Abstract
In this paper, a one-dimensional thermodynamic model was developed to evaluate the device-level performance of thermoelectric cooler (TEC) with the Thomson effect, contact resistance, gap heat leakage, heat sink, and heat load taken into account. The model was generalized and simplified by introducing dimensionless parameters. Experimental measurements showed good agreement with analytical results. The parametric analysis indicated that the influence of the Thomson effect on cooling capacity continued to expand with increasing current, while the effect on COP hardly changed with current. Low thermal contact resistance was beneficial to obtain lower hot-junction temperature, which can even reduce 2 K compared with the electrical contact resistance in the case study. The gap heat leakage was a negative factor affecting the cooling performance. When the thermal resistance of the heat sink was small, the negative effect of heat leakage on performance would be further enlarged. The enhancement of heat load temperature would increase the cooling power of the TEC. For example, an increase of 5 K in heat load can increase the cooling capacity by about 4%. However, once the current exceeded the optimum value, the raising effect on the cooling power would be weakened. The research can provide an analytical approach for the designer to perform trade studies to optimize the TEC system.
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Abbreviations
- A :
-
leg cross-sectional area/m2
- COP:
-
coefficient of performance
- E :
-
electrical potential/V
- I :
-
electrical current/A
- j :
-
electrical current density/A·m−2
- K :
-
thermal conductance/W·K−1
- K* :
-
dimensionless thermal conductance
- k :
-
thermal conductivity/W·m−1·K−1
- L :
-
leg length or leg height/m
- n :
-
n pairs of P, N-type thermoelements
- P :
-
input power/W
- Q :
-
heat flow rate/W
- Q c :
-
heat absorption at cold-side/W
- Q h :
-
heat rejection at hot-side/W
- q :
-
heat flux/W·m−2
- R :
-
electrical resistance/Ω
- R e,cl :
-
electrical contact resistance of the thermoelement-solder interface/Ω·m2
- R e,c2 :
-
electrical contact resistance of the Cu-solder interface/Ω·m2
- R e,Cu :
-
electrical resistance of copper connector/Ω
- R e,sol :
-
electrical resistance of solder/Ω
- R k,c1 :
-
thermal contact resistance of the thermoelement-solder interface/K·m2·W−1
- R k,c2 :
-
thermal contact resistance of the Cu-solder interface/K·m2·W−1
- R k,Cu :
-
thermal resistance of copper connector/K·W−1
- R k,G :
-
thermal resistance of gap/K·W−1
- R k,hs :
-
thermal resistance of heat sink/K·W−1
- R k,load :
-
thermal resistance of heat load/K·W−1
- R k,sol :
-
thermal resistance of solder/K·W−1
- R k,sub :
-
thermal resistance of substrate/K·W−1
- R k,TIM :
-
thermal resistance of TIM/K·W−1
- T :
-
temperature/K
- ΔT :
-
temperature difference, ΔT=Th−Tc/K
- x :
-
displacement in the direction of leg length/m
- α :
-
Seebeck coefficient/V·K−1
- β :
-
ratio of the Joule heat to the thermal conduction
- β*:
-
reduced dimensionless parameter the ratio of the Joule heat to the thermal conduction
- γ* :
-
reduced dimensionless parameter
- Θ c :
-
dimensionless Peltier heat at the hot-junction of the thermoelement
- Θ h :
-
dimensionless heat rejection at the hot-junction of the thermoelement
- θ :
-
dimensionless length
- ξ :
-
dimensionless length
- Π c :
-
dimensionless Peltier heat at the cold-junction of the thermoelement
- Π h :
-
dimensionless Peltier heat at the hot-junction of the thermoelement
- ρ :
-
electric resistivity/Ω·m
- τ :
-
thomson coefficient/V·K−1
- ϕ :
-
heat generation/W·m−3
- Ψ :
-
dimensionless power input
- a:
-
ambient
- Cu:
-
copper connector
- gap:
-
filling gap
- H,C:
-
hot, cold-end of the thermoelectric cooler
- h,c:
-
hot, cold-junction of the thermoelement
- Load:
-
heat load
- P,N:
-
P, N-type
- sub:
-
substrate
- sol:
-
solder
- TE:
-
thermoelement
References
Majumdar A., Thermoelectric devices: Helping chips to keep their cool. Nature Nanotechnology, 2009, 4(4): 214–215.
Engelmann G., Laumen M., Gottschlich J., et al., Temperature controlled power semiconductor characterization using thermoelectric coolers. IEEE Transactions on Industry Applications, 2018, 54(3): 2598–2605.
Karampasis E., Papanikolaou N., Voglitsis D., et al., Active thermoelectric cooling solutions for airspace applications: the thermicool project. IEEE Access, 2017, 5: 2288–2299.
He R.R., Zhong H.Y., Cai Y., et al., Theoretical and experimental investigations of thermoelectric refrigeration box used for medical service. Procedia Engineering, 2017, 205: 1215–1222.
Shen L., Pu X., Sun Y., et al., A study on thermoelectric technology application in net zero energy buildings. Energy, 2016, 113: 9–24.
Rowe D.M., Thermoelectrics handbook: Macro to nano. CRC press, 2005.
Lee H.S., The Thomson effect and the ideal equation on thermoelectric coolers. Energy, 2013, 56(7): 61–69.
Chen W.H., Liao C.Y., Hung C.I., A numerical study on the performance of miniature thermoelectric cooler affected by Thomson effect. Applied Energy, 2012, 89(1): 464–473.
