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PreprintarXiv licencearXiv

Exact branch-transfer criterion for common-mode Thomson heat cancellation in thermoelectric couples

  • Peng Kang
  • Da Wan
  • Shulin Bai
  • Wei Yin
  • Peng Wang
  • Chenglong Wen
  • Zhen Li
  • Yu Liu
  • Lei Zheng
  • Li-Dong Zhao
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Abstract

Thermoelectric p- and n-type legs are commonly paired by matching their Seebeck magnitudes, although a cooler responds to heat transported through its complete electrical and thermal network. We decompose the leg coefficients into differential thermopower α=Sp−Sn and common thermopower M=(Sp+Sn)/2. In a connected steady-state scalar thermoelectric network, a temperature-independent co-shift applied to every electrically active segment is an exact terminal null. A temperature-dependent perturbation of the legs relative to fixed leads is instead physical. At fixed current and shared isothermal endpoints, its first-order cold-port response is the action of Γm=T dm/dT on the difference between the p- and n-branch oriented collection measures. We prove that every continuous Γm cancels if and only if these measures are equal. In the constant-property, linear-common-mode limit, matching Ri/Kileg is sufficient and does not require identical legs. One- and two-dimensional calculations confirm the analytic reductions within their stated domains. For split thermal pads, the analysis gives the exact array law ΔQc,Σ=∑j CjIjΔTc,j and, for series elements with isothermal hot pairs, IΔVΣ=−ΔQc,Σ. A representative seven-pair model gives corresponding increments of 7.87 mW and −2.80 mV. Branch transfer and endpoint topology therefore provide distinct material-pairing and device-test criteria for common-mode Thomson heat.

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Cite

BibTeXRIS
BibTeX
@misc{kang2026exact,
  title = {{Exact branch-transfer criterion for common-mode Thomson heat cancellation in thermoelectric couples}},
  author = {Peng Kang and Da Wan and Shulin Bai and Wei Yin and Peng Wang and Chenglong Wen and Zhen Li and Yu Liu and Lei Zheng and Li-Dong Zhao},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.27519},
  eprint = {2608.27519},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.27519},
}
RIS
TY  - UNPB
TI  - Exact branch-transfer criterion for common-mode Thomson heat cancellation in thermoelectric couples
AU  - Peng Kang
AU  - Da Wan
AU  - Shulin Bai
AU  - Wei Yin
AU  - Peng Wang
AU  - Chenglong Wen
AU  - Zhen Li
AU  - Yu Liu
AU  - Lei Zheng
AU  - Li-Dong Zhao
PY  - 2026
DA  - 2026/08/27
PB  - arXiv
DO  - 10.48550/arxiv.2608.27519
UR  - https://arxiv.org/abs/2608.27519
AB  - Thermoelectric p- and n-type legs are commonly paired by matching their Seebeck magnitudes, although a cooler responds to heat transported through its complete electrical and thermal network. We decompose the leg coefficients into differential thermopower α=S_p−S_n and common thermopower M=(S_p+S_n)/2. In a connected steady-state scalar thermoelectric network, a temperature-independent co-shift applied to every electrically active segment is an exact terminal null. A temperature-dependent perturbation of the legs relative to fixed leads is instead physical. At fixed current and shared isothermal endpoints, its first-order cold-port response is the action of Γ_m=T dm/dT on the difference between the p- and n-branch oriented collection measures. We prove that every continuous Γ_m cancels if and only if these measures are equal. In the constant-property, linear-common-mode limit, matching R_i/K_i^leg is sufficient and does not require identical legs. One- and two-dimensional calculations confirm the analytic reductions within their stated domains. For split thermal pads, the analysis gives the exact array law ΔQ_c,Σ=∑_j C_jI_jΔT_c,j and, for series elements with isothermal hot pairs, IΔV_Σ=−ΔQ_c,Σ. A representative seven-pair model gives corresponding increments of 7.87 mW and −2.80 mV. Branch transfer and endpoint topology therefore provide distinct material-pairing and device-test criteria for common-mode Thomson heat.
ER  -