**3. Influence of pressure distribution**

In contact resistance measurement with the 'steady state method,' uncertainty calculation must be taken into account due to the large number of measures that are made. The uncertainty calculation method used is the same as other authors in the literature [35–38] when applying the same method to measure thermal contact resistances. **Table 3** shows the uncer-

Firstly, results of the interface thermal resistance using aluminum bars are shown in **Figure 4a**. For all the studied interfaces, the behavior with respect pressure follows a similar trend: the thermal resistance decreases with pressure. Hence, the worst value is obtained at low pressures. In addition, it is confirmed that is better to use TIM instead of not using it; the highest thermal resistance corresponds to the absence of TIM. The thermal grease improves the contact without TIM, but when the pressure is higher, its presence is negligible. The reason is that the grease pumps out of the interface at high pressures. Therefore, thermal grease would not improve the contact in assemblies at elevated pressures. Graphite sheets seem to be better: thermal contact resistance is enhanced at every pressure point. The smallest value

Secondly, results of cupper-tungsten alloy bars are shown in **Figure 4b**. These bars have a higher hardness, and its influence can be observed in the results. Due to its higher hardness, thermal resistance without TIM is again the worst one and almost three times higher than with aluminum. In contrast, graphite sheet shows different results than before: its thermal resistance at low pressures is higher than thermal grease. Nevertheless, if the pressure increases, the behavior of the graphite sheets improves, being better than the thermal grease. Thus, on very hard surfaces thermal grease is very effective at low pressures due to its fluid-

Hence, it can be said that thermal contact resistance must definitely be considered in thermoelectric assemblies because it produces a temperature drop across the interfaces that decreases the efficiency of thermoelectric generators. In order to reduce these thermal contact resistances, the use of thermal interface materials has been demonstrated regardless the

**)** *U<sup>i</sup>*

Temperature (thermocouple) ± 0.3 K Temperature sensor location ± 300 μm Force ± 0.2% Hole distance ± 10 μm Thermal conductivity ± 10%

/W for the Aluminum

of thermal resistance obtained for graphite sheet is 2.19 × 10−5 K·m2

ity, and graphite sheet needs higher pressures to work well.

tainty values of the equipment.

**2.3. Results and discussion**

128 Bringing Thermoelectricity into Reality

interface at 1183 kPa.

**Measured parameter (***x<sup>i</sup>*

**Table 3.** Uncertainties table.

Last section has shown the importance of achieving a low thermal contact resistance in the assembly of thermoelectric generators since it can affect the performance of the whole system. However, this is not always an easy task, and the introduction of thermal interface materials becomes necessary to ensure a good contact at microscopic level. Furthermore, the combination of pressure with these thermal interface materials improves even further the contact between surfaces as shown in **Figure 4**. These graphs analyze different thermal interface materials and different uniform pressure distributions. But what happens if the pressure distribution is not uniform?

Pressure distribution basically depends on the assembly, i.e. the location and the torque applied to the screws. Hence, if there is an uneven torque in the screws or if the location is not appropriate or even if the exerted torque is too big that it provokes the bending of the heat exchangers, it could happen that only some parts of the thermoelectric modules are in contact with the heat exchangers, leading to changes associated with the thermal contact resistance explained in last section [39, 40]. As a consequence, temperature mismatches appear and therefore problems of decreased power output arise [41]. Thus, although it is not normally taken into account, it is important to consider the clamping force in the assembly of thermoelectric generators [42, 43]. In this sense, the present section analyzes different screw configurations and torques to demonstrate the importance of the clamping pressure and its distribution in the assembly of thermoelectric generators.

**Figure 4.** (a) Thermal resistance of TIMs in an aluminum interface at 100°C and (b) thermal resistance of TIMs in a copper-tungsten alloy interface at 100°C.

### **3.1. Methodology**

### *3.1.1. Description of the studied configurations*

In order to analyze how the pressure is distributed with regard the location of the screws and their torque, two different thermoelectric generators have been used with graphite as interface material since it has been demonstrated that it leads to better results than the other studied TIMs. In both generators, the heat source is represented by a heating plate made up of electrical resistances, in contact with the thermoelectric modules, which dissipate the non-converted heat to the ambient thanks to a fin dissipater assisted by a ventilator. The dimensions are the only difference between them. Hence, one of the generators is prepared for holding two thermoelectric modules while the bigger dimensions of the second one allows the implementation of four modules. For each generator, two possible screw configurations clamped with different torques have been analyzed. The location of the screws is depicted in **Figure 5**, while the studied torques are summarized in **Table 4**.