Lam T.T., Yuan S.W., Fong E., et al., Analytical study of transient performance of thermoelectric coolers considering the Thomson effect. International Journal of Thermal Sciences, 2018, 130: 435–448.
Snyder G. J., Toberer E. S., Khanna R., et al., Improved thermoelectric cooling based on the Thomson effect. Physical Review B, 2012, 86(4): 045202.
Zhou Y., Zhang T., Wang F., et al., Numerical study and optimization of a combined thermoelectric assisted indirect evaporative cooling system. Journal of Thermal Science, 2020, 29(5): 1345–1354.
Min G., Rowe D., Improved model for calculating the coefficient of performance of a Peltier module. Energy Conversion and Management, 2000, 41(2): 163–171.
Jeong E.S., A new approach to optimize thermoelectric cooling modules. Cryogenics, 2014, 59(1): 38–43.
Da Silva L.W., Kaviany M., Micro-thermoelectric cooler: interfacial effects on thermal and electrical transport. International Journal of Heat and Mass Transfer, 2004, 47(10–11): 2417–2435.
Su Y., Lu J., Huang B., Free-standing planar thin-film thermoelectric microrefrigerators and the effects of thermal and electrical contact resistances. International Journal of Heat and Mass Transfer, 2018, 117: 436–446.
Sun D., Shen L., Sun M., et al., An effective method of evaluating the device-level thermophysical properties and performance of micro-thermoelectric coolers. Applied Energy, 2018, 219: 93–104.
Qiu C., Shi W., Comprehensive modeling for optimized design of a thermoelectric cooler with non-constant cross-section: Theoretical considerations. Applied Thermal Engineering, 2020, 176: 115384.
Marchenko O.V., Performance modeling of thermoelectric devices by perturbation method. International Journal of Thermal Sciences, 2018, 129: 334–342.
Wang X., Yu J., Ma M., Optimization of heat sink configuration for thermoelectric cooling system based on entropy generation analysis. International Journal of Heat and Mass Transfer, 2013, 63: 361–365.
Wu Y., Zuo L., Chen J., et al., A model to analyze the device level performance of thermoelectric generator. Energy, 2016, 115: 591–603.
Melnikov A.A., Kostishin V.G., Alenkov V.V., Dimensionless model of a thermoelectric cooling device operating at real heat transfer conditions: maximum cooling capacity mode. Journal of Electronic Materials, 2017, 46(5): 2737–2745.
Zhang H. Y., A general approach in evaluating and optimizing thermoelectric coolers. International Journal of Refrigeration, 2010, 33(6): 1187–1196.
Cai Y., Liu D., Zhao F.Y., et al., Performance analysis and assessment of thermoelectric micro cooler for electronic devices. Energy Conversion and Management, 2016, 124: 203–211.
Pearson M.R., Lents C.E., Dimensionless optimization of thermoelectric cooler performance when integrated within a thermal resistance network. Journal of Heat Transfer, 2016, 138(8): 081301.
Zhou Y., Yu J., Design optimization of thermoelectric cooling systems for applications in electronic devices. International Journal of Refrigeration, 2012, 35(4): 1139–1144.
Lu X., Zhao D., Ma T., et al., Thermal resistance matching for thermoelectric cooling systems. Energy Conversion and Management, 2018, 169: 186–193.
Tan H., Fu H., Yu J., Evaluating optimal cooling temperature of a single-stage thermoelectric cooler using thermodynamic second law. Applied Thermal Engineering, 2017, 123: 845–851.
Gonzalez-Hernandez S., Unification of optimization criteria and energetic analysis of a thermoelectric cooler and heater. Physica A: Statistical Mechanics and its Applications, 2020, 555: 124700.
Guo X., Zhang H., Wang J., et al., A new hybrid system composed of high-temperature proton exchange fuel cell and two-stage thermoelectric generator with Thomson effect: Energy and exergy analyses. Energy, 2020, 195: 117000.
Zhao D., Tan G., A review of thermoelectric cooling: materials, modeling and applications. Applied Thermal Engineering, 2014, 66(1–2): 15–24.
Russel M.K., Ewing D., Ching C.Y., Characterization of a thermoelectric cooler based thermal management system under different operating conditions. Applied Thermal Engineering, 2013, 50(1): 652–659.
Sun D., Shen L., Chen H., et al., Modeling and analysis of the influence of Thomson effect on micro-thermoelectric coolers considering interfacial and size effects. Energy, 2020, 196: 117116.
Gong T., Gao L., Wu Y., et al., Transient thermal stress analysis of a thermoelectric cooler under pulsed thermal loading. Applied Thermal Engineering, 2019, 162: 114240.
Acknowledgments
This study was financially supported by the National Natural Science Foundation of China (NSFC) (Grant No. 52106032), the Science Challenge Program (Grant No. TZ2018003), the National Natural Science Foundation of China (Grant No. 51778511), the Hubei Provincial Natural Science Foundation of China (Grant No. 2018CFA029), and the Key Project of ESI Discipline Development of Wuhan University of Technology (WUT Grant No. 2017001).
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Gong, T., Gao, L., Wu, Y. et al. A Model to Evaluate the Device-Level Performance of Thermoelectric Cooler with Thomson Effect Considered. J. Therm. Sci. 31, 712–726 (2022). https://doi.org/10.1007/s11630-022-1591-z
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DOI: https://doi.org/10.1007/s11630-022-1591-z