Advertisement

Beyond zT: Is There a Limit to Thermoelectric Figure of Merit?

  • Yuriy LobunetsEmail author
Topical Collection: International Conference on Thermoelectrics 2018
First Online:
  • 37 Downloads
Part of the following topical collections:
  1. International Conference on Thermoelectrics 2018
  2. International Conference on Thermoelectrics 2018

Abstract

The concept of the dimensionless thermoelectric figure of merit zT was derived by A.F. Ioffe and has been widely used to assess the desirability of thermoelectric materials for devices. Solid state physics does not set limits on this criterion, but it can be shown that such restrictions are imposed by the laws of thermodynamics. The physical meaning of zT can be interpreted as the ratio of the virtual efficiency of a thermoelectric generator (TEG) ηo and the Carnot efficiency ηc: zT = ηo/ηc. Hence, the conclusion about the zT restriction: lim(zT) ≤ 1, which is correlated with the data on the properties of well-studied thermoelectric materials, but contradicts much new experimental data. This contradiction serves as a pretext for further study of possible constraints on zT. An additional bonus from this analysis is the possibility of the experimental determination of zT by direct measurement of temperatures, heat flux, and open circle voltage. An analysis of the expanded mathematical model of a TEG shows that the influence of the Biot criterion on the power capacity of the TEG significantly exceeds the influence of zT. That is, it is possible to compensate for the high thermal conductivity of materials due to more intense heat transfer. This approach to improving the characteristics is demonstrated by developing a TEG for the conversion of latent heat of liquid natural gas (LNG).

Keywords

Thermoelectric figure of merit specific power of thermoelectric generator CryoTEG 

List of Symbols

Bi

Biot criterion

I

Electrical current (A)

j

Current density (A/cm2)

J

Dimensionless current density

e

Seebeck coefficient (V/K)

E

Electromotive force (V)

λ

Thermal conductivity (W/cm-K)

σ

Electrical conductivity (Ω/cm)

h

Thermocouple leg length (cm)

n

Number of thermoelectric elements on module

s

Thermoelectric leg cross sectional area (cm2)

To

Determining temperature (K)

Th

Hot junction temperature (K)

Tc

Cold junction temperature (K)

ΔT

Junction temperature difference (K)

th

Heat carrier temperature (K)

tc

Coolant temperature (K)

Δt

Temperature difference heat carriers (K)

Θ = T/To

Dimensionless temperature

\( \theta = t/T_{o} \)

Dimensionless temperature of fluid

z

Thermoelectric figure-of-merit (K−1)

zTo

Dimensionless thermoelectric figure-of-merit

N

Electrical power (W)

Nx

Dimensionless power

Q

Heat power flow (W)

η

Efficiency

ηc

Carnot efficiency

α

Heat transfer coefficient (W/cm2 K)

Rα,λ

Thermal resistance (cm2 K/W)

R

Electrical resistance (Ω)

RL

Electrical load resistance (Ω)

m = RL/R

Load factor

LCOE

Levelized cost of electricity ($/kWh)

Y = y/h

Dimensionless coordinate

This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

Acknowledgments

This work was supported by the US National Science Foundation under Award Number #1722127, SBIR Phase I: Integrated Thermoelectric Heat Exchanger (iTEG-HX) for Carbon Neutral Electricity Production through Recovery of Cold Energy from Regasification of LNG.

References

  1. 1.
    A.F. Ioffe, Semiconductor Thermoelements and Thermoelectric Cooling (London: Infosearch, 1957).Google Scholar
  2. 2.
    Y.M. Lobunets, Thermoelectricity 2, 65 (2014).Google Scholar
  3. 3.
    S. Carnot, Reflections on the Motive Power of Heat (New York: John Wiley & Sons, 1890).Google Scholar
  4. 4.
    J.P. Heremans, M.S. Dresselhaus, L.E. Bell, and D.T. Morelli, Nat. Nanotechnol. 8, 471 (2013).CrossRefGoogle Scholar
  5. 5.
    Y.M. Lobunets, Patent UA125129 (2018).Google Scholar
  6. 6.
    T.C. Harman, J.H. Cahn, and M.J. Logan, Appl. Phys. 30, 1351 (1959).CrossRefGoogle Scholar
  7. 7.
    S. LeBlanc, S.K. Yee, M.L. Scullin, C. Dames, and K.E. Goodson, Renew. Sustain. Energy Rev. 32, 313 (2014).CrossRefGoogle Scholar
  8. 8.
    T.J. Hendricks, S. Yee, and S. LeBlanc, J. Electron. Mater. 45, 1751 (2016).Google Scholar
  9. 9.
    S.K. Yee, S. LeBlanc, K.E. Goodson, and C. Dames, Energy Environ. Sci. 6, 2561 (2013).CrossRefGoogle Scholar
  10. 10.
    Cryogenic power generation system recovering LNG’s cryogenic energy and generating power for energy and CO2 emission savings. http://www.osakagas.co.jp/en/rd/technical/1198907_6995.html.
  11. 11.
    W. Sun, P. Hu, Z. Chen, and L. Jia, Energy Convers. Manag. 46, 789 (2005).Google Scholar
  12. 12.
    M. Kambe, R. Morita, K. Omoto, Y. Koji, T. Yoshida, and K. Noishiki, Power Energy Syst. 2, 1304 (2008).CrossRefGoogle Scholar

Copyright information

© The Minerals, Metals & Materials Society 2019

Authors and Affiliations

  1. 1.Solid Cell Inc.RochesterUSA

Personalised recommendations

Cite article

Buy options