Traditional fossil fuel power generation process typically has low efficiency. Large amount of the energy loss in Rankine cycle steam turbines (ST) is due to the temperature difference between the combustion flame temperature ∼2250 K (adiabatic) and the high pressure steam temperature up to 900 K. However, some of this energy can be harvested using solid-state thermoelectric (TE) power generators which are placed into the gap between the flame temperature and the steam temperature that produce additional electrical power. This study investigates the potential placement of TE on water tube wall inside a boiler at a coal-fired power plant. Three-dimensional (3D) numerical model of a simplified TE module is developed, and hot gas temperature and steam temperature from the boiler are used as boundary conditions at the hot side and cold side of the TE. The numerical results are compared with analytical calculations. The 3D effects of the thermal spreading in the TE module are investigated. Parameters such as TE leg cross section area and TE fill factor are examined in order to maximize the electrical power production of the TE without sacrificing the boiler efficiency (i.e., reducing the steam temperature). The study also looks into the various locations inside the boiler that have good potential for TE installation.
TE generators utilize TE effect to directly convert thermal energy into electric. TE generators produce voltage when there is a temperature difference between the hot side and the cold side of TE generators.
TE generators have been receiving relatively a lot of attention for the waste heat recovery applications. Masahide et al. , Yodovard , Hsu et al. , and Kumar et al.  applied the TE technology to recover heat from vehicle exhaust and engine and convert it into electrical power to provide auxiliary power for the vehicle. TE generators have also been used to generate electricity from solar power [5–8]. Chen et al.  presented an analysis of system efficiency and evaluation of impact of TE power cycle application to thermal energy systems.
Yazawa et al.  proposed adding a TE power generator into the gap between the flame temperature and the steam temperature. Yazawa et al. developed a generic model and analyzed energy economy for a combined TE generator on top of a ST cycle. The temperature or this application will be much higher than those of the waste heat recovery applications which have been heavily investigated. The TE materials can be tuned for the targeted high temperatures. Yazawa and Shakouri  reported that the TE module can be designed for optimum by changing the element thickness to match the external thermal resistances.
The primary objective of this study is to investigate the potential placement of TE on water tube wall inside a boiler at a coal-fired power plant. The present study looks into the 3D effects of the thermal spreading in the TE module. Parameters such as TE leg cross section area and TE fill factor are examined in order to maximize the electrical power production of the TE without sacrificing the boiler efficiency (i.e., reducing the steam temperature).
Figure 1 presents the schematic of the simplified TE module studied. The model only consists of a single TE leg. The TE module consists of outer shells, electrodes, and TE leg. The materials for the outer shells and the electrodes are molybdenum and spattered molybdenum, respectively. The TE module hot side is exposed to the hot gas, the cold side is attached to the boiler tube surface. The dimension of the TE module and its material properties are listed in Table 1. The fill factor (fractional area coverage of TE element relative to cross section are of heat flow) of the TE leg is 40%.
and ZT, the dimensionless figure-of-merit of the TE material and Z is defined as Z = σS2/β. T is the mean temperature across the TE leg.
where q is the heat flux through the TE leg.
Figure 3 presents the boundary conditions applied to the assembly. The hot side temperature (Thot) is the temperature of the hot gas inside the boiler chamber; and the heat transfer coefficient is hhot. The cold side temperature (Tcold) is the temperature of the steam inside the steam tube, and the heat transfer coefficient is hcold. The values of the heat transfer coefficients and the temperatures used in this study are listed in Table 1. These values are obtained from results of a computational fluid dynamics simulation of an industrial boiler of a 520 MW coal-fired power plant unit by Lou et al. , which is shown in Fig. 4. Please note that the temperature range in this plot has been adjusted to show more even color distributions. The maximum temperature inside the boiler is 2399 K. Since the single TE leg module being studied is only a section of the actual TE module which consists of many TE legs, symmetry boundary condition is imposed on the side surfaces of the TE module and boiler tube. The symmetry boundary conditions sets gradient of the temperature at the wall to be zero (∂T/∂n = 0). The outer surfaces of the electrodes and the TE leg are assumed to be perfectly insulated (q = 0).
Material properties and baseline configuration are listed in Table 1.
