*6.1. Experimental Outputs of Current, Power and Thermal E*ffi*ciency*

The current, power and thermal efficiency as the performance parameters of the thermoelectric generator system for waste heat recovery are experimentally tested with the hot gas inlet temperatures of 315.12 ◦C, 419.26 ◦C, 521.70 ◦C and 621.61 ◦C and the voltage load range of 0 to 10 V. During the experiments, the voltage load is varied with time for each hot gas inlet temperature. Two experimental data sets for the development of a numerical method, ANN models and ANFIS models are considered as the training data set and testing data set of the thermoelectric generator system for waste heat recovery. The training data set (first) with variations of the current, power and thermal efficiency of thermoelectric generator system for waste heat recovery for hot gas inlet temperatures of 315.12 ◦C, 419.26 ◦C, 521.70 ◦C and 621.61 ◦C and voltage load range of 0 to 10 V is selected and the testing data set (second) with the variation of current, power and thermal efficiency of thermoelectric generator system for waste heat recovery for hot gas inlet temperature of 419.26 ◦C and voltage load range of 0 to 5.5 V is selected based on the experiments.

Figure 5 shows the variations of the current, power and thermal efficiency for the training and testing data sets. For all hot gas inlet temperatures, the current of the thermoelectric generator system for waste heat recovery is linearly decreased and the power and thermal efficiency of the thermoelectric generator system for waste heat recovery show the parabolic variations with the voltage load of range 0 to 10 V for the training data set and 0 to 5.5 V for the testing data set, respectively. The current, power and thermal efficiency of the thermoelectric generator system for waste heat recovery increase with the increase of the hot gas inlet temperature from 315.12 ◦C to 621.61 ◦C. Therefore, the maximum and average values of the current, power and thermal efficiency of the thermoelectric generator system for waste heat recovery are increased with the increase of the hot gas inlet temperature. For the training data set, the maximum current of 4.1, 7.13, 9.42 and 10.95 A and average current of 2.28, 3.90, 4.99 and 5.95 A, the maximum power of 3.40, 9.75, 17.55 and 24.8 W and average power of 1.94, 5.93, 11.10 and 15.22 W and the maximum efficiency of 1.28, 2.16, 2.87 and 3.39% and average efficiency of 0.72, 1.30, 1.81 and 2.07% are selected experimentally at the hot gas inlet temperatures of 315.12 ◦C, 419.26 ◦C, 521.70 ◦C and 621.61 ◦C, respectively. For the testing data set, the hot gas inlet temperature of 419.26 ◦C is the same as the training data set, but the voltage load condition is different with time as shown in Figure 5. Thus, for the testing data set at the hot gas inlet temperatures of 419.26 ◦C, the maximum current is 8.1 A and the average current is 4.41 A. The maximum power is 11.4 W and the average power is 6.95 W. The maximum efficiency is 2.35% and the average efficiency is 1.43%. As a result, the current, power and thermal efficiency of the thermoelectric generator system for waste heat recovery

sets.

at the hot gas inlet temperature of 419.26 ◦C are different for the training and testing data sets because *Symmetry*  of the di **2020** fferent voltage loads. , *12*, x FOR PEER REVIEW 10 of 30

**Figure 5.** Variation of (**a**) current, (**b**) power, and (**c**) thermal efficiency for training and testing data **Figure 5.** Variation of (**a**) current, (**b**) power, and (**c**) thermal efficiency for training and testing data sets.

#### *6.2. Prediction Results from the Numerical Method 6.2. Prediction Results from the Numerical Method*

The numerical simulation of the thermoelectric generator system for waste heat recovery at the hot gas inlet temperatures of 419.26 ◦C, cold water temperature of 30 ◦C, hot gas mass flow rate of 0.018 kg/s and cold-water mass flow rate of 0.075 kg/s is performed. From the numerical simulation of the thermoelectric generator system for waste heat recovery with various boundary conditions of the hot gas and cold water, the hot and cold surfaces of the thermoelectric modules are simulated. The numerical simulation of the thermoelectric generator system for waste heat recovery at the hot gas inlet temperatures of 419.26 °C, cold water temperature of 30 °C, hot gas mass flow rate of 0.018 kg/s and cold-water mass flow rate of 0.075 kg/s is performed. From the numerical simulation of the thermoelectric generator system for waste heat recovery with various boundary conditions of the hot gas and cold water, the hot and cold surfaces of the thermoelectric modules are simulated.

*Symmetry* **2020**, *12*, x FOR PEER REVIEW 11 of 30

The temperature of the hot gas decreases with the direction from the inlet to the outlet of the heat exchanger, but the temperature of the cold water increases as the cold water flows from the inlet to the outlet of the cold-water channel. This is because the hot gas transfers the heat and the cold water absorbs the heat from the thermoelectric modules. Therefore, the hot surface and cold surface temperatures of the thermoelectric module are varied with locations because the temperature distributions of the hot gas and cold water depend on the locations. The temperature of the hot gas decreases with the direction from the inlet to the outlet of the heat exchanger, but the temperature of the cold water increases as the cold water flows from the inlet to the outlet of the cold-water channel. This is because the hot gas transfers the heat and the cold water absorbs the heat from the thermoelectric modules. Therefore, the hot surface and cold surface temperatures of the thermoelectric module are varied with locations because the temperature distributions of the hot gas and cold water depend on the locations.

