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Perturbation Methods for Real-Time In Situ Evaluation of Hot-Side Thermal Resistances in Thermoelectric Energy Recovery Systems

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Abstract

Thermoelectric (TE) power systems in high-temperature industrial, transportation, and military energy systems require high-performance hot-side and cold-side heat transfer to provide the critical temperature differential and transfer the required thermal energy to create the power output. Hot- and cold-side heat transfer performance is typically characterized by the hot-side and cold-side thermal resistance, R h,th and R c,th, respectively. This heat transfer performance determines the hot-side temperature, T h, and cold-side temperature, T c, conditions when operating in energy recovery environments with available temperature differentials characterized by an external driving temperature, T src, and ambient temperature, T amb. It is crucial to monitor and track the hot-side thermal performance at all times during TE energy recovery system operation, thereby allowing one to track the system “health,” predict future expected system performance, and anticipate/prevent system failures. This paper describes the use of a perturbation methodology and a direct coupling between the TE current, voltage, and hot-side energy flow to extract a real-time in situ evaluation of hot-side thermal resistances. External measurable TE parameters, either system current or T src, can be perturbed during system operation, and the resulting TE system response can then be coupled mathematically to the hot-side thermal transfer performance (i.e., thermal resistance). This paper discusses the mathematical formalism of this technique, and TE module experimental data showing successful application of real-time current perturbation. This technique provides a pathway for developing faster, real-time system monitoring and diagnostics to alleviate system performance degradation, or prevent system damage from dramatic changes in hot-side thermal transfer conditions in industrial, transportation, and spacecraft TE power systems.

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Abbreviations

A :

Thermoelectric element area (m2)

I :

TE device current (A)

K :

TE device total thermal conductance (W/K)

L :

Thermoelectric element length (m or mm)

m :

Resistance ratio (=R o/R i)

N :

Number of TE couples

P :

Power (W)

R i :

Internal resistance of TE device (Ω)

R contact :

Electrical contact resistance across TE couple (Ω)

R o :

External load resistance (Ω)

R h,th :

TE hot-side thermal resistance (K/W)

R c,th :

TE cold-side thermal resistance (K/W)

T :

Temperature (K)

V :

Voltage (V)

q :

Heat flow (W)

α T :

Total Seebeck coefficient, α n  + α p (V/K)

ΔT :

Temperature differential (K)

κ :

Thermal conductivity of thermoelectric material [W/(m K)]

ρ :

Electrical resistivity of thermoelectric material (Ω m)

ω :

Generic thermoelectric property in temperature-integrated property averaging equation

amb:

Associated with ambient environment

c:

TE cold side

h:

TE hot side

i:

Internal to TE device

HEX:

Heat exchanger

Loss:

Associated with heat loss

max:

Maximum power condition

n :

n-Type TE material property

o:

Associated with external resistance

p :

p-Type TE material property

oc:

Open-circuit conditions

src:

Associated with heat source

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Acknowledgements

This work was carried out under NASA Space Act Agreement No. 43-17508, a contract between NASA and General Motors with funding from the US Department of Energy, at the Jet Propulsion Laboratory, California Institute of Technology, under a contract to the National Aeronautics and Space Administration.

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Authors and Affiliations

  1. Power and Sensors Section, Thermal Energy Conversion Group, NASA-Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA

    Terry J. Hendricks

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  1. Terry J. Hendricks
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Correspondence to Terry J. Hendricks.

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Hendricks, T.J. Perturbation Methods for Real-Time In Situ Evaluation of Hot-Side Thermal Resistances in Thermoelectric Energy Recovery Systems. J. Electron. Mater. 44, 1909–1918 (2015). https://doi.org/10.1007/s11664-014-3591-6

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  • DOI: https://doi.org/10.1007/s11664-014-3591-6

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