Integrated TEG model

Figure ‎4.11 The Equivalent circuits of TEGs

The integrated TEG model is comprised of the TE module model and the model of the heat exchanger system, as shown in Figure 4.11. In order to simplify the numerical model, the ideal hot and the cold sources are employed in this work. It is assumed that the hot side heat exchanger is attached to an ideal heat source with a constant temperature , while the heat sink is open to an ideal cold source (ambient air) with a constant temperature . is the rate of heat transfer from the heat source to the hot side heat exchanger at temperature , and is the rate of heat releasing from the heat sink at temperature to ambient. Then Equations 4.19 and 4.20 can be rewritten as follows：

(4.38)

A cubic equation for can be obtained by combining Equations (4.38-4.41).

Three roots can be obtained from Equation 4.42.

√ of the TEG can be calculated by integrating the real root.

(4.47) (4.48) (4.49) 4.3.2 Model validation

A laboratory prototype of a TEG was built, as shown in Figure 4.12, to determine the accuracy of the computational model. As stated in the previous work, a Bi2Te3 TE module is well suited for low temperature applications. The prototype was built by using a commercially available TE module TEC1-12706 (TEC1-12706, 2008)with a size of . The TE module has been inserted between the massive aluminium plate with the size of and an aluminium heat sink with size of . An electric heater was employed to simulate the constant heat source. A thermal insulation box, which is designed by using some pieces of spong to surround the TE module, has been employed in the prototype in order to thermally insulate the TE module from air. Then the heat flow of the TEG can be consider only be dissipated from the cold side of the TE module through the heat sink to air. In order to maintain a constant room temperature, the prototype has been set in the room with air conditioning, where the room temperature is maintained at . According to the experimental test, the thermal balance is reached in around 30 minutes. Hence, the prototype of TEG has been tested after the thermal equilibrium was reached. Moreover, in order to demonstrate the maximum power point of the TEG, a 1K potentiometer has been connected to the TEG to imitate the electrical load .

Figure ‎4.12 Test prototype of thermal energy harvesting 4.3.2.1 Parameter setting

In order to simulate the experimental conditions by using the proposed model, some parameters of the system should be determined. Normally, the TE properties for both p-type and n-type Bi2Te3 semiconductors, which are the Seebeck coefficient ( ), the thermal resistance of the thermal couple ( ) and the internal resistance of the module ( ), should be determined before simulation. But unfortunately, the manufactures of TE modules use the following parameters to specify their products, as shown in Table 4.3.

By inserting the parameters from Table 4.3 into Equaitons 4.50, 4.51 and 4.52, the prameters of the proposed model can be calculated. And thus: ,

The experimental results of physical TE modules are compared with the computer simulation result shown in Figure 4.13. According to the figure, the accuracy of the

computational model can be observed to be around 89%, which means there is a great agreement between measurement and simulation.

Figure ‎4.13 Power generated for different 4.3.2.2 Capabilities of a TE module

As stated in the previous sections, the capability of a TE module is the crucial factor in determining the TEG’s conversion efficiency. The capability of a TE module is determined by the TE material parameters, including Seebeck coefficient, internal electrical resistance, and thermal resistance. For the limited heat environment, the maximum system performance can be obtained when the thermal resistance of the TE module equals to the thermal resistance of the heat exchanger system. For the infinite heat environment, the following parameters have been evaluated by the model.

In order to determine the relationship between Seebeck coefficient and the power generated by the TEG, four groups of Seebeck coefficients have been compared by using the simulation model, as shown in Figure 4.14 a. By observing the curves, when the Seebeck coefficient improved 35%, more than 80% of power can be generated by the same system. This is why plenty of research works focus on developing high coefficient TE materials for improving TEG’s efficiency. The experimental results of

V/K have been compared with the simulation results to show the accuracy of the model, and the results show this to be 90%.

The second parameter being considered in this chapter is the internal resistance of the TE module. Figure 4.14b shows different internal resistances of the TE module influences the output power of the TEG. It can be seen that, the less internal resistance of the TE module has, the more electric power can be generated. According to this rule, the TE module with less internal resistance is preferred in a highly efficient thermal energy harvesting system design. The corresponding internal resistance of 2.3ohms has been evaluated in the laboratory. The accuracy of the model is 91%.

Thirdly, in order to determine how the thermal resistance of the TE module affects the system performance, the thermal resistance of the TE legs and the external thermal resistance of the TE module have been simulated respectively. The simulation results are shown in Figures 4.14 c and d, respectively. In these two figures, the same trend has been found by examining the curves. The maximum power can be generated when the lowest thermal resistance of the module exists. The corresponding experimental results ( are obtained in the laboratory.

The accuracy in these two cases are 91.2% and 90.6%, respectively. Hence, a conclusion can be made that a good TE module should combine a high Seebeck coefficient, a low thermal resistance and a low electric resistance. The simulation results match the corresponding experimental results.

Figure ‎4.14 (a) Power generated with different Seebeck coefficient (b) Power generated with different internal electric resistances (c) Power generated with different internal thermal resistances (d) power generated with different external thermal resistance of the module