 | 1.0289 | 0.9692 | 1.2178 | 1.0315 | |
1.5 | 1.0434 | 0.9544 | 1.2802 | 1.0475 | |
2.0 | 1.0579 | 0.9400 | 1.3521 | 1.0637 | |
CuO | 0.05 | 1.0027 | 0.9972 | 1.0184 | 1.0045 |
0.16 | 1.0086 | 0.9912 | 1.0275 | 1.0143 | |
0.36 | 1.0193 | 0.9804 | 1.0371 | 1.0322 | |
0.50 | 1.0269 | 0.9729 | 1.0423 | 1.0447 | |
0.80 | 1.0430 | 0.9574 | 1.0519 | 1.0715 |
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Ting, H.-H.; Hou, S.-S. Numerical Study of Laminar Flow and Convective Heat Transfer Utilizing Nanofluids in Equilateral Triangular Ducts with Constant Heat Flux. Materials 2016, 9, 576. https://doi.org/10.3390/ma9070576
Ting H-H, Hou S-S. Numerical Study of Laminar Flow and Convective Heat Transfer Utilizing Nanofluids in Equilateral Triangular Ducts with Constant Heat Flux. Materials. 2016; 9(7):576. https://doi.org/10.3390/ma9070576
Chicago/Turabian StyleTing, Hsien-Hung, and Shuhn-Shyurng Hou. 2016. "Numerical Study of Laminar Flow and Convective Heat Transfer Utilizing Nanofluids in Equilateral Triangular Ducts with Constant Heat Flux" Materials 9, no. 7: 576. https://doi.org/10.3390/ma9070576