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A Model to Evaluate the Device-Level Performance of Thermoelectric Cooler with Thomson Effect Considered

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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

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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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Authors and Affiliations

  1. Microsystem & Terahertz Research Center, China Academy of Engineering Physics, Chengdu, 610200, China

    Tingrui Gong, Lei Gao, Haoshu Tan, Feng Qin, Xiong Xin & Juntao Li

  2. Institute of Electronic Engineering, China Academy of Engineering Physics, Mianyang, 621999, China

    Tingrui Gong, Lei Gao, Haoshu Tan, Feng Qin, Xiong Xin & Juntao Li

  3. School of Civil Engineering and Architecture, Wuhan University of Technology, Wuhan, 430070, China

    Yongjia Wu & Tingzhen Ming

  4. Department of Refrigeration & Cryogenics Engineering, Huazhong University of Science and Technology, Wuhan, 430074, China

    Limei Shen

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  1. Tingrui Gong
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Correspondence to Tingrui Gong.

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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

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