**2. Interface contact**

When two surfaces are confronted, it may seem that there exists a perfect contact among them. However, due to their roughness, surfaces are only in touch at some points, being mostly separated by air gaps that reduce the heat transmission in the interface (**Figure 2**). In thermoelectric generators, this fact attenuates the temperature difference across the thermoelectric modules, and therefore, decreases the output power. Thus, the present section explains how to quantify and improve the contact between the modules and each heat exchanger that compose a thermoelectric generator.

**Figure 2.** Representation of the interface filled with air. Red lines simulate the heat flux through the interface [26].

#### **2.1. Thermal interface materials**

In order to improve the contact and achieve a low temperature drop, thermal interface materials (TIMs) are used [27]. Their purpose consists in filling the gaps with materials that have a higher thermal conductivity than air. There are many families of thermal interface materials such as graphite sheets, thermal greases, phase change materials, indium or elastomers [28–30]. With the objective of checking if the presence of TIMs improves the real contact, this section analyzes three of the most common interface configurations for thermoelectric generators: without TIM, with graphite sheets, and with silicone thermal grease. The specific characteristics of these TIMs are described in **Table 1**.

The effect of the thermal contact is modeled through the thermal contact resistance (Eq. (2)), which depends on the temperature drop across the interface ∆T, the heat flux *Q*˙ and the area A. This parameter takes into consideration that, due to imperfections in the material's surface, the real contact area is just a small fraction of the apparent contact area; and it is defined in such a way that it is also independent of the TIM's thickness, which varies with pressure.

$$R\_{\alpha} = \frac{\Delta T \cdot A}{\dot{Q}} \tag{2}$$

thermocouples embedded in these bars and since their conductivities are perfectly known, the temperature drop across the interface (∆T) can be indirectly calculated by extrapolation (**Figure 3a**). Thermal contact resistance is therefore calculated with Eq. (2). Heat flux across the interface of Eq. (2) is generated by an electrical resistance and dissipated by a heat sink with a fan. Its calculation is possible thanks to the reference bars conductivity, thermo-

**Figure 3.** (a) Extrapolation method and (b) thermal contact resistance test bench for thermoelectric generation applications.

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Two dissimilar materials of the reference bars were used to test TIMs: highly conductive but soft 1050 Aluminum alloy and a cupper-tungsten alloy which presents an excellent relation between thermal conductivity and hardness. The specific properties (thermal conductivity,

For each material, the three mentioned possible interfaces were studied: no TIM, graphite sheets and silicone thermal grease. All the experiments were performed under the same conditions. The only variable was pressure, one of the most influent parameters in thermal interface resistances, and which was exerted by a linear actuator. The studied pressures range between 50 and 1200 kPa because the pressure recommended by the thermoelectric modules

**Material Thermal conductivity (W/m·K) Hardness (HB) Ra (μm) Rz (μm)** Al 1050 229 21 0.090 1.275 W75Cu25 170 200 0.126 1.215

hardness, and roughness) of each of these materials are described in **Table 2**.

couples measurements and their distance.

manufacturer is around 1000 kPa [34].

**Table 2.** Materials and properties of the fluxmeter bars.

This thermal resistance depends on many parameters: materials of the contact (with their respective roughness, hardness, and conductivity), their geometry, interface temperature, or contact pressure among others. Therefore, it is difficult to obtain a general expression valid for all assembly possibilities and that considers all the variables. All the expressions available in the literature are restricted to particular geometries and only take into account some of the depending parameters [31–33]. In this sense, the present section focuses on obtaining the thermal contact resistance for the standard dimensions of a thermoelectric module (40×40 mm<sup>2</sup> ) depending on the clamping pressure and considering a side temperature of 100°C.

#### **2.2. Methodology**

Due to the broad parameter dependence of the thermal contact resistance, the test bench of **Figure 3b** has been used in order to measure thermal contact resistances for thermoelectric modules' dimensions in a controlled environment. This device is based on the principle of 'steady state' measurements across thermal interface material junctions.

Hence, a known heat is forced to flow through two 40×40 mm<sup>2</sup> reference bars (usually called fluxmeters) separated by the TIM of interest and under a certain pressure. Thanks to


**Table 1.** Properties of thermal Interface materials.

**Figure 3.** (a) Extrapolation method and (b) thermal contact resistance test bench for thermoelectric generation applications.

thermocouples embedded in these bars and since their conductivities are perfectly known, the temperature drop across the interface (∆T) can be indirectly calculated by extrapolation (**Figure 3a**). Thermal contact resistance is therefore calculated with Eq. (2). Heat flux across the interface of Eq. (2) is generated by an electrical resistance and dissipated by a heat sink with a fan. Its calculation is possible thanks to the reference bars conductivity, thermocouples measurements and their distance.