The temperature distributions of the hot and cold surfaces of the thermoelectric modules with locations (*x* and *y* coordinates) at the hot gas inlet temperature of 419.26 ◦C are showed in Figure 6. Figure 6 shows the temperature distributions of the hot and cold surfaces of the top six thermoelectric modules and the corresponding bottom six thermoelectric modules. In addition, the hot surface temperatures of the thermoelectric module near the inlet of the heat exchanger show higher than those of the thermoelectric modules near the outlet of the heat exchanger. Thus, the current, power and thermal efficiency results of the thermoelectric generator system for waste heat recovery are simulated using the temperature distributions of the hot and cold surfaces of the thermoelectric modules and the voltage load conditions of the testing data set. The temperature distributions of the hot and cold surfaces of the thermoelectric modules with locations (*x* and *y* coordinates) at the hot gas inlet temperature of 419.26 °C are showed in Figure 6. Figure 6 shows the temperature distributions of the hot and cold surfaces of the top six thermoelectric modules and the corresponding bottom six thermoelectric modules. In addition, the hot surface temperatures of the thermoelectric module near the inlet of the heat exchanger show higher than those of the thermoelectric modules near the outlet of the heat exchanger. Thus, the current, power and thermal efficiency results of the thermoelectric generator system for waste heat recovery are simulated using the temperature distributions of the hot and cold surfaces of the thermoelectric modules and the voltage load conditions of the testing data set.

**Figure 6.** *Cont*.

**Figure 6.** Temperature distributions (**a**) Module 1-hot surface, (**b**) Module 1-cold surface, (**c**) Module 2-hot surface, (**d**) Module 2-cold surface, (**e**) Module 3-hot surface, (**f**) Module 3-cold surface, (**g**) Module 4-hot surface, (**h**) Module 4-cold surface, (**i**) Module 5-hot surface, (**j**) Module 5-cold surface, (**k**) Module 6-hot surface, (**l**) Module 6-cold surface with locations (*x* and *y* coordinates) at 419.26 °C. **Figure 6.** Temperature distributions (**a**) Module 1-hot surface, (**b**) Module 1-cold surface, (**c**) Module 2-hot surface, (**d**) Module 2-cold surface, (**e**) Module 3-hot surface, (**f**) Module 3-cold surface, (**g**) Module4-hot surface, (**h**) Module 4-cold surface, (**i**) Module 5-hot surface, (**j**) Module 5-cold surface, (**k**) Module6-hot surface, (**l**) Module 6-cold surface with locations (*<sup>x</sup>* and *<sup>y</sup>* coordinates) at 419.26 ◦C.

The comparisons of experimental and numerical results of the current, power and thermal efficiency of the thermoelectric generator system for waste heat recovery for the testing data set are shown in Figure 7. The error between the experimental and numerical values for the current of the thermoelectric generator system for waste heat recovery is validated within 2% except for the initial and end voltage conditions. In addition, the error between the experimental and numerical results for the power and thermal efficiency of the thermoelectric generator system for waste heat recovery is validated within 4% except for the initial and end voltage conditions. The comparisons of experimental and numerical results of the current, power and thermal efficiency of the thermoelectric generator system for waste heat recovery for the testing data set are shown in Figure 7. The error between the experimental and numerical values for the current of the thermoelectric generator system for waste heat recovery is validated within 2% except for the initial and end voltage conditions. In addition, the error between the experimental and numerical results for the power and thermal efficiency of the thermoelectric generator system for waste heat recovery is validated within 4% except for the initial and end voltage conditions.

The accuracy of numerical method for the current, power and thermal efficiency of the thermoelectric generator system for waste heat recovery is shown in Table 2. The numerical results of the current, power and thermal efficiency of the thermoelectric generator system for waste heat recovery show a good agreement with the corresponding experimental results [3]. The selection of the accurate boundary condition, meshing configuration with conduction and inflation effects, discretization method and suitable solver result in closer agreement between the numerical and experimental results of the thermoelectric generator system for waste heat recovery. Therefore, the experimental approach of the thermoelectric generator system for waste heat recovery with high manufacturing and installation costs, higher complexity and higher level of efforts could be replaced with a numerical approach of the thermoelectric generator system for waste heat recovery. The accuracy of numerical method for the current, power and thermal efficiency of the thermoelectric generator system for waste heat recovery is shown in Table 2. The numerical results of the current, power and thermal efficiency of the thermoelectric generator system for waste heat recovery show a good agreement with the corresponding experimental results [3]. The selection of the accurate boundary condition, meshing configuration with conduction and inflation effects, discretization method and suitable solver result in closer agreement between the numerical and experimental results of the thermoelectric generator system for waste heat recovery. Therefore, the experimental approach of the thermoelectric generator system for waste heat recovery with high manufacturing and installation costs, higher complexity and higher level of efforts could be replaced with a numerical approach of the thermoelectric generator system for waste heat recovery.

**Figure 7.** The comparisons of experimental and numerical results of the current, power and thermal efficiency for testing data set. **Figure 7.** The comparisons of experimental and numerical results of the current, power and thermal efficiency for testing data set.



Thermal efficiency 0.99992 0.01422 0.99102
