# Investigation and Computational Modelling of Variable TEG Leg Geometries

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## Abstract

**:**

## Highlights

## 1. Introduction

## 2. Equivalent Electric Circuit for TEGs and Boundary Conditions

#### 2.1. Boundary Conditions

- A heat transfer module was used for the measurement of the temperature difference in the thermoelectric generator by conduction and convection with surface-to-surface temperature distribution.
- All surfaces except the hot and cold junction surfaces are adiabatic. Therefore, convective heat transfer was not considered for this simulation.
- A steady-state condition was assumed for the thermoelectric modules. Addıtıonally, on the surfaces of the TEG, an adiabatic situation is considered, with no heat loss.
- Thermal boundary conditions are known as heat source (hot surface) and heat sink (cold surface) with defined temperatures of 293 K and 393 K, respectively, for the cold source and hot surface. In the module, a coherent mesh to describe the electrical and thermomechanical properties was considered.
- Internal electrical and thermal contact resistance are neglected.

#### 2.2. Numerical Model

#### 2.3. Analysis of Thermal Stresses

## 3. Conceptual Geometries

## 4. Result and Discussion

^{−4}V) in comparison to the other generated meshes.

#### 4.1. Temperature Distribution Analyses

#### 4.2. Electrical Analysis

#### 4.3. Thermal Stress Analysis

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## References

- Malinauskaite, J.; Jouhara, H.; Ahmad, L.; Milani, M.; Montorsi, L.; Venturelli, M. Energy efficiency in industry: EU and national policies in Italy and the UK. Energy
**2019**, 172, 255–269. [Google Scholar] [CrossRef] - Fierro, J.J.; Escudero-Atehortua, A.; Nieto-Londoño, C.; Giraldo, M.; Jouhara, H.; Wrobel, L.C. Evaluation of waste heat recovery technologies for the cement industry. Int. J. Thermofluids
**2020**, 7–8, 100040. [Google Scholar] [CrossRef] - Venturelli, M.; Brough, D.; Milani, M.; Montorsi, L.; Jouhara, H. Comprehensive numerical model for the analysis of potential heat recovery solutions in a ceramic industry. Int. J. Thermofluids
**2021**, 10, 100080. [Google Scholar] [CrossRef] - Brough, D.; Ramos, J.; Delpech, B.; Jouhara, H. Development and validation of a TRNSYS type to simulate heat pipe heat exchangers in transient applications of waste heat recovery. Int. J. Thermofluids
**2021**, 9, 100056. [Google Scholar] [CrossRef] - Egilegor, B.; Jouhara, H.; Zuazua, J.; Al-Mansour, F.; Plesnik, K.; Montorsi, L.; Manzini, L. ETEKINA: Analysis of the potential for waste heat recovery in three sectors: Aluminium low pressure die casting, steel sector and ceramic tiles manufacturing sector. Int. J. Thermofluids
**2019**, 1–2, 100002. [Google Scholar] [CrossRef] - Xiao, J.; Yang, T.; Li, P.; Zhai, P.; Zhang, Q. Thermal design and management for performance optimization of solar thermoelectric generator. Appl. Energy
**2012**, 93, 33–38. [Google Scholar] [CrossRef] - Talawo, R.-C.; Fotso, B.E.M.; Fogue, M. An experimental study of a solar thermoelectric generator with vortex tube for hybrid vehicle. Int. J. Thermofluids
**2021**, 10, 100079. [Google Scholar] [CrossRef] - Jouhara, H.; Żabnieńska-Góra, A.; Khordehgah, N.; Doraghi, Q.; Ahmad, L.; Norman, L.; Axcell, B.; Wrobel, L.; Dai, S. Thermoelectric generator (TEG) technologies and applications. Int. J. Thermofluids
**2021**, 9, 100063. [Google Scholar] [CrossRef] - Maghrabie, H.M.; Elsaid, K.; Sayed, E.; Abdelkareem, M.; Wilberforce, T.; Ramadan, M.; Olabi, A.G. Intensification of heat exchanger performance utilizing nano fluids. Int. J. Thermofluids
**2021**, 10, 100071. [Google Scholar] [CrossRef] - Soleimani, S.; Eckels, S. A review of drag reduction and heat transfer enhancement by riblet surfaces in closed and open channel flow. Int. J. Thermofluids
**2021**, 9, 100053. [Google Scholar] [CrossRef] - Gao, J.-L.; Du, Q.-G.; Zhang, X.-D.; Jiang, X.-Q. Thermal Stress Analysis and Structure Parameter Selection for a Bi
_{2}Te_{3}-Based Thermoelectric Module. J. Electron. Mater.**2011**, 40, 884–888. [Google Scholar] [CrossRef] - Erturun, U.; Erermis, K.; Mossi, K. Effect of various leg geometries on thermo-mechanical and power generation performance of thermoelectric devices. Appl. Therm. Eng.