Two dissimilar materials of the reference bars were used to test TIMs: highly conductive but soft 1050 Aluminum alloy and a cupper-tungsten alloy which presents an excellent relation between thermal conductivity and hardness. The specific properties (thermal conductivity, hardness, and roughness) of each of these materials are described in **Table 2**.

For each material, the three mentioned possible interfaces were studied: no TIM, graphite sheets and silicone thermal grease. All the experiments were performed under the same conditions. The only variable was pressure, one of the most influent parameters in thermal interface resistances, and which was exerted by a linear actuator. The studied pressures range between 50 and 1200 kPa because the pressure recommended by the thermoelectric modules manufacturer is around 1000 kPa [34].


**Table 2.** Materials and properties of the fluxmeter bars.

**2.1. Thermal interface materials**

126 Bringing Thermoelectricity into Reality

characteristics of these TIMs are described in **Table 1**.

*Rco* <sup>=</sup> \_\_\_\_\_\_

**2.2. Methodology**

grease

Polydimethylsiloxane oil-based silicone thermal

**Table 1.** Properties of thermal Interface materials.

In order to improve the contact and achieve a low temperature drop, thermal interface materials (TIMs) are used [27]. Their purpose consists in filling the gaps with materials that have a higher thermal conductivity than air. There are many families of thermal interface materials such as graphite sheets, thermal greases, phase change materials, indium or elastomers [28–30]. With the objective of checking if the presence of TIMs improves the real contact, this section analyzes three of the most common interface configurations for thermoelectric generators: without TIM, with graphite sheets, and with silicone thermal grease. The specific

The effect of the thermal contact is modeled through the thermal contact resistance (Eq. (2)), which depends on the temperature drop across the interface ∆T, the heat flux *Q*˙ and the area A. This parameter takes into consideration that, due to imperfections in the material's surface, the real contact area is just a small fraction of the apparent contact area; and it is defined in such a way that it is also independent of the TIM's thickness, which varies with pressure.

Δ*T* ⋅ *A*

This thermal resistance depends on many parameters: materials of the contact (with their respective roughness, hardness, and conductivity), their geometry, interface temperature, or contact pressure among others. Therefore, it is difficult to obtain a general expression valid for all assembly possibilities and that considers all the variables. All the expressions available in the literature are restricted to particular geometries and only take into account some of the depending parameters [31–33]. In this sense, the present section focuses on obtaining the thermal contact resistance for the standard dimensions of a thermoelectric module (40×40 mm<sup>2</sup>

Due to the broad parameter dependence of the thermal contact resistance, the test bench of **Figure 3b** has been used in order to measure thermal contact resistances for thermoelectric modules' dimensions in a controlled environment. This device is based on the principle of

called fluxmeters) separated by the TIM of interest and under a certain pressure. Thanks to

**(W/m·K)**

Graphite sheet 10 −40 to 400 0.127

**Thermal conductivity** 

**Operation temperature (°C)**

0.41 −40 to 250 —

depending on the clamping pressure and considering a side temperature of 100°C.

'steady state' measurements across thermal interface material junctions.

Hence, a known heat is forced to flow through two 40×40 mm<sup>2</sup>

*<sup>Q</sup>*̇ (2)

)

reference bars (usually

**Thickness (mm)**

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 uncertainty values of the equipment.

pressure. Among the studied TIMs, graphite is better for most of the cases. Nonetheless, hardness seems to be an important parameter to consider, with graphite being the most affected by this at low pressures. Thus, on very hard surfaces working with at low pressures,

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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 dis-

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

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

thermal grease presents a better behavior, reducing the temperature drop.

**3. Influence of pressure distribution**

distribution in the assembly of thermoelectric generators.

tribution is not uniform?

copper-tungsten alloy interface at 100°C.

#### **2.3. Results and discussion**

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 of thermal resistance obtained for graphite sheet is 2.19 × 10−5 K·m2 /W for the Aluminum interface at 1183 kPa.

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

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


**Table 3.** Uncertainties table.

pressure. Among the studied TIMs, graphite is better for most of the cases. Nonetheless, hardness seems to be an important parameter to consider, with graphite being the most affected by this at low pressures. Thus, on very hard surfaces working with at low pressures, thermal grease presents a better behavior, reducing the temperature drop.
