# The Thermoelectric Analysis of Different Heat Flux Conduction Materials for Power Generation Board

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## Abstract

**:**

## 1. Introduction

## 2. Theory Analysis of TEG

#### 2.1. Thermal Model of TE Board

_{in}− T

_{out}) of both ends. T

_{h}and T

_{c}are the hot and cold junction temperatures, respectively. Additionally, K

_{mh}is the thermal conductance of the thermally conductive material, and K

_{w}is the thermal conductance of the board [16,17]. This coefficient can be up to 5300 W/m·K for suspended grapheme [18,19]. The ordinary grapheme, in this paper, is 1200 W/m·K.

_{p.n}is the heat flux flow between n-type and p-type legs, S

_{p,n}represents the cross-sectional area of the n-type and p-type legs, and dx is a length. Therefore, the sum of Q

_{p}and Q

_{n}has been established for the heat flux flow Q of a TE module.

_{h}and αIT

_{c}are two boundary points of the rate of heat flux transfer as:

_{1}and K

_{2}are the thermal conductance between the hot board source and the hot TEG surface and cold board source and cold TEG surface, respectively. K

_{w}is the thermal conductance of the board, and K

_{mh}is the thermal conductance of the thermally conductive material between the board and the hot TEG surface. Additionally, in the proposed system, the ceramic plates were used as an outer layer in TE module, so K

_{1}is considered as a constant that is equal to K

_{2}.

_{2}Te

_{3}TE module [16]. Based on Equations (14)–(16), the conversion efficiency of the TE board can be obtained as:

_{mh}.

#### 2.2. Control and Electrical Model of TE Board

_{B}is the terminal voltage from the TE Board system, and V

_{o}is the voltage of different loads, such as battery, supercapacitor and other equipment.

_{D}

_{2}flows to T and then the diode D

_{2}will be off. The inductor voltage v

_{L}is:

_{o},

_{t}= t

_{on},

_{off},

_{o}and inductor current can be expressed as follows:

## 3. Analysis and Comparison of Thermally Conductive Materials with TEGs

#### 3.1. Analysis of the Characteristics of TEG

#### 3.2. Analysis of the Characteristics of TEG with Different Thermally Conductive Materials

^{−7}mm)) have been attached to the surface of TE modules. The prototype without any thermally conductive material was also tested for the control study. Figure 7a–c shows photographs of the TE modules attached with aluminum, grapheme and air, respectively.

## 4. Experimental Results and Discussion

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**The schematic of the fundamental unit of a TE module embedded in a board with a thermally conductive material.

**Figure 4.**Measured results of the output current versus different loads of TEG module in five temperature difference situations.

**Figure 5.**Measurement results of the output voltage versus different loads of TEG module in five temperature difference situations.

**Figure 6.**Measured results of the output power versus different loads of TEG module in five temperature difference situations.

**Figure 7.**Photographs of the prototype of TE board power generation system with different thermally conductive materials, (

**a**) Air; (

**b**) Aluminum; and (

**c**) Graphene.

**Figure 8.**Simulation results of conversion efficiency of TE board with using different thermally conductive materials.

**Figure 11.**Measured waveform of the output voltage (Channel 1) of the TE board without attaching the thermally conductive material.

**Figure 12.**Measured waveform of the output voltage (Channel 1) of the TE board with aluminum attached as the thermally conductive material.

**Figure 13.**Measured waveform of the output voltage (Channel 1) of the TE board with graphene attached as the thermally conductive material.

**Figure 14.**Channel 1 is output voltage, Channel 2 is output current, and Channel 3 is constant output voltage of buck converter for supercapacitor is 5.0 V.

**Figure 16.**The output power of TE board with different thermally conductive materials in different loads.

**Figure 17.**Conversion efficiency of TE board attached with different thermally conductive materials against temperature difference.

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**MDPI and ACS Style**

Li, S.; Lam, K.H.; Cheng, K.W.E. The Thermoelectric Analysis of Different Heat Flux Conduction Materials for Power Generation Board. *Energies* **2017**, *10*, 1781.
https://doi.org/10.3390/en10111781

**AMA Style**

Li S, Lam KH, Cheng KWE. The Thermoelectric Analysis of Different Heat Flux Conduction Materials for Power Generation Board. *Energies*. 2017; 10(11):1781.
https://doi.org/10.3390/en10111781

**Chicago/Turabian Style**

Li, Siyang, Kwok Ho Lam, and Ka Wai Eric Cheng. 2017. "The Thermoelectric Analysis of Different Heat Flux Conduction Materials for Power Generation Board" *Energies* 10, no. 11: 1781.
https://doi.org/10.3390/en10111781