**2014**, 73, 128–141. [Google Scholar] [CrossRef] - Zhang, X.; Zhao, L.-D. Thermoelectric materials: Energy conversion between heat and electricity. J. Mater.
**2015**, 1, 92–105. [Google Scholar] [CrossRef][Green Version] - Fraisse, G.; Lazard, M.; Goupil, C.; Serrat, J.Y. Study of a thermoelement’s behaviour through a modelling based on electrical analogy. Int. J. Heat Mass Transf.
**2010**, 53, 3503–3512. [Google Scholar] [CrossRef][Green Version] - Al-Merbati, A.S.; Yilbas, B.S.; Sahin, A.Z. Thermodynamics and thermal stress analysis of thermoelectric power generator: Influence of pin geometry on device performance. Appl. Therm. Eng.
**2013**, 50, 683–692. [Google Scholar] [CrossRef] - Shittu, S.; Li, G.; Zhao, X.; Ma, X.; Akhlaghi, Y.G.; Ayodele, E. High performance and thermal stress analysis of a segmented annular thermoelectric generator. Energy Convers. Manag.
**2019**, 184, 180–193. [Google Scholar] [CrossRef] - Tian, M.-W.; Mihardjo, L.W.W.; Moria, H.; Asaadi, S.; Pourhedayat, S.; Sadighi Dizaji, H.; Wae-hayee, M. Economy, energy, exergy and mechanical study of co-axial ring shape configuration of legs as a novel structure for cylindrical thermoelectric generator. Appl. Therm. Eng.
**2021**, 184, 116274. [Google Scholar] [CrossRef] - Sahin, A.Z.; Yilbas, B.S. The thermoelement as thermoelectric power generator: Effect of leg geometry on the efficiency and power generation. Energy Convers. Manag.
**2013**, 65, 26–32. [Google Scholar] [CrossRef] - Xiao, H.; Gou, X.; Yang, S. Detailed Modeling and Irreversible Transfer Process Analysis of a Multi-Element Thermoelectric Generator System. J. Electron. Mater.
**2011**, 40, 1195–1201. [Google Scholar] [CrossRef] - Lamba, R.; Kaushik, S.C. Thermodynamic analysis of thermoelectric generator including influence of Thomson effect and leg geometry configuration. Energy Convers. Manag.
**2017**, 144, 388–398. [Google Scholar] [CrossRef] - Montecucco, A.; Siviter, J.; Knox, A.R. Constant heat characterisation and geometrical optimisation of thermoelectric generators. Appl. Energy
**2015**, 149, 248–258. [Google Scholar] [CrossRef][Green Version] - Haidar, J.G.; Ghojel, J.I. Waste heat recovery from the exhaust of low-power diesel engine using thermoelectric generators. In Proceedings of the ICT2001, 20 International Conference on Thermoelectrics (Cat. No.01TH8589), Beijing, China, 8–11 June 2001; pp. 413–418. [Google Scholar]
- Fan, L.; Zhang, G.; Wang, R.; Jiao, K. A comprehensive and time-efficient model for determination of thermoelectric generator length and cross-section area. Energy Convers. Manag.
**2016**, 122, 85–94. [Google Scholar] [CrossRef] - Singh, S.; Ibeagwu, O.I.; Lamba, R. Thermodynamic evaluation of irreversibility and optimum performance of a concentrated PV-TEG cogenerated hybrid system. Sol. Energy
**2018**, 170, 896–905. [Google Scholar] [CrossRef] - Zhang, Y.; Cleary, M.; Wang, X.; Kempf, N.; Schoensee, L.; Yang, J.; Joshi, G.; Meda, L. High-temperature and high-power-density nanostructured thermoelectric generator for automotive waste heat recovery. Energy Convers. Manag.
**2015**, 105, 946–950. [Google Scholar] [CrossRef][Green Version] - COMSOL. Heat Transfer Module, 2018.
- Massaguer, E.; Massaguer, A.; Montoro, L.; Gonzalez, J.R. Development and validation of a new TRNSYS type for the simulation of thermoelectric generators. Appl. Energy
**2014**, 134, 65–74. [Google Scholar] [CrossRef] - Li, G.; Zhao, X.; Jin, Y.; Chen, X.; Ji, J.; Shittu, S. Performance Analysis and Discussion on the Thermoelectric Element Footprint for PV–TE Maximum Power Generation. J. Electron. Mater.
**2018**, 47, 5344–5351. [Google Scholar] [CrossRef][Green Version] - Antonova, E.E.; Looman, D.C. Finite elements for thermoelectric device analysis in ANSYS. In Proceedings of the ICT 2005, 24th International Conference on Thermoelectrics, Clemson, SC, USA, 19–23 June 2005; pp. 215–218. [Google Scholar]
- Landau, L.D.; Pitaevskii, L.P.; Lifshitz, E.M. Pitaevsky LP Electrodynamics of Continuous Media, 2nd ed.; Elsevier: Amsterdam, The Netherlands, 2004. [Google Scholar]
- GitHub. Dielectric Permittivity. Available online: https://em.geosci.xyz/content/physical_properties/dielectric_permittivity/index.html#contents (accessed on 26 March 2021).
- Ming, T.; Yang, W.; Wu, Y.; Xiang, Y.; Huang, X.; Cheng, J.; Li, X.; Zhao, J. Numerical analysis on the thermal behavior of a segmented thermoelectric generator. Int. J. Hydrogen Energy
**2017**, 42, 3521–3535. [Google Scholar] [CrossRef] - Ootao, Y.; Tanigawa, Y. Three-dimensional solution for transient thermal stresses of functionally graded rectangular plate due to nonuniform heat supply. Int. J. Mech. Sci.
**2005**, 47, 1769–1788. [Google Scholar] [CrossRef] - Ibeagwu, O.I. Modelling and comprehensive analysis of TEGs with diverse variable leg geometry. Energy
**2019**, 180, 90–106. [Google Scholar] [CrossRef]

