**3.1 Forced convection experiments**

(dotted) versus KTEG can be seen in **Figure 5**. Three different KS cases have been considered to highlight the fact that, the larger KS, the larger the power output, even for a constant KTEG. It can be seen that when KTEG = KS, the maximum power condition when KLK = 0, then the temperature drop across the μTEG is 50% of the

Similar to the electrical case, many papers discussing thermal matching focus on reaching a temperature drop in the μTEG equal to the temperature drop across KS [5, 24, 25]. When this KS represents a heat exchanger, some authors suggest a low KS heat exchanger to match KTEG and therefore maximize the power output according. While this approach assures operation at the mathematical local maximum for a given KS, it is a bad practice because it ignores the absolute maximum,

Looking at **Figure 5**, if KTEG = 1 W/K, this reasoning would imply that KS = 1 W/K would be necessary, and 50% of the total available temperature difference would drop across the μTEG. However, with a better heat exchanger, KS = 10 W/K or even KS = 100 W/K, then ΔT will asymptotically approach ΔTA, and the power output will

*PL*, *max* <sup>¼</sup> ð Þ *<sup>S</sup>* � <sup>Δ</sup>*TA*

*Pmax (left, blue curves) and ΔT/ΔTA (right, red curves) versus KTEG for different KS values. For KTEG = 1, thermal matching conditions would call for KS = 1, but larger Pmax values are possible for larger values of KS.*

In conclusion, both load matching and thermal matching are conditions that are mathematically true, but from a practical point of view, care must be taken when designing a μTEG to maximize its power output. First of all, its electrical internal resistance (RTEG) must be minimized, and after that, power output can be maximized by connecting a load which matches that of the μTEG, or simply an IC implementing an MPPT algorithm. On the thermal side, as RTEG is minimized, the thermal conductance (KTEG) is consequently maximized. Then, as the μTEG is already optimized, and it is not possible to further increase KTEG, the only option is to act on the external components, which in this case is the heat exchanger, and to choose one with an as large as possible KS, so that almost all of the available ΔT will

2

(5)

4*RTEG*

available temperature difference.

asymptotically reach:

**Figure 5.**

**356**

be internally transferred to the μTEG.

which takes place at larger KS values for a given KTEG.

*Heat Transfer - Design, Experimentation and Applications*

As the working scenario for the μTEG devices is dominated by a temperature difference between the hot and the cold parts, heat convection could play also an important role on how these temperatures are established. Convection is a mechanism of heat flux originated from the movement of the surrounding fluid, which will be typically air for the usual applications of the presented devices. Depending on how this movement is induced, convection can be classified as natural or forced.

Natural convection is based on the warming up of the air that is close to a heat source that, due to the lowering of its density, tends to move upwards, giving its place to colder air and so promoting the heat exchange. In forced convection, air is forced to move and then renew by an external force.

In order to demonstrate the improvement in the performance of the device, three different sets of experimental measurements have been performed on a device at three different convection conditions. The first one corresponds to natural convection, which occurs when the device is operated by letting it rest on top of a hot surface exposed to ambient at room conditions. The second and third sets of measurements correspond to forced convection regimes. In the second case, this is accomplished by the use of a standard CPU fan (see **Figure 6**) placed over the device, while in the third, an air jet, obtained through a syringe connected to the compressed air line in the laboratory, is directed towards the device. More details are available at [26].

Such experimental measurements have been performed on two different devices, featuring 30 and 60 μm long silicon NWs (by filling 3 and 6 trenches as described in section 2.1). Consequently, each one of the devices has different electrical and thermal resistances.

The obtained experimental results are shown in **Figure 7**. The devices have been measured at different temperatures of the hot plate (from 50 to 200 °C in 25 °C steps).

The measurement results show a very clear improvement in the performance as a result of forced convection. The maximum output power obtained when the device is mounted under the fan is multiplied by 3 when compared with the natural convection regime, while when under the more directed and higher flow air jet, the performance increases nearly three orders of magnitude: from a few nW to almost 0.7 μW. Moreover, the more performant air convection is, the less relevant become the thermal properties of the thermoelectric material. In natural and air forced convection cases, the larger output power corresponds to the longest nanowires, whereas in the air jet forced convection the opposite is true. This happens because the longer nanowires also have a larger electrical resistance, and its larger thermal

The performance improvement obtained by means of this approach can be observed in **Figure 8**, which shows a plot of the Seebeck voltage output of the device placed on a hot plate at 150 °C when the cold finger is being attached. It can be observed that the voltage increases rapidly after contact, and it rises even more when the applied force to the cold finger is increased slightly, so demonstrating the

reduction of the thermal resistance when the physical contact is improved.

*Managing Heat Transfer Issues in Thermoelectric Microgenerators*

*DOI: http://dx.doi.org/10.5772/intechopen.96246*

**Figure 8.**

**Figure 9.**

**359**

*Voltage evolution while the cold finger is being attached and detached.*

*Power curves for a device, with and without the cold finger, on a hot plate at 250 °C.*

#### **Figure 6.**

*Experimental setup used for the thermoelectrical characterization of μTEG devices under a forced convection regime induced by a CPU fan located on the top. The device is mounted on the thermal chuck of a Linkam station.*

**Figure 7.**

*Maximum power versus chip surface temperature for three different heat convection regimes and on two different devices (adapted from [26]).*

resistance is not significant in this case where the platform to ambient thermal resistance is enough to assure a large ΔT.

