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Geometry Optimization of a Segmented Thermoelectric Generator Based on Multi-parameter and Nonlinear Optimization Method

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Abstract

As no single thermoelectric material has presented a high figure-of-merit (ZT) over a very wide temperature range, segmented thermoelectric generators (STEGs), where the p- and n-legs are formed of different thermoelectric material segments joined in series, have been developed to improve the performance of thermoelectric generators. A crucial but difficult problem in a STEG design is to determine the optimal values of the geometrical parameters, like the relative lengths of each segment and the cross-sectional area ratio of the n- and p-legs. Herein, a multi-parameter and nonlinear optimization method, based on the Improved Powell Algorithm in conjunction with the discrete numerical model, was implemented to solve the STEG’s geometrical optimization problem. The multi-parameter optimal results were validated by comparison with the optimal outcomes obtained from the single-parameter optimization method. Finally, the effect of the hot- and cold-junction temperatures on the geometry optimization was investigated. Results show that the optimal geometry parameters for maximizing the specific output power of a STEG are different from those for maximizing the conversion efficiency. Data also suggest that the optimal geometry parameters and the interfacial temperatures of the adjacent segments optimized for maximum specific output power or conversion efficiency vary with changing hot- and cold-junction temperatures. Through the geometry optimization, the CoSb3/Bi2Te3-based STEG can obtain a maximum specific output power up to 1725.3 W/kg and a maximum efficiency of 13.4% when operating at a hot-junction temperature of 823 K and a cold-junction temperature of 298 K.

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Abbreviations

STEG:

Segmented thermoelectric generator

STEGs:

Segmented thermoelectric generators

TEG:

Thermoelectric generator

TEGs:

Thermoelectric generators

DNM:

Discrete numerical model

α :

Seebeck coefficient (V/K)

σ :

Electrical conductivity (S/m)

κ :

Thermal conductivity (W/(mK))

K :

Heat transfer coefficient (W/K)

T :

Temperature (K)

ZT:

Figure-of-merit

CP:

Characteristic power (CP = T 2 Zκ)

T nf :

Interface temperature between the hot-segment and the cold-segment in the n-leg (K)

T pf :

Interface temperature between the hot-segment and the cold-segment in the p-leg (K)

T c :

Temperature at the cold-junction of the thermoelectric module (K)

T h :

Temperature at the hot-junction of the thermoelectric module (K)

ρ nh :

Density of the hot-segment material in the n-leg (kg/m3)

ρ ph :

Density of the hot-segment material in the p-leg (kg/m3)

ρ nc :

Density of the cold-segment material in the n-leg (kg/m3)

ρ pc :

Density of the cold-segment material in the p-leg (kg/m3)

N nh :

Element number of the hot-segment in the n-leg

N ph :

Element number of the hot-segment in the p-leg

N nc :

Element number of the cold-segment in the n-leg

N pc :

Element number of the cold-segment in the p-leg

L :

Total length of the thermoelectric leg (m)

L nh :

Length of the hot-segment of the n-leg (m)

L nc :

Length of the cold-segment of the n-leg (m)

L ph :

Length of the hot-segment of the p-leg (m)

L pc :

Length of the cold-segment of the p-leg (m)

A n :

Cross-sectional area of the n-leg (m2)

A p :

Cross-sectional area of the p-leg (m2)

S nh :

Ratio of the hot-segment length to the total length of the n-leg (S nh = L nh/L)

S ph :

Ratio of the hot-segment length to the total length of the p-leg (S ph = L ph/L)

a :

Cross-sectional area ratio of the n-leg and the p-leg (a = A n /A p )

S nh,opt :

The optimal value of S nh

S ph,opt :

The optimal value of S ph

a opt :

The optimal value of a

I :

Current flowing through the thermoelectric legs under the matched-load condition (A)

R :

Total resistance of the STEG (Ω)

R in :

Internal resistance of the STEG (Ω)

R L :

Load resistance (Ω)

P m :

Specific output power (W/kg)

η :

Conversion efficiency (%)

i :

Element sequence number

n :

n-type thermoelectric leg

p :

p-type thermoelectric leg

c:

Cold-junction of thermoelectric module

h:

Hot-junction of thermoelectric module

nh:

Hot-segment in the n-leg

nc:

Cold-segment in the n-leg

ph:

Hot-segment in the p-leg

pc:

Cold-segment in the p-leg

opt:

The optimal value

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Acknowledgements

This work was financially supported by the National Natural Science Foundation of China (No. 51272198), the National High-tech R&D Program of China (863 Program, No. 2012AA051104), the International S&T Cooperation Program of China (2014DFA63070), and the Fundamental Research Funds for the Central Universities (WUT, Nos. 2014-VII-009 and 2014-zy-063).

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Authors and Affiliations

  1. School of Mechanical and Electrical Engineering, Wuhan University of Technology, Wuhan, 430070, Hubei, China

    Lanlan Cai, Peng Li & Qi Luo

  2. State Key Laboratory of Advanced Technology for Materials Synthesis and Processing, Wuhan University of Technology, Wuhan, 430070, Hubei, China

    Pengcheng Zhai & Qingjie Zhang

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  1. Lanlan Cai
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  2. Peng Li
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Correspondence to Peng Li.

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Cai, L., Li, P., Luo, Q. et al. Geometry Optimization of a Segmented Thermoelectric Generator Based on Multi-parameter and Nonlinear Optimization Method. J. Electron. Mater. 46, 1552–1566 (2017). https://doi.org/10.1007/s11664-016-5198-6

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