# Coupled Thermoelectric Devices: Theory and Experiment

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Procedure

## 3. Mathematical Model

#### 3.1. Single Thermoelectric

#### 3.2. Coupled Thermoelectrics

## 4. Results and Discussion

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Appendix A. Thermal Figure of Merit

## References

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**Figure 1.**Sketch of the experimental device, not drawn to scale. The coordinate system we use is shown. The thermoelectric modules are denoted by ${M}_{i}$. The thermoelectric devices are actioned by imposing electric currents ${I}_{i}$ with DC voltage power supplies ${V}_{i}$. The i denotes the first (1) and second (2) module. The rectangular plate is kept hot by circulating warm water in the reservoir. Temperature is measured in the top of module one (${M}_{1}$).

**Figure 2.**Scheme of two coupled thermoelectric devices. This study is devoted to the thermal analysis of the thermoelectric materials denoted by n type. The devices are actioned by injecting an electric current ${I}_{i}$. The thickness (width) is denoted by ${L}_{i}$. The i denotes the first (1) and second (2) device.

**Figure 3.**$\Delta T$ as function of the electric current. (

**a**) single device; (

**b**) coupled devices—experimental measurements.

**Figure 4.**$\Delta T$ as function of the electric current. (

**a**) single device; (

**b**) coupled devices—theoretical predictions.

**Figure 5.**(

**a**) temperature distribution along coupled devices; (

**b**) entropy generation profile. For clarity in the $\dot{S}$ profile comparison, the blue line is multiplied by a factor of 3.98 and the left part of the black line ($-1<x<0$) is multiplied by 7.99—theoretical predictions.

**Figure 6.**Total entropy generation $\dot{\overline{S}}$ as function of the applied electric current. (

**a**) single device; (

**b**) coupled devices—theoretical predictions.

**Figure 7.**Thermal figure of merit $Z{T}_{h}$ as a function of the total entropy generation $\dot{\overline{S}}$. (

**a**) single device; (

**b**) coupled devices. In (b), each of the curves displayed is generated by varying ${J}_{2}$ from 0 to 1.6—theoretical predictions.

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**MDPI and ACS Style**

Rojas, J.A.; Rivera, I.; Figueroa, A.; Vázquez, F. Coupled Thermoelectric Devices: Theory and Experiment. *Entropy* **2016**, *18*, 255.
https://doi.org/10.3390/e18070255

**AMA Style**

Rojas JA, Rivera I, Figueroa A, Vázquez F. Coupled Thermoelectric Devices: Theory and Experiment. *Entropy*. 2016; 18(7):255.
https://doi.org/10.3390/e18070255

**Chicago/Turabian Style**

Rojas, Jaziel A., Iván Rivera, Aldo Figueroa, and Federico Vázquez. 2016. "Coupled Thermoelectric Devices: Theory and Experiment" *Entropy* 18, no. 7: 255.
https://doi.org/10.3390/e18070255