## 3 Results  
### Discussion  
Having successfully conducted the simulation for a segmented module (32 couples) with the cold side and interface temperatures of 300 k and 450 k, respectively. The hot side temperature for three different sets of simulations are 500 k, 600 k, and 800 k. For optimization, various simulations were carried out. The length of the legs should be long enough to gain optimum efficiency and minimum thermal stress, and should be short enough to produce high output power [47]. Thus, 6 mm was selected. From the cold side, the temperature at which Bi\({}_{2}\)Te\({}_{3}\) and Sb\({}_{2}\)Te\({}_{3}\) have the highest efficiency occurs at approximately one third of the length of the leg. Thus, the segmentation ratio is uniformed and found to be 2:1 skutterudites to chalcogenides, respectively. The cross-sectional area of the p-type leg was selected to be 4 mm \(\times\) 4 mm. The resistivities of n-type and p-type legs for both skutterudites and chalcogenides materials are different. Having the same cross-sectional area will make the current pass through the leg with the highest resistance, which will result in a low output efficiency of the leg. For an optimal efficiency of the module, the n-type cross-sectional area should be less than p-type cross-sectional area via \(\frac{A_{n}}{A_{p}}=\sqrt{\frac{Q_{p}\cdot P_{p}}{Q_{w}\cdot N_{e}}}\)[44]. The module has an overall dimension of 40 mm \(\times\) 40 mm \(\times\) 7 mm. As mentioned earlier, the compatibility factor is a key to increasing the conversion efficiency of the module. Figures 3 and 4 show the p-type and n-type compatibility factors of the materials, respectively. For the module simulation, the material properties were fully assigned and the heat transfer in the solids was defined (i.e., the temperature gradients of 500 K, 300 k, 200 k were specified). On the cold side, the ground was assigned to the n-type leg and the terminal was assigned to the p-type leg. Electrical circuit physics were added to include an electrical load resistor to the circuit. An external I Vs U 1, which operates as a voltage source within the circuit, was labelled properly to correspond to the resistor and ground node labels. The value of the internal resistance was calculated from Equation (3) at T\(\Delta\) = 500 k is 0.2 \(\Omega\). The maximum power occurs when \(\frac{R_{L}}{R}=1\). The condition for attaining maximum conversion efficiency differs to that of the maximum power. The thermoelectric effect, electromagnetic heat source, and boundary electromagnetic heat source were selected, while the boundary thermoelectric effect and temperature coupling were deselected. The type of physics controlled mesh was chosen, and the stationary study was selected for the computation of the results. Open circuit simulations for temperature gradients of 200 k, 300 k, and 500 k give an output voltage of 2.44 V, 3.82 V, and 6.2 V, and a matched load output power of 6.2 W, 15.2 W, and 45 W, respectively. Figure 4: N-type compatibility factor of the materials. Figure 3: P-type compatibility factor of the materials. To determine the maximum power and the maximum conversion efficiency, a parametric sweep of the load resistance was conducted. For each simulation, a 1D plot was selected from the result, then the y-axis data drop box displayed the current terminal and voltage terminal values for computing power, while the total net heat rate for T1 (hot side) was used to compute the efficiency. At a temperature gradient of 500 k, the calculated conversion efficiency of the unsegmented skutterudite n-type Ba\({}_{0.1}\)Yb\({}_{0.2}\)Fe\({}_{0.1}\)Co\({}_{9.9}\)Sb\({}_{12}\) and p-type Ce\({}_{0.5}\)Yb\({}_{0.5}\)Fe\({}_{3.25}\)Co\({}_{0.75}\)Sb\({}_{12}\) based TEG module is 10%, while its maximum simulated efficiency is 9.2%. However, at the same temperature the calculated conversion efficiency of the segmented TEG device is 17.2%, while the maximum simulated conversion efficiency is 15.7%.