# 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

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**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