Thermally Developing Flow and Heat Transfer in Elliptical Minichannels with Constant Wall Temperature
Abstract
:1. Introduction
2. Mathematical Formulations
2.1. Solution Method
2.2. Grid Independence
2.3. Model Validation
3. Results and Discussion
3.1. Local Nusselt Number
3.2. Thermal Entrance Length
4. Conclusions
Author Contributions
Funding
Conflicts of Interest
Nomenclature
A | flow area, m2 |
a | minor semi-axis of ellipse, m |
b | major semi-axis of ellipse, m |
cp | specific heat, J/(kg K) |
Dh | hydraulic diameter, m |
e | eccentricity of the ellipse |
h | convective heat transfer coefficient, W/(m2 K) |
Kn | Knudsen number |
L | channel length, m |
Nu | Nusselt number, = hDh/λ |
P | wetted perimeter, m |
p | pressure, |
Pr | Prandtl number = μcp/λ |
q’’ | wall heat flux, W/m2 |
Re | Reynolds number, = |
T | temperature, K |
U | non-dimensional velocity |
u | velocity, m/s |
X, Y, Z | non-dimensional Cartesian coordinates |
x, y, z | Cartesian coordinates, m |
x* | dimensionless axial distance, = x/(DhRePr) |
Greek symbols | |
α | non-dimensional minor semi-axis of ellipse |
β | non-dimensional major semi-axis of ellipse |
ε | aspect ratio, = a/b |
θ | dimensionless temperature |
λ | fluid thermal conductivity, W/(m K) |
μ | dynamic viscosity, |
ρ | fluid density, kg/m3 |
Г | cross section contour |
Ω | cross-section domain |
Subscripts | |
m | mean |
th | thermal |
w | wall |
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Aspect Ratio | Re = 500 | Re = 1000 | Re = 2000 | |||
---|---|---|---|---|---|---|
C | N | C | N | C | N | |
ε = 0.2 | 0.794 | 2.60 | 0.920 | 2.80 | 0.955 | 2.80 |
ε = 0.33 | 0.785 | 3.00 | 0.900 | 3.24 | 0.944 | 3.24 |
ε = 0.5 | 0.776 | 3.40 | 0.887 | 3.80 | 0.927 | 3.80 |
ε = 0.75 | 0.759 | 3.80 | 0.883 | 4.78 | 0.916 | 4.78 |
ε = 1 | 0.753 | 3.80 | 0.879 | 4.78 | 0.902 | 4.78 |
n | −0.379 | −0.357 | −0.350 |
Re | x* | ε = 0.2 | ε = 0.33 | ε = 0.5 | ε = 0.75 | ε = 1 |
---|---|---|---|---|---|---|
25 | 0.0001 | 237.7 | 237.5 | 237.4 | 237.2 | 237.2 |
0.0002 | 119.5 | 119.4 | 119.4 | 119.2 | 119.1 | |
0.0005 | 49.12 | 49.01 | 48.85 | 48.68 | 48.66 | |
0.001 | 26.77 | 26.57 | 26.24 | 26.19 | 26.05 | |
0.005 | 8.622 | 8.385 | 8.146 | 7.988 | 7.940 | |
0.01 | 6.256 | 6.017 | 5.803 | 5.645 | 5.604 | |
50 | 0.0001 | 120.7 | 120.6 | 120.6 | 120.5 | 120.2 |
0.0002 | 60.29 | 60.25 | 60.24 | 60.06 | 59.82 | |
0.0005 | 27.56 | 27.36 | 26.97 | 26.73 | 26.93 | |
0.001 | 17.02 | 16.73 | 16.46 | 16.30 | 16.29 | |
0.005 | 7.215 | 6.966 | 6.755 | 6.599 | 6.558 | |
0.01 | 5.742 | 5.512 | 5.306 | 5.152 | 5.114 | |
125 | 0.0001 | 50.13 | 50.03 | 49.86 | 49.69 | 49.53 |
0.0002 | 29.92 | 29.67 | 29.16 | 28.89 | 29.16 | |
0.0005 | 17.33 | 16.99 | 16.72 | 16.51 | 16.49 | |
0.001 | 12.18 | 11.87 | 11.63 | 11.43 | 11.40 | |
0.005 | 6.696 | 6.526 | 6.308 | 6.139 | 6.116 | |
0.01 | 5.578 | 5.353 | 5.148 | 4.985 | 4.958 | |
250 | 0.0001 | 33.19 | 32.90 | 32.45 | 32.31 | 32.30 |
0.0002 | 22.43 | 22.06 | 21.66 | 21.47 | 21.46 | |
0.0005 | 14.81 | 14.45 | 14.20 | 14.00 | 13.93 | |
0.001 | 11.22 | 11.00 | 10.76 | 10.58 | 10.53 | |
0.005 | 6.677 | 6.441 | 6.234 | 6.079 | 6.041 | |
0.01 | 5.550 | 5.325 | 5.121 | 4.968 | 4.931 |
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Su, L.; Duan, Z.; He, B.; Ma, H.; Xu, Z. Thermally Developing Flow and Heat Transfer in Elliptical Minichannels with Constant Wall Temperature. Micromachines 2019, 10, 713. https://doi.org/10.3390/mi10100713
Su L, Duan Z, He B, Ma H, Xu Z. Thermally Developing Flow and Heat Transfer in Elliptical Minichannels with Constant Wall Temperature. Micromachines. 2019; 10(10):713. https://doi.org/10.3390/mi10100713
Chicago/Turabian StyleSu, Liangbin, Zhipeng Duan, Boshu He, Hao Ma, and Zairan Xu. 2019. "Thermally Developing Flow and Heat Transfer in Elliptical Minichannels with Constant Wall Temperature" Micromachines 10, no. 10: 713. https://doi.org/10.3390/mi10100713