## 2 Materials and Methods
### Testing Methodology
#### 2.2.3 Measured Parameters  
Laboratory tests included the measurement of both thermal and electrical parameters. In terms of thermal parameters, the focus was primarily on the thermal power supplied to the \"skin model\" heating plate necessary to maintain its constant temperature at 35 \({}^{\circ}\)C in specific climatic conditions. This power was then converted into the heat flux transferred by the cooling system together with the heat sink using the equation:\[\mathrm{P_{c}}=\mathrm{P_{z}}-\mathrm{P_{0}}, \tag{1}\]  
where:  
\(\mathrm{P_{c}}\)--heat flux transferred by the cooling system (TEC with a heat sink) at a given electric power and in given climatic conditions, \(W\);  
\(\mathrm{P_{z}}\)--thermal power supplied to the heating plate to keep its temperature constant at a given electric power supplied to the TEC in given climatic conditions, \(W\);  
\(\mathrm{P_{0}}\)--thermal power supplied to the heating plate with the TEC power supply turned off, thus corresponding to the heat exchanged directly between the plate and the environment, \(W\).  
In the case of isothermal tests, the direct heat flux from the plate to the environment was 0 \(W\); therefore, the heat flux transferred by the TEC system was identical to the thermal power supplied to the heating plate.  
In terms of electrical parameters, during the tests, TEC current and voltage were measured, which were then used to determine the electric power using the equations:  
\[\mathrm{P_{e}}=\mathrm{U_{r}}\times\mathrm{I}, \tag{2}\]  
\[\mathrm{U_{r}}=\mathrm{U}-\mathrm{R_{w}}\times\mathrm{I}, \tag{3}\]  
where:  
\(\mathrm{P_{e}}\)--electric power, \(W\);  
\(\mathrm{U_{r}}\)--actual TEC voltage, taking into account the resistance of electric wires, \(\mathrm{V}\);  
\(\mathrm{I}\)--TEC current, \(\mathrm{A}\);  
\(\mathrm{U}\)--measured voltage, \(\mathrm{V}\);  
\(\mathrm{R_{w}}\)--common (factory-made) wire resistance, 15.6 \(\mathrm{m}\Omega\).  
The related measurement uncertainty of power is, therefore, a function of the uncertainties of the voltage and current meters given in Section 2.2.1. It can be approximated with:  
\[\mathrm{\Delta P_{rel}}/\mathrm{P}\approx\mathrm{\Delta U_{rel}}/\mathrm{U} \times\mathrm{\Delta I_{rel}}/\mathrm{I} \tag{4}\]  
for the relative part, where \(\mathrm{\Delta U_{rel}}/\mathrm{U}\) and \(\mathrm{\Delta I_{rel}}/\mathrm{I}\) are the relative parts of uncertainties of the voltmeter and of the ammeter, respectively; and with  
\[\mathrm{\Delta P_{abs}}\approx\left(1+\mathrm{\Delta U_{rel}}/\mathrm{U} \right)\times\mathrm{U}\times\mathrm{\Delta I_{abs}}+\left(1+\mathrm{\Delta I _{rel}}/\mathrm{I}\right)\times\mathrm{I}\times\mathrm{\Delta U_{abs}} \tag{5}\]  
for the absolute part, where \(\mathrm{\Delta U_{abs}}\) and \(\mathrm{\Delta I_{abs}}\) are the absolute parts of uncertainties of the voltmeter and of the ammeter, respectively.  
The measurement error related to the \(\mathrm{R_{w}}\times\mathrm{I}\) term may be neglected, as the common wire resistance \(\mathrm{R_{w}}\) is much smaller than the Pelter module resistance (which is of the order of several ohms) to which the \(\mathrm{U}\) term is proportional.