#### **3.2 Cold finger approach**

In the previous subsection, it has been experimentally demonstrated how important a good thermal connection with the surrounding ambient is in order to improve the overall performance of μTEG devices. Nevertheless, forced convection scenarios are not always available and artificially forcing them needs additional energy consuming devices. Therefore, in order to explore a passive strategy to diminish the thermal resistance to the surrounding ambient, the effect of contacting the microplatform with a metallic probe has been assessed. With this experiment, the feasibility of the addition of a heat exchanging structure as a general strategy for the reduction of the thermal resistance to the ambient will be demonstrated.

The experimental setup consists of a metallic probe dipped in thermally conducting paste, which is carefully positioned on the micro-platform by the use of a micro-manipulator.

*Managing Heat Transfer Issues in Thermoelectric Microgenerators DOI: http://dx.doi.org/10.5772/intechopen.96246*

The performance improvement obtained by means of this approach can be observed in **Figure 8**, which shows a plot of the Seebeck voltage output of the device placed on a hot plate at 150 °C when the cold finger is being attached. It can be observed that the voltage increases rapidly after contact, and it rises even more when the applied force to the cold finger is increased slightly, so demonstrating the reduction of the thermal resistance when the physical contact is improved.

**Figure 8.** *Voltage evolution while the cold finger is being attached and detached.*

**Figure 9.** *Power curves for a device, with and without the cold finger, on a hot plate at 250 °C.*

resistance is not significant in this case where the platform to ambient thermal

*Maximum power versus chip surface temperature for three different heat convection regimes and on two*

*Experimental setup used for the thermoelectrical characterization of μTEG devices under a forced convection regime induced by a CPU fan located on the top. The device is mounted on the thermal chuck of a Linkam*

In the previous subsection, it has been experimentally demonstrated how important a good thermal connection with the surrounding ambient is in order to improve the overall performance of μTEG devices. Nevertheless, forced convection scenarios are not always available and artificially forcing them needs additional energy consuming devices. Therefore, in order to explore a passive strategy to diminish the thermal resistance to the surrounding ambient, the effect of contacting the microplatform with a metallic probe has been assessed. With this experiment, the feasibility of the addition of a heat exchanging structure as a general strategy for the reduction of the thermal resistance to the ambient will be demonstrated. The experimental setup consists of a metallic probe dipped in thermally conducting paste, which is carefully positioned on the micro-platform by the use of

resistance is enough to assure a large ΔT.

*Heat Transfer - Design, Experimentation and Applications*

**3.2 Cold finger approach**

*different devices (adapted from [26]).*

**Figure 7.**

**Figure 6.**

*station.*

a micro-manipulator.

**358**

In **Figure 9** the power curves obtained from the same device at a hot plate temperature of 250 °C with and without the cold finger are shown. It can be seen an important improvement in the performance of two orders of magnitude, from 1.3 to 142 nW, so proving the effectiveness of the cold finger approach as a proof of concept validating the further development of more effective heat exchanging structures.

improvement on performance. The thermal and electrical properties of the mate-

The model boundary conditions include a constant hot temperature at the bottom (Thot = 100 °C) and natural convection on the vertical and horizontal walls of the heat exchanger through a heat exchange coefficient directly calculated in COMSOL for an air ambient temperature of 27 °C. When such element is not present, the heat exchange coefficient is applied directly on the platforms surface. **Figure 11** shows the temperature distribution for the whole model under such conditions. As it can be seen, even with a heat exchanger, the lowest temperature reached in the cold part is slightly below 70 °C although the ambient temperature is 27 °C. This is because the thermal resistance from the heat exchanger to the ambient is approximately one third of the total thermal resistance while the thermal resistance from the bottom of the PCB (actually most of this is from the silicon chip) to

rials used in the model are listed in **Table 1**.

*DOI: http://dx.doi.org/10.5772/intechopen.96246*

*Managing Heat Transfer Issues in Thermoelectric Microgenerators*

the heat exchanger is approximately two thirds of it.

**<sup>κ</sup> (W<sup>m</sup><sup>1</sup>**

Silicon <sup>150</sup> <sup>12</sup><sup>10</sup><sup>3</sup> Silicon oxide 1.4 — Silicon nitride 30 —

Tungsten <sup>174</sup> 7.76<sup>10</sup>6 (2) Thermal paste 5 — Copper 401 — FR4 (PCB) 0.3 — Spacer (PMMA) 0.2 —

*Thermal and electrical properties of the materials used in the model.*

*Temperature distribution for the whole model with Thot = 100 °C.*

*been measured to obtain this value.*

**Table 1.**

**Figure 11.**

**361**

**<sup>K</sup><sup>1</sup>**

Silicon NWs <sup>25</sup> (1) <sup>12</sup><sup>10</sup>3 (1) <sup>250</sup><sup>10</sup><sup>6</sup>

*(1)Silicon NWs are modeled as a block, not individual nanowires, and the block material properties assume an occupation of only 5% of the total area with nanowires, while the remaining 95% has air material properties. (2)Tungsten electrical conductivity is different from the bulk literature values. The sheet resistance on a real device has*

**) <sup>σ</sup> (S<sup>m</sup><sup>1</sup>**

**) S (V<sup>K</sup><sup>1</sup>**

**)**
