# Heat Transfer in Thermoelectric Generators for Waste Energy Recovery in Piston Engines
## 4 Results
### Study of Recirculation Regions  
The recirculation seen in the base case (Figure 8) has been studied in this subsection. The recirculation appears in the corners of the squared central section, and the region with negative axial velocity roughly takes up about half the cross-sectional area (Figure 9a). This recirculation necessarily creates a central high axial velocity zone of approximately 40 m/s to maintain the exhaust mass flow rate.  
Two modifications to the inlet cone were made to alter this recirculation. The first is an increase in the longitude of the inlet cone to make the area expansion more gradual (see Figure 4a). As can be seen in Figure 9b, the area of recirculation is reduced. The second modification was to insert flow splitters in the inlet cone (Figure 4b). As can be seen, the recirculation pattern changes, and now the recirculation regions appear in the upper and lower parts of the heat exchanger (Figure 9c). In terms of area, the recirculation region takes up around two-thirds of the cross-sectional area at the end of the inlet cone. It can be concluded that the minimum recirculation appears on the enlarged inlet cone.  
Figure 8: Streamlines colored by velocity (m/s) in the base case design. Recirculation regions are visible near the inlet of the cross-sectional area expansion.  
Figure 7: Wall temperature (\({}^{\circ}\)C) in the (**a**) exhaust pipe and (**b**) base design.  
Let us now discuss the effect of these recirculation patterns on the heat transferred to the walls (Figure 10). Despite having lower recirculation, the enlarged inlet design (Figure 10b) presents temperatures slightly lower than the base case (Figure 10a). This is due to the larger cone exposed to the ambient light that this design presents before the central geometry. More heat is dissipated before the flow reaches the central body, where the thermoelectric modules are to be placed. In the split inlet, clearly the recirculation region concentrated in the upper and lower parts makes for worse heat transfer to the wall near the inlet of the central square-shaped body (Figure 10c).  
To summarize, recirculation hinders heat transfer to the wall as it moves the incoming hot gas stream away from the wall. Nevertheless, it is also important to keep the inlet cone short since heat transferred through the cone walls is lost since thermoelectric modules cannot be placed there.  
In terms of pressure drop, the enlarged inlet design is more beneficial (Table 5). This is due to a less steep expansion of the duct, which reduces the recirculation and irreversibility of the flow. However, less heat and less wall temperature are achieved compared with the base case. In addition, the added length makes the implementation of these devices more difficult. For this reason, the base case with the initial inlet cone (base case, Figure 3b) was selected for the final TEG.  
Figure 10: Surface temperatures (\({}^{\circ}\)C) of the central body with the different inlet cones.  
Figure 9: Axial velocity (m/s) at the end of the inlet cone. Dark blue are values out of scale, i.e., negative axial velocity values.