## 2 Materials and Methodology  
### Principle and Mechanism of the TEG Module  
A thermoelectric generator is a direct energy conversion device. TEGs have no moving components and do not have any intermediate modes of operation. They convert thermal or heat energy into electricity [17]. TEGs have two sides, one that is hot and the other that is cool. It is possible to achieve the Seebeck effect [18] in a thermoelectric material when a temperature differential is formed on opposite sides of the material. As a consequence, energy is transferred from a lower to a higher level and a voltage differential is developed. The voltage difference between the hot and cold sides of a TEG is proportional to the temperature difference between them. The current density that results from this is as follows:  
\[J=\sigma(-\Delta V+Eemf) \tag{1}\]  
where \(E\) denotes the electric field, \(\sigma\) represents the conductivity of electricity, \(emf\) (electromotive force) in another meaning represents the Seebeck effect, and \(\Delta V\) denotes a voltage difference. Heat dissipation or absorption processes at the junction of p- and n-type ma terials are described by the Peltier effect [19; 20]. When the Peltier model absorbs heat, it generates electricity. When it dissipates heat, it consumes power. TEGs are made up of components with large concentrations of positive charges in p-type junctions and high concentrations of negative charges in n-type junctions. A significant number of positive charges or holes are doped into a p-type material, resulting in a positive Seebeck coefficient [21]. A negative Seebeck coefficient is obtained when an n-type material is doped with a large concentration of negative charges or electrons. Figure 1 shows a schematic of a TEG module. \(Q_{h}\) represents the rate of heat absorption and \(Q_{c}\) is the heat dissipation at the hot and cold junctions of a TEG module, respectively, which is calculated as follows [18; 22]:  
\[Q_{h}=\big{(}K_{p}+K_{n}\big{)}\big{(}T_{h}-T_{c}\big{)}+\big{(}\alpha_{p}- \alpha_{n}\big{)}\ IT_{h}-\frac{I^{2}R}{2} \tag{2}\]  
\[Q_{c}=\big{(}K_{p}+K_{n}\big{)}\big{(}T_{h}-T_{c}\big{)}+\big{(}\alpha_{p}- \alpha_{n}\big{)}\ IT_{c}+\frac{I^{2}R}{2} \tag{3}\]  
The thermal conductivities of the p-type and n-type TEG legs, respectively, are denoted by \(K_{p}\) and \(K_{n}\). The hot and cold junction temperatures are denoted by \(T_{h}\) and \(T_{c}\), respectively, while the Seebeck coefficients of the p-type and n-type TEG legs are \(\alpha_{p}\) and \(\alpha_{n}\), respectively. The electrical power of a TEG, as shown in Figure 1, is simply the voltage across the external load and the current in the circuit, calculated using a power balancing formula. Output power can be obtained in the following way:  
\[W=Q_{h}-Q_{c}=V.I \tag{4}\]  
Rearranging and simplifying Equations (2)-(4) yields the following results:  
\[V=\big{(}\alpha_{p}-\alpha_{n}\big{)}\big{(}T_{h}-T_{c}\big{)}-IR \tag{5}\]  
When Equation (5) is simplified and the assumptions that \(\Delta T=\big{(}T_{h}-T_{c}\big{)}\) and \(\alpha=\big{(}\alpha_{p}-\alpha_{n}\big{)}\) are made, the following result is obtained:  
\[V=\alpha\times\Delta T-IR \tag{6}\]  
Figure 1: Schematic depiction of a TEG module. If there is an electric current flowing, the output voltage is shown in Equation (6). It is possible to compute the open circuit voltage [23] as:  
\[\text{Voc}=\alpha\times\Delta T \tag{7}\]  
\[\Delta T=T_{h}-T_{c} \tag{8}\]  
The Seebeck coefficient is represented by \(\alpha\) and Voc is the open circuit voltage of a TEG module. Increasing the voltage can be accomplished by connecting numerous TEG modules in series or parallel [24]. Bismuth telluride was employed to make the TEG modules used in this study. The TEG module parameters in [17; 25] were used in the current study. A TEG panel was created by connecting TEG modules in series and parallel.