Heat Transfer Enhancement of TiO2/Water Nanofluid at Laminar and Turbulent Flows: A Numerical Approach for Evaluating the Effect of Nanoparticle Loadings
Abstract
:1. Introduction
2. Numerical Model of Nanofluids
2.1. Thermophysical Properties
2.2. Grid Optimization
2.3. Two-Phase Mixture Model
2.4. Conservation Equations
2.5. Boundary Conditions
2.6. Numerical Procedure
3. Results and Discussion
3.1. Validation of Numerical Results
3.2. Laminar Model Flow for Application of Nanofluids
3.2.1. Local Convective Heat Transfer Coefficient
3.2.2. Axial Velocity in Radial Direction
3.2.3. Temperature Contours of Nanofluids
3.3. Turbulent Model Flow for Application of Nanofluids
4. Conclusions
Author Contributions
Acknowledgments
Conflicts of Interest
Nomenclature
Cp | Specific heat [J/kg·K] | Greek symbols | |
C1, C2, Cμ | Turbulent constant | ϕ | Volume fraction [%] |
D | Diameter [m] | μ | Dynamic viscosity [kg/m s] |
E | Energy | ρ | Density [kg/m3] |
f | Friction factor | Velocity vector [m/s] | |
Gk | Heat rate production of kinetic energy [kg/m s3] | ε | Turbulent dissipation rate [m2/s3] |
h | Heat transfer coefficient [W/m K] | ||
k | Thermal conductivity [W/m K] | ||
keff | Effective thermal conductivity [W/m K] | ||
L | Length [m] | Subscripts | |
m | Volumetric flow rate [kg/s] | ave | Average |
n | Number of phase | bf | Base fluid |
Nu | Nusselt number | k | Turbulent kinetic energy |
P | Pressure [Pa] | m | Mixture |
Pr | Prandtl number | np | Nanoparticle |
q” | Heat flux [W/m2] | nf | Nanofluid |
Re | Reynolds number | w | Wall |
SE | Volumetric heat | ||
r | Pipe radius [m] | ||
T | Temperature [K] |
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Parameter | Value | Unit |
---|---|---|
Length, L | 2.0 | m |
Inner diameter, Di | 5.0 | mm |
Number of cells, Nx × Ny | 15 × 800 | - |
Bias factor | 60 (axial direction) | - |
6 (radial direction) | ||
Nanoparticle (nominal diameter) | TiO2 (21 nm) | - |
Thermal conductivity of nanoparticle, knp | 13.7 | W m−1 K−1 |
Nanoparticle density, | 4170 | kg m−3 |
Nanoparticle volume fraction, φ | 0.24/0.60/1.18 | Vol.% |
Density of nanofluid | See Equation (1) | kg m−3 |
Heat specific of nanofluid | See Equation (2) | J kg−1 K−1 |
Viscosity of nanofluids, µnf | See Equation (3) | Pa s |
Effective thermal conductivity, keff | See Equation (4) | W m−1 K−1 |
Heat flux, q” | 4000 | W m−2 |
Reynolds number | - | - |
Laminar flow | 500, 1200 | - |
Turbulent flow | 4000–14,000 | - |
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Kristiawan, B.; Santoso, B.; Wijayanta, A.T.; Aziz, M.; Miyazaki, T. Heat Transfer Enhancement of TiO2/Water Nanofluid at Laminar and Turbulent Flows: A Numerical Approach for Evaluating the Effect of Nanoparticle Loadings. Energies 2018, 11, 1584. https://doi.org/10.3390/en11061584
Kristiawan B, Santoso B, Wijayanta AT, Aziz M, Miyazaki T. Heat Transfer Enhancement of TiO2/Water Nanofluid at Laminar and Turbulent Flows: A Numerical Approach for Evaluating the Effect of Nanoparticle Loadings. Energies. 2018; 11(6):1584. https://doi.org/10.3390/en11061584
Chicago/Turabian StyleKristiawan, Budi, Budi Santoso, Agung Tri Wijayanta, Muhammad Aziz, and Takahiko Miyazaki. 2018. "Heat Transfer Enhancement of TiO2/Water Nanofluid at Laminar and Turbulent Flows: A Numerical Approach for Evaluating the Effect of Nanoparticle Loadings" Energies 11, no. 6: 1584. https://doi.org/10.3390/en11061584