Results and Discussions
Figure 5 presents the temperature distribution on the TE module for the baseline configuration (40% fill factor and 0.1 mm leg thickness). As expected, the temperature at the center of the top shell, where the TE leg is located, is lower than the temperature near the edges. And the opposite occurs on the shell's bottom surface. The average hot side temperature of TE leg is 1437.6 K, and the average cold side temperature is 1016.0 K. Its figure-of-merit, ZT, is 0.81; and, the generic power output per TE leg unit area, wTE,leg, is 4.70 × 104 W/m2. The generic power output per TE module unit area, wTE, is 1.87 × 104 W/m2. The efficiency of the module, ηTE, is 6.9%.
where wo is the work output per unit area of the steam cycle without the installation of the TE module. For this baseline configuration, Δw is −36.2%.
Effects of TE Leg Thickness.
The TE module size was changed to study the effects of the TE leg thickness (d). Only the leg thickness was changed; the fill factor (fractional area coverage of TE element relative to cross section are of heat flow) was not changed, i.e., the length and the width of the TE leg were kept the same. The results are summarized in Table 2.
TE efficiency increases as the TE leg thickness increases due to the higher temperature difference between the top and the bottom of the TE leg (Th and Tc). However, increasing the TE leg thickness increases the heat flow resistance and, thus, reduces the steam cycle work output. The steam cycle's work output loss is greater than the work output gained from the TE leg, so the net work output is a loss. The smallest loss is obtained from the TE with leg thickness of 0.3 mm, which has 14.8% total work output loss.
Effects of Adding Fin on TE Module.
In order to increase heat flow through the TE module, a fin is added to its outer shell as shown in Fig. 6. The fin width is 3 mm and the fin height is varied from 2 mm to 10 mm. Temperature distribution on the TE module with fin with the height of 6 mm is shown in Fig. 7. From the results listed in Table 3, it is seen that the increasing the fin length increases the work output of both the TE and the steam cycle as more heat is able to pass through the module due to the presence of the fin. For fin height of 4 mm and higher, there is a total work output gain.
One of the design criteria is to minimize the effects of the TE on the steam cycle work, i.e., minimize the steam cycle work loss. However, depending on the size of the fin, the heat flow increase due to the fin can result in a heat flux to the steam side to be higher than that of the bare tube (wo), as seen in the case of TE with fin height 6 mm, 8 mm, and 10 mm in Table 3. In order to have a fair evaluation of the potential work output increase by adding the TE module, only TE design which yields steam work output (wsteam) equal or less than that of the bare tube (wo) are considered. In other words, there will be no additional steam work output gained. The steam work output (wsteam) of the TE with fin height of 4 mm is 2.24 × 105 W/m2 very close to the work output of the bare tube (wo = 2.24 × 105 W/m2), and its work output gain is 6.2%. The fin height is further optimized such that wsteam matches wo. The optimized fin height is 4.3 mm and the corresponding percentage of work output gain in 7.1%.
Table 4 also shows the results for different TE fill factors. Similar to the 40% fill factor case, the fin height is optimized such that there is no work output loss for the steam side. The work output gain (which ranges from 6.6% to 7.5%) is slightly higher for TE with higher fill factor. The TE with higher fill factor design requires thicker leg. The higher fill factor and thicker leg means that the TE will require more TE leg material to produce; thus, will cost more to produce. The impact of fill factor is moderate, so the smaller fill factor is preferred in order to reduce the mass of the TE material used significantly. Fill factor of 40% and leg thickness of 0.43 mm are chosen.
Effects of TE Module Locations.
The hot side temperature of the TE module was varied to represent different locations of TE module installation inside the boiler. Figure 8 shows the average gas temperature near the boiler wall at various locations. The temperatures chosen are 1500 K, 1300 K, and 1150 K, to represent the locations as the gas move downstream from combustion zone. The cold side temperature was not changed.
TE configuration with fill factor of 40% and fin width of 3 mm is used. The TE leg thickness used are 0.3 mm, 0.4 mm, 0.5 mm, and 0.55 mm for the 1680 K, 1500 K, 1300 K, and 1150 K gas temperature, respectively. The TE fin height was optimized for each gas temperature and the results are summarized in Table 5. The percentage of work output gain ranges from 7.1% in the hotter section to 4.4% in the cooler section.
A 3D numerical model was used to investigate the potential placement of TE modules inside a boiler at a coal-fired power plant. Adding TE by itself directly on the tube outer surface increases the heat flow resistance and, thus, reduces the steam cycle work output. A fin can be added to the TE module to increase the heat flow and to avoid the steam cycle work output loss. Different TE configurations (fill factor and leg thickness, and fin height) were examined. The TE module size was optimized for different locations with different flue gas temperatures inside the boiler. Our analysis shows that TE with ZT ∼ 0.61–0.88 at 843–1440 K range can increase power generated in different areas of the boiler by 4.4–7.1%. The overall output power of the plant can increase by ∼6.5%.