###### Abstract
Nevertheless, the quest for more efficient TEGs continues, with current research focusing on nanostructured materials and novel geometries to enhance thermoelectric performance. Recent research has focused on enhancing the thermoelectric performance of materials through nanostructuring and novel geometries. [PERSON] [11] and [PERSON] [12] both highlight the role of nanostructuring in reducing lattice thermal conductivity, a key factor in improving thermoelectric performance. This is further supported by [PERSON] [13], who discusses the use of solution-based chemistry approaches to prepare thermoelectric nanomaterials with reduced thermal conductivity. [PERSON] [14] and [PERSON] [15] both emphasize the importance of using eco-friendly and low-cost elements in nanostructured thermoelectric materials. [PERSON] [16] and [PERSON] [17] discuss novel nanostructuring methods, such as phonon-selective scattering and the use of nanocomposite materials, to enhance thermoelectric performance. [PERSON] [18; 19] and colleagues extensively examined the heat exchangers used in thermoelectric waste heat recovery systems, focusing specifically on hexagonal and compact heat exchangers in typical automotive settings [20]. Their analysis demonstrated the successful conversion of heat into electricity, illustrating the potential of TEGs in automotive applications. This underscores the broader relevance of TEGs in various sectors,  
Figure 1: This diagram provides a detailed representation of the architecture and component layout of a thermoelectric chip, illustrating its functional and structural elements. including industrial and residential energy recovery, where their adaptability to different heat sources can be leveraged. Improving thermoelectric materials and device construction is necessary to enhance waste heat recovery devices' total thermoelectric conversion efficiency [21]. [PERSON] et al. [22] found that optimizing the structure of a device is very important. The evolution of thermoelectric materials from traditional bismuth telluride to more advanced compounds has opened up new possibilities in device efficiency and application. They saw that increasing the thermal contact area and decreasing the height of the thermoelectric element led to significant improvements in power production and heat conversion. This highlights the critical role of material science and engineering in optimizing TEGs for higher performance and broader applicability. [PERSON] et al. [23] simulated thermoelectric elements with various shapes. They found that even basic hollow and layered structures could generate more considerable temperature differences and more power compared to conventional cuboid structures. These findings point to the need for continued innovation in TEG design, exploring different geometries and configurations to maximize efficiency. [PERSON] et al. [24] performed comprehensive numerical investigations on the influence of thermoelectric element configuration and heat transfer surface area in cooling modules, determining the most favorable operating currents to achieve the maximum cooling capacity and performance under different conditions. Such studies are pivotal in guiding the design and optimization of next-generation thermoelectric devices. [PERSON] et al. [25] highlighted that annular thermoelectric generators can potentially reduce thermal contact resistance from geometric mismatches with circular sources/sinks. This suggests a significant direction for TEG development, focusing on minimizing energy losses and maximizing compatibility with various heat sources. In a comparison of flat-plate and annular thermoelectric generators (ATEG), [PERSON] et al. [26] discovered that ATEGs outperformed FTEGs when exposed to cylindrical heat sources with higher inlet temperatures and heat transfer coefficients. The superior performance of ATEGs in such scenarios underlines their potential in specific industrial applications where cylindrical heat sources are prevalent. [PERSON] et al.