The analysis has been performed in two steps. On the one hand, a qualitative analysis has allowed the visual determination of the pressure distribution. On the other hand, the comparison of each of the pixels with a scale by means of the closest neighbor method has permitted

6 1 6 1.5 6 2

The Importance of the Assembly in Thermoelectric Generators

http://dx.doi.org/10.5772/intechopen.75697

131

5 2

Based on the pressure films, it is obvious that there does not exist a uniform pressure distribution in the modules. **Figure 6a** shows the distribution obtained in the configuration with two modules and four screws. As it can be observed, only those parts closer to the screws have a significant pressure. The central part of the configuration seems not to be in such a good

If another two screws are introduced in order to reduce the mentioned bending (**Figure 6b**–**d**), the pressure distribution becomes more uniform. The reason why the distribution is not equally uniform at both sides of the modules is due to the different distance of the screws to the modules. Nonetheless, as expected, it is achieved a higher intensity of this pressure as the

**Figure 6.** Pressure films for (a) 4 screws, 1 Nm; (b) 6 screws, 1 Nm; (c) 6 screws, 1.5 Nm; and (d) 6 screws, 2 Nm.

a statistical analysis, with the median as the most important parameter.

**Number of modules Number of screws Torque (Nm)**

**2** 4 1

**4** 4 1

**Table 4.** Summary of the studied torques for the different configurations.

contact due to the bending of the base of the dissipator.

**3.2. Results and discussion**

*3.2.1. Qualitative analysis*

torque increases.

### *3.1.2. Study of the pressure distribution*

Pressure distribution has been studied thanks to PRESCALE Pressure Measurement Films by Fujifilm [44]. These films change their color intensity depending on the pressure applied, changing from white to dark magenta as pressure increases. In this particular case, films ranged between 0.6 and 2.5 MPa have been used.

For each of the experiments, a film has been placed between the thermoelectric modules and the fin dissipater located at the cold side. With this film suitably located, the generator has been assembled with the corresponding torques. As a consequence, the films changed their color in those areas where more pressure was exerted. After the generator was perfectly assembled, the set was cautiously dismantled and the films analyzed. Experiments were repeated three times each in order to ensure their repetitiveness.

**Figure 5.** The four studied screw configurations for the considered thermoelectric generators.


**Table 4.** Summary of the studied torques for the different configurations.

The analysis has been performed in two steps. On the one hand, a qualitative analysis has allowed the visual determination of the pressure distribution. On the other hand, the comparison of each of the pixels with a scale by means of the closest neighbor method has permitted a statistical analysis, with the median as the most important parameter.

#### **3.2. Results and discussion**

#### *3.2.1. Qualitative analysis*

**Figure 5.** The four studied screw configurations for the considered thermoelectric generators.

**3.1. Methodology**

130 Bringing Thermoelectricity into Reality

*3.1.1. Description of the studied configurations*

*3.1.2. Study of the pressure distribution*

ranged between 0.6 and 2.5 MPa have been used.

times each in order to ensure their repetitiveness.

**Figure 5**, while the studied torques are summarized in **Table 4**.

In order to analyze how the pressure is distributed with regard the location of the screws and their torque, two different thermoelectric generators have been used with graphite as interface material since it has been demonstrated that it leads to better results than the other studied TIMs. In both generators, the heat source is represented by a heating plate made up of electrical resistances, in contact with the thermoelectric modules, which dissipate the non-converted heat to the ambient thanks to a fin dissipater assisted by a ventilator. The dimensions are the only difference between them. Hence, one of the generators is prepared for holding two thermoelectric modules while the bigger dimensions of the second one allows the implementation of four modules. For each generator, two possible screw configurations clamped with different torques have been analyzed. The location of the screws is depicted in

Pressure distribution has been studied thanks to PRESCALE Pressure Measurement Films by Fujifilm [44]. These films change their color intensity depending on the pressure applied, changing from white to dark magenta as pressure increases. In this particular case, films

For each of the experiments, a film has been placed between the thermoelectric modules and the fin dissipater located at the cold side. With this film suitably located, the generator has been assembled with the corresponding torques. As a consequence, the films changed their color in those areas where more pressure was exerted. After the generator was perfectly assembled, the set was cautiously dismantled and the films analyzed. Experiments were repeated three Based on the pressure films, it is obvious that there does not exist a uniform pressure distribution in the modules. **Figure 6a** shows the distribution obtained in the configuration with two modules and four screws. As it can be observed, only those parts closer to the screws have a significant pressure. The central part of the configuration seems not to be in such a good contact due to the bending of the base of the dissipator.

If another two screws are introduced in order to reduce the mentioned bending (**Figure 6b**–**d**), the pressure distribution becomes more uniform. The reason why the distribution is not equally uniform at both sides of the modules is due to the different distance of the screws to the modules. Nonetheless, as expected, it is achieved a higher intensity of this pressure as the torque increases.

**Figure 6.** Pressure films for (a) 4 screws, 1 Nm; (b) 6 screws, 1 Nm; (c) 6 screws, 1.5 Nm; and (d) 6 screws, 2 Nm.

In the case of having four modules in an assembly with only four screws, the fact that pressure is not uniformly distributed becomes more noticeable. Only the four corners, where screws are actually located, are working under an appreciable pressure (**Figure 7a**).

If an additional screw is located in the center so that the bending of the dissipater is reduced and the pressure is increased in order to improve the contact, the improvements obtained are minimal (**Figure 7b**) due to the big distance between the additional screw and the modules. Thus, it is recommended that each module has its own tightening.