**Figure 1.**TEG Equivalent electrical circuit [16].

**Figure 2.**Geometry of the TEG legs analysed: (

**A**) Rectangular shape, (

**B**) Diamond shape and (

**C**) Cone shape.

**Figure 3.**Comparison of TEG Temperature Distributions of (

**A**) Rectangular shape, (

**B**) Diamond shape, (

**C**) Cone shape and (

**D**) temperature distributions for the geometries analysed.

**Figure 4.**The electric potential produced in (

**A**) Rectangular shape, (

**B**) Diamond shape, (

**C**) Cone shape and (

**D**) Voltage Comparison.

**Figure 6.**The Stress analysis in (

**A**) Rectangular shape, (

**B**) Diamond shape, (

**C**) Cone shape and (

**D**) Von Mises Comparison.

Material | Thermal Conductivity (W/m K) | Electrical Conductivity (S/m) | Seebeck Coefficient (V/K) | Young’s Modulus (Pa) | Poisson’s Ratio |
---|---|---|---|---|---|

$B{i}_{2}T{e}_{3}-Ptype$ | k(T) | Sigma(T) | S(T) | 6.5 × 10^{10} | 0.23 |

$B{i}_{2}T{e}_{3}-Ntype$ | k(T) | Sigma(T) | −S(T) | 6.5 × 10^{10} | 0.23 |

Copper | 400 | 5.9 × 10^{7} | - | 110 × 10^{9} | 0.35 |

Alumina | 27 | - | - | 330 × 10^{9} | 0.22 |

Model Name | Rectangular | Cone | Diamond | |
---|---|---|---|---|

Parameter | ||||

Cu (mm) | 0.1 × 1 × 2.5 | 0.1 × 1 × 3.25 | 0.1 × 1 × 2.5 | |

Alumina (mm) | 0.3 × 2 × 6 | 0.3 × 2 × 6 | 0.3 × 2 × 6 | |

Hot Junction Cross Sectional Area (mm^{2}) | 1 × 1 | 1.77 | 0.5 × 0.5 | |

Cold Junction Cross Sectional Area (mm^{2}) | 1 × 1 | 0.78 | 0.5 × 0.5 | |

Cross Sectional Area (mm^{2}) at the Middle | 1 × 1 | 1.17 | 1 × 1 |

**Table 3.**Summary of the mesh types under consideration: TEG geometry, number of elements and mesh type.

Model | Number of Elements | Average Element Quality | Mesh Type |
---|---|---|---|

Cone-Leg | 1538 | 0.494 | Coarser |

15,308 | 0.628 | Normal | |

96,911 | 0.661 | Extra-Fine | |

Diamond | 488 | 0.327 | Coarser |

5776 | 0.598 | Normal | |

41,222 | 0.670 | Extra-Fine | |

Rectangular | 540 | 0.405 | Coarser |

9001 | 0.623 | Normal | |

61,209 | 0.669 | Extra-Fine |

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**MDPI and ACS Style**

Doraghi, Q.; Khordehgah, N.; Żabnieńska-Góra, A.; Ahmad, L.; Norman, L.; Ahmad, D.; Jouhara, H.
Investigation and Computational Modelling of Variable TEG Leg Geometries. *ChemEngineering* **2021**, *5*, 45.
https://doi.org/10.3390/chemengineering5030045

**AMA Style**

Doraghi Q, Khordehgah N, Żabnieńska-Góra A, Ahmad L, Norman L, Ahmad D, Jouhara H.
Investigation and Computational Modelling of Variable TEG Leg Geometries. *ChemEngineering*. 2021; 5(3):45.
https://doi.org/10.3390/chemengineering5030045

**Chicago/Turabian Style**

Doraghi, Qusay, Navid Khordehgah, Alina Żabnieńska-Góra, Lujean Ahmad, Les Norman, Darem Ahmad, and Hussam Jouhara.
2021. "Investigation and Computational Modelling of Variable TEG Leg Geometries" *ChemEngineering* 5, no. 3: 45.
https://doi.org/10.3390/chemengineering5030045