The world is making various efforts to reduce greenhouse gas (GHG) emissions, the main culprits of global warming. The Republic of Korea, the world’s seventh largest emitter of GHGs, aims to reduce GHG emissions by 37 % compared to “business as usual” by 2030 according to the Paris Climate Agreement. Measures such as the conversion from fossil fuels to new and renewable energies are being considered as a way to reduce GHG emissions. However, efforts in each industry and alternative energy resources to existing fossil fuels are required to achieve the 2030 GHG emissions reduction goal.

Recently, research on energy conversion has been conducted to recover renewable energy, such as waste heat, from industrial processes. Among the research on energy conversion, thermoelectric power generation using the Peltier element is being studied because this element is small and simple. Moreover, research related to thermoelectric power generation is actively being conducted [1][2].

Thermoelectric power generation generates electricity from heat using the “Seebeck effect,” which generates a voltage when there is a temperature difference between two different types of metals or semiconductors, and directly recovers waste heat as electrical energy without using other fossil fuels. It is a material technology that best responds to GHG reduction policies through energy saving [3]. Thermoelectric device technology is widely applied in automobiles, aerospace/aviation, semiconductors, optics, computers, power generation, and home appliances [4][5][6]. To apply these technologies to various fields and increase the efficiency of the systems, research is being conducted in research institutes and companies; however, research applied to ships is insufficient.

The purpose of this study is to incorporate a thermoelectric power generation system on a ship to recover the waste heat given off as exhaust gas from the ship. In addition, we intend to understand the temperature distribution and efficiency inside the system by considering the heat balance between the heat source and the thermoelectric element. Calculations are performed using MathCad Prime 3.0 in the engineering tools.

Table 1 lists the conditions of the heat source, and Table 2 lists the specifications of the thermoelectric element. To simplify the analysis, it is assumed that the properties of the Peltier element do not depend on temperature.

Figure 1 shows the thermal analysis model. The heat balance between the Peltier element and the heat source is calculated following the procedure detailed by the conventional research of an author [7] as follows:

Figure 1: 
Thermal analysis model of the thermoelectric generator system

• ① Calculate the intermediate temperature T_av(=[T_H+T_C])/2 between the heat sources and assume that this is the same as the intermediate temperature between the high-temperature side and the low-temperature side of the Peltier element.

• ② In the Peltier element, the temperature difference "T_hj–T_cj" is used as a parameter, and the initial calculated values of the high-temperature side temperature T_hj and the low-temperature side temperature T_cj of the Peltier element are obtained.

• ③ Set the number and arrangement of modules used in the system, and obtain the current I in the entire system from Table 2 and ②. Regarding the module arrangement, Table 3 shows the calculation methods according to the case of arranged in series and arranged in parallel. Additionally, the circuit diagram of the thermoelectric element is shown in Figure 2, and the external resistance R_o is estimated from R_o = M0R, where the conversion efficiency is maximized. M₀ is calculated using Equation (1).

The current I is calculated from the electromotive force V, as shown in Equation (2).

• ④ In this analysis, two types are set: four in series and four in series × four in parallel to prove the effect of heat transfer.

• ⑤ The energy balance at the high- and low-temperature sides of the thermoelectric module is shown by Equations (3) and (4), respectively.

• ⑥ The temperature difference between the high- and low-temperature sides of the thermoelectric element can be obtained using Equation (5).

• ⑦ Equation (6) is calculated from the heat balance on the high-temperature side of the thermoelectric element.

Here, the coefficients F₁, F₂, F₃, and F₄ in Equation (6) are obtained using the following equations:

• ⑧ Equation (7) is calculated from the heat balance of the low-temperature side in the thermoelectric element.

Here, the coefficients F₅, F₆, and F₇ are obtained by the following equations:

• ⑨ For each parameter, the value obtained in Equation (5) is compared with the values obtained by Equations (6) and (7), and the parameter with a small error is set as a reasonable value.

• ⑩ The conversion efficiency η in the system is calculated by Equation (8).

In this study, to introduce a thermoelectric power generation system in a ship, the following results were derived by setting the specifications of the heat source and thermoelectric element, and estimating the temperature distribution inside the system considering the heat balance between the heat source and thermoelectric element.

• 1.When one of the heat source media was a gas and the other a liquid, there was a deviation between the temperature distribution data estimated from the Peltier element performance and the temperature distribution data considered from the heat balance. To reduce this deviation, it is important to accurately calculate the high- and low-temperature side temperatures of the thermoelectric element to evaluate the Peltier element performance, including the difference in the overall heat transfer coefficient.
• 2. As in CASES 1 and 3, when the medium of the heat source was a gas on one side and a liquid on the other side, considering the heat transfer rate between the heat source and the thermoelectric element, there was an effect of increasing the number of thermoelectric elements. This is because the overall heat transfer coefficient of the gas, which was the heat source on the high-temperature side, was very low compared to the value of the liquid.
• 3. In addition, when the heat source medium was liquid, the effect hardly occurred even if the number of thermoelectric elements was increased. This is because the overall heat transfer coefficient at the high-temperature side and cooling side was sufficiently high.