Transverse Thermoelectricity in Fibrous Composite Materials
Abstract
:1. Introduction
2. Mathematical Modeling
3. Cooling Performance
4. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
Nomenclature
F | Fiber Phase |
M | Matrix phase |
KCL | Kirchhoff Circuit Laws |
COP | Coefficient of performance |
f | Fiber volume fraction |
λA | Thermal conductivity of material A |
ρA | Electrical resistivity of material A |
SA | Seebeck coefficient of material A |
λx/y/z | Thermal conductivity in x, y, and z directions |
ρx/y/z | Electrical resistivity in in x, y, and z directions |
Sx/y/z | Seebeck coefficient in in x, y, and z directions |
λij | Elements of thermal conductivity tensor |
ρij | Elements of electrical resistivity tensor |
Sij | Elements of Seebeck coefficient tensor |
P | Material properties (λ, ρ, or S) |
jy | Current density in y direction |
L | Device length |
d | Device thickness |
α | Rotation angle of aligned fibers |
Th | Heat sink temperature |
Tc | Cooling surface temperature |
ΔT | Temperature difference |
Ztrans | Transverse figure of merit |
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Material | T (K) | S (μV/K) | ρ (Ω·m) | λ (W·m−1·K−1) | Reference |
---|---|---|---|---|---|
Bi0.5Sb1.5Te3 | 300 | 220.00 | 1.20 × 10−5 | 1.10 | [28] |
PbTe | 700 | 236.00 | 2.25 × 10−5 | 1.44 | [29] |
Si0.2Ge0.8 | 1000 | 232.00 | 2.48 × 10−5 | 2.56 | [29] |
Bi | 300 | −110.00 | 1.05 × 10−6 | 8.20 | [10] |
Pb | 300 | −1.05 | 2.13 × 10−7 | 35.30 | [30,31] |
In | 300 | 1.68 | 8.40 × 10−8 | 83.70 | [30,32] |
Sn | 300 | −1.00 | 1.05 × 10−7 | 62.50 | [30,32] |
Al | 300 | −1.66 | 2.62 × 10−8 | 247.00 | [30,32] |
Ni | 300 | −19.50 | 7.20 × 10−8 | 90.70 | [30,31] |
700 | −25.80 | 1.70 × 10−7 | 72.20 | [30,33] | |
1000 | −29.90 | 4.20 × 10−7 | 71.80 | [30,33] | |
Cu | 300 | 1.83 | 1.67 × 10−8 | 400.00 | [30,31] |
700 | 2.83 | 3.83 × 10−8 | 372.50 | [30,31] | |
1000 | 5.36 | 7.92 × 10−8 | 357.00 | [30,31] | |
Ag | 300 | 1.51 | 1.63 × 10−8 | 429.00 | [30,31] |
700 | 2.82 | 4.21 × 10−8 | 404.00 | [30,31] | |
1000 | 7.95 | 6.52 × 10−8 | 379.00 | [30,31] | |
Au | 300 | 1.94 | 2.01 × 10−8 | 317.00 | [30,31] |
700 | 2.86 | 5.82 × 10−8 | 291.00 | [30,31] | |
1000 | 3.85 | 8.85 × 10−8 | 270.00 | [30,31] |
Fiber Volume Fraction (f) | KCL Model | FEA Simulation | |
---|---|---|---|
Square Fiber | Circular Fiber | ||
0.1 | 38.0 K | 31.8 K | 31.8 K |
0.2 | 34.1 K | 31.6 K | 32.7 K |
0.3 | 32.0 K | 31.4 K | 31.2 K |
0.4 | 31.3 K | 31.2 K | 30. 6 K |
0.5 | 31.7 K | 32.3 K | 31.8 K |
Temperature (K) | Matrix Material | Fiber Material | Fiber Volume Fraction (f) | Rotation Angle (α, Degree) | ZtransT |
---|---|---|---|---|---|
300 K | Bi0.5Sb1.5Te3 | Ni | 0.40 | 12.60 | 0.35 |
Al | 0.50 | 8.10 | 0.32 | ||
Au | 0.55 | 7.20 | 0.32 | ||
Ag | 0.51 | 6.30 | 0.31 | ||
Cu | 0.56 | 6.30 | 0.31 | ||
Bi | 0.40 | 34.20 | 0.31 | ||
In | 0.39 | 13.50 | 0.29 | ||
Sn | 0.40 | 15.30 | 0.28 | ||
Pb | 0.38 | 19.80 | 0.27 | ||
700 K | PbTe | Ni | 0.36 | 15.30 | 0.42 |
Au | 0.48 | 7.20 | 0.35 | ||
Cu | 0.48 | 7.20 | 0.33 | ||
Ag | 0.43 | 8.10 | 0.33 | ||
1000 K | Si0.2Ge0.8 | Ni | 0.37 | 20.70 | 0.27 |
Au | 0.36 | 10.80 | 0.26 | ||
Ag | 0.40 | 9.00 | 0.25 | ||
Cu | 0.37 | 9.90 | 0.25 |
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Qian, B.; Ren, F. Transverse Thermoelectricity in Fibrous Composite Materials. Energies 2017, 10, 1006. https://doi.org/10.3390/en10071006
Qian B, Ren F. Transverse Thermoelectricity in Fibrous Composite Materials. Energies. 2017; 10(7):1006. https://doi.org/10.3390/en10071006
Chicago/Turabian StyleQian, Bosen, and Fei Ren. 2017. "Transverse Thermoelectricity in Fibrous Composite Materials" Energies 10, no. 7: 1006. https://doi.org/10.3390/en10071006