3.4.1. Single Stage Arrangement

The variation of maximum efficiency with the temperature difference for the single stage thermoelectric module with three leg geometries and two materials is shown in Figure 8a. Maximum efficiency is the ratio of maximum power to the heat absorbed [13]. Similar to that of maximum power, the leg geometries had no effect on maximum efficiency for the same material [1,6,10]. For all the leg geometries and materials, as the temperature difference increased, the maximum efficiency also increased. For the same leg geometry, the Bi2Te<sup>3</sup> material showed superior increase in maximum efficiency compared to the SiGe material over the entire temperature difference range due to high *ZT* [4]. Although the Bi2Te<sup>3</sup> material was operated up to a temperature difference of 480 ◦<sup>C</sup> due to its low melting point temperature, it still showed the highest value of maximum efficiency at a temperature difference of 480 ◦C, compared to the maximum efficiency value for the SiGe material at a temperature difference of 980 ◦C. At temperature difference of 480 ◦C, the Bi2Te<sup>3</sup> material had a higher maximum power, thus showing higher maximum efficiency than SiGe. From a temperature difference of 480 to 980 ◦C, the SiGe material showed increase in maximum power and the heat absorbed also increased due to increase in temperature difference, which resulted in lower maximum efficiency for the SiGe material than that of the Bi2Te<sup>3</sup> material. Maximum efficiency of 12.2% was observed at a temperature difference of 480 ◦C for all the leg geometries with the Bi2Te<sup>3</sup> material. However, maximum efficiency of 5.1% was obtained for all the leg geometries with the SiGe material at a temperature difference of 980 ◦C.

(**a**) Single stage arrangement

(**b**) Two-stage arrangement

**Figure 8.** *Cont*.

**Figure 8.** Maximum efficiency for (**a**) single stage arrangement (**b**) two-stage arrangement, and (**c**) single stage segmented arrangement. **Figure 8.** Maximum efficiency for (**a**) single stage arrangement (**b**) two-stage arrangement, and (**c**) single stage segmented arrangement.

#### 3.4.2. Two-stage Arrangement 3.4.2. Two-Stage Arrangement

entire temperature difference range.

3.4.3. Single Stage Segmented Arrangement

Figure 8b shows maximum efficiency variations with temperature difference for the two-stage arrangement of the thermoelectric module with various leg geometries and materials. For the same leg geometry, the Bi2Te3 material showed the highest values of maximum efficiency with temperature difference, compared to the SiGe+Bi2Te3 and SiGe materials but up to a temperature difference of 480 °C. However, from temperature difference of 480 °C, the SiGe+Bi2Te3 material showed increase in maximum efficiency up to the temperature difference corresponding to the optimum temperature condition. The SiGe material showed the lowest values of maximum efficiency until the temperature difference of 980 °C. Although Bi2Te3 as well as SiGe+Bi2Te3 materials are operated till a particular temperature difference because of the limitation of their melting point temperatures, they still showed comparatively higher values of maximum efficiencies than the SiGe material. For the same material, leg geometry had very less effect on maximum efficiency because of the same optimum voltage load and same internal resistance [1,6,10]. In the case of SiGe, Bi2Te3 and SiGe+Bi2Te3 materials, square prism, cylindrical, and trapezoidal legs showed almost the same maximum efficiency variation with temperature difference. At a temperature difference of 980 °C and for the SiGe material, the square prism legs and cylindrical legs showed maximum efficiency of 4.6% and the cylindrical legs showed maximum efficiency of 4.7%. For the Bi2Te3 material and temperature difference of 480 °C, the square prism legs and cylindrical legs showed maximum efficiency of 10.8% and the cylindrical legs showed maximum efficiency of 11.1%. In the case of the SiGe+Bi2Te3 material, the square prism legs showed maximum efficiency of 15% at a temperature difference of 880 °C and the cylindrical as well as trapezoidal legs showed maximum efficiencies of 14.6% and 14.4%, respectively, at a temperature difference of 830 °C. The maximum efficiency of the two-stage arrangement of the thermoelectric module with leg geometries and materials increased over the Figure 8b shows maximum efficiency variations with temperature difference for the two-stage arrangement of the thermoelectric module with various leg geometries and materials. For the same leg geometry, the Bi2Te<sup>3</sup> material showed the highest values of maximum efficiency with temperature difference, compared to the SiGe+Bi2Te<sup>3</sup> and SiGe materials but up to a temperature difference of <sup>480</sup> ◦C. However, from temperature difference of 480 ◦C, the SiGe+Bi2Te<sup>3</sup> material showed increase in maximum efficiency up to the temperature difference corresponding to the optimum temperature condition. The SiGe material showed the lowest values of maximum efficiency until the temperature difference of 980 ◦C. Although Bi2Te<sup>3</sup> as well as SiGe+Bi2Te<sup>3</sup> materials are operated till a particular temperature difference because of the limitation of their melting point temperatures, they still showed comparatively higher values of maximum efficiencies than the SiGe material. For the same material, leg geometry had very less effect on maximum efficiency because of the same optimum voltage load and same internal resistance [1,6,10]. In the case of SiGe, Bi2Te<sup>3</sup> and SiGe+Bi2Te<sup>3</sup> materials, square prism, cylindrical, and trapezoidal legs showed almost the same maximum efficiency variation with temperature difference. At a temperature difference of 980 ◦C and for the SiGe material, the square prism legs and cylindrical legs showed maximum efficiency of 4.6% and the cylindrical legs showed maximum efficiency of 4.7%. For the Bi2Te<sup>3</sup> material and temperature difference of 480 ◦C, the square prism legs and cylindrical legs showed maximum efficiency of 10.8% and the cylindrical legs showed maximum efficiency of 11.1%. In the case of the SiGe+Bi2Te<sup>3</sup> material, the square prism legs showed maximum efficiency of 15% at a temperature difference of 880 ◦C and the cylindrical as well as trapezoidal legs showed maximum efficiencies of 14.6% and 14.4%, respectively, at a temperature difference of 830 ◦C. The maximum efficiency of the two-stage arrangement of the thermoelectric module with leg geometries and materials increased over the entire temperature difference range.
