## 4 Laboratory Characterization
Figure 5 depicts, for the two thermoelectric modules M1 and M2, the voltage (left axis) and the power generated (right axis) with respect to the intensity. From left to right, the values correspond to open-circuit (OC), 4.7 \(\Omega\), 3.2 \(\Omega\), 2.2 \(\Omega\), 1 \(\Omega\) and short-circuit (SC). As can be observed, the behavior of both thermoelectric modules is quite similar. As the load electrical resistance decreases, the intensity increases and the voltage decreases, with a linear relationship between them. In both cases, the open-circuit voltage is approximately 1.89 V while the short-circuit intensity presents a value of around 0.71 A (0.68 A M1, and 0.74 A M2). Regarding power generation, depending on the electrical load resistance connected to the thermoelectric modules, generation varies, obtaining its maximum with a load resistance equal to the electrical internal resistance of the thermoelectric module. Hence, given an available temperature difference between sources of 58.81 \({}^{\circ}\)C on average, module 1 (M1) generates a maximum of 0.34 W with a 2.2 \(\Omega\) load resistance, which corresponds with a current of 0.38 A. On its behalf, module 2 (M2) presents a slightly higher maximum generation, 0.36 W, also with a load resistance of 2.2 \(\Omega\), that in this case corresponds with an intensity of 0.40 A. The small disparities between both thermoelectric modules are due to the different thermal contacts arisen from the assembly as well as to the differences in the heat exchangers, which were manually manufactured. These disparities can be seen with more detail in Table 1. This table firstly displays, for each case, the temperatures of the heat source \(T_{source}\), the hot and the cold side of the thermoelectric modules \(T_{H}\) and \(T_{C}\), and the ambient temperature \(T_{amb}\). Based on the temperature difference of the cold side heat exchanger (\(T_{C}-T_{amb}\)) and its characterization, it is possible to make an iterative process and obtain the heat flux that is being released to the environment \(Q_{CHE}\) (Equation (1)). With this heat flux and the generated power \(P\), from the energy balance shown in Equation (2) the heat absorbed from the heat source \(Q\) can be obtained, permitting the calculation of the efficiency of the thermoelectric modules (Equation (3)). Thus, it can be observed that the heat flux that goes through M2 is 4.75%  
Figure 5: Voltage (left axis) and power generated (right axis) of the two thermoelectric modules studied, M1 and M2, with respect the intensity. The values correspond, from left to right, to open-circuit (OC), 4.7 \(\Omega\), 3.2 \(\Omega\), 2.2 \(\Omega\), 1 \(\Omega\) and short-circuit (SC). higher than the one that goes through M1. This explains the higher generation of M2, which works with an efficiency of 1% with the optimal load resistance. \[\dot{Q}=P+\dot{Q}_{CHE} \tag{2}\]  
\[\eta=\frac{P}{Q} \tag{3}\]  
Thanks to the calculated heat flux and the measured temperatures, the thermal resistance of the hot side heat exchanger (HHE) has also been calculated (Equation (4)). Hence, the hot side heat exchanger of M1 presents a thermal resistance of 0.36 K/W on average, while the one of M2 is a bit smaller, 0.35 K/W. In comparison with the cold side heat exchanger (CHE), the value of which remains practically constant at 0.24 K/W, these resistances are 33 and 30.9% higher respectively. As a consequence, the temperature difference in the hot side heat exchangers is higher than in the cold ones (12.26 versus 8.15 \({}^{\circ}\)C on average). \[R_{HHE}=\frac{T_{source}-T_{H}}{\dot{Q}} \tag{4}\]