Thermoelectric Power Generation Optimization by Thermal Design Means Thermoelectric Power Generation Optimization by Thermal Design Means

One of the biggest challenges of the twenty‐first century is to satisfy the demand for electrical energy in an environmentally speaking clean way. Thus, it is very important to search for new alternative energy sources along with increasing the efficiency of current processes. Thermoelectric power generation, by means of harvesting waste heat and converting it into electricity, can help to achieve above‐mentioned goal. Nowadays, efficiency of thermoelectric power generators limits them to become key technology in electric power generation, but their performance has potential of being optimized, if thermal design of such generators is optimized. Heat exchangers located on both sides of thermoelectric modules (TEMs), mass flow of refrigerants and occupancy ratio (the area covered by TEMs related to base area), among others, need to be fine‐tuned in order to obtain the maximum net power generation (thermoelectric power generation minus consumption of auxiliary equipment). Finned dissipator, cold plate, heat pipe and thermosiphon are experimentally tested to maximize net thermoelectric generation on real‐working furnace based on computational model. Maximum generation of 137 MWh/year using thermosiphons is achieved with 32% of area covered by TEMs.


Introduction
The excessive use of fossil fuels has lead into severe environmental issues. Consequently, global warming, greenhouse gases emissions, climate change, acid rain and ozone depletion are commonly heard on the media. Moreover, combustible resources are limited, and more restrict environmental regulations are arising. Hence, one of the biggest challenges of the twenty-first century is to satisfy energetic demand in environmentally friendly manner.
In order to fulfill the previous aim, new tendencies are springing, such as smart utilization of energy throughout boosting savings, avoiding waste and developing more efficient, so as less fuel consuming, equipment and through the development of renewable energies. Thermoelectric generation contributes to diminish the impact that fossil fuels generate. A better exploitation of fossil fuels is possible due to their potential to harvest waste heat and convert it into electricity, improving efficiency of energy generating systems.
Nowadays, thermoelectrics is an emerging technology, which converts waste heat into electricity. Solid-state operation of thermoelectric generators (TEGs) eliminates the presence of moving parts and/or chemical reactions, and thus the maintenance is reduced to minimum. It cancels greenhouse gases emissions to environment, and long lives are achieved due to safe operation of thermoelectric generators.
Waste heat is defined as by-product heat of a process, which is not exploited afterward, but it is emitted to the ambient. Nowadays, great amount of produced energy is lavished as waste heat, and at least 40% of the primary energy utilized in industrialized countries is emitted to the ambient as waste heat [1]. Nevertheless, most of this waste heat presents low temperature levels (low temperature grade heat), as Figure 1 presents, explaining the most studied use up to the moment, heating of fluids for heating or other purposes [2][3][4]. It has been estimated, that double the heating needs of the United States, the 16.4 % of the primary energy consumed worldwide, could be supplied with waste heat [1]. Particular temperature grade, that waste heat presents, restricts applicable technologies to harvest it with effective conversion to electricity. However, thermoelectricity is a promising technology to recover low temperature grade waste heat [5]. Several studies have ratified promising future, that TEGs demonstrate ability to produce electric energy from waste heat of different applications. Some of them are introduced here: Bi 2 Te 3 -PbTe TEG obtains 211 kW electrical power from waste heat of Portland Cement Rotary Kilns [6]; study conducted in Japan presents potential of recovering radiant heat from steelmaking processes with 10-kW-class grid-connected TEG system [7]; thermoelectric power density of approximately 193.1 W/m 2 is obtained from waste heat of biomass gasifier [8], while power density nearly 100 W/m 2 is obtained from combustion chamber [9]; thermoelectric generator integrated within photovoltaic/thermal absorber improves total efficiency of generating system [10]; nearly 5 kWh/yearm 2 can be produced from solar ponds [11]; and the most common and studied TEGs, which recover waste heat from exhaust gas of vehicles in order to improve their efficiency [12][13][14].
Efficiency, that normally TEGs present between 5 and 10% [15,16], is deterrent to make these systems attractive enough to pass the thin line between laboratory experimentation and simulation and commercialization and expansion of this technology. Nowadays, the two issues that are the main objectives are to improve efficiency of thermoelectric generation systems: the first objective is development and improvement of thermoelectric materials through modification of conventional materials with new technologies, such as introducing nanostructures into conventional semiconductors [17,18] or creating novel thermoelectric materials, such as polymers [19], oxides [20], half-heusler [21] or skutterudites [22]; the second objective is to optimize thermal design of the system. To achieve the latter objective, different approaches can be studied and implemented, for example, heat exchangers located on both sides of thermoelectric modules can be optimized through many different approaches that will be detailed afterwards, and also the number of thermoelectric modules (TEMs) has to be properly selected to reach the maximum thermoelectric generation. Occupancy ratio δ, parameter that includes number of used TEMs M TEM , that is, ratio between area covered by TEMs A TEM and base area A b of heat exchangers (Eq. (1)), is crucial parameter to optimize thermoelectric generation: Although it seems, that higher number of thermoelectric modules would mean higher thermoelectric power generation, thermal resistance per thermoelectric module of heat exchangers worsens, if occupancy ratio rises, resulting in reduction in thermoelectric power generation per TEM. Each application presents optimum point, where thermoelectric power generation is maximum [23][24][25]. Moreover, reduction in the number of modules does not only imply increase in thermoelectric power generation, but also decrease in initial investment.
Optimization of heat exchangers attached to hot and cold sides of TEMs is very important to maximize thermoelectric power generation, and improvement in thermal resistances will result in higher temperature difference between hot and cold TEM sides close to temperature difference between heat exchangers, and, hence, will provide higher thermoelectric power generation [26][27][28][29]. Optimization of heat dissipation systems can be done by modifying their geometry, such as increasing number, height or spacing of fins of finned dissipator [30,31] or by properly selecting channel's diameter, internal distribution and/or internal inserts of cold plates [32][33][34][35]. Besides, inclusion of novel heat exchangers, such as heat pipes [23,36] or thermosiphons [37][38][39], could procure higher thermoelectric power generation. Nevertheless, increase in power generation does not necessarily mean improvement in net generation (usable energy obtained from any application) due to increase in the consumption of auxiliary equipment, coolant pump or fans, in order to optimize the thermal behavior of the systems [9,33,34,40].
In this chapter, computational optimization of real furnace located in Spain is performed giving experimental data of thermal resistances of different kinds of heat exchangers (finned dissipator, cold plate, heat pipe and thermosiphon) as function of occupancy ratio, mass flow of refrigerants and heat power to dissipate. Net power generation, that is, thermoelectric power generation minus power consumption of auxiliary equipment Eq. (2), is computed and maximized by means of previously mentioned parameters:

Computational methodology
Thermoelectric generators produce electricity when there is temperature gradient between hot and cold sides of TEM. Therefore, harvesting of waste heat to produce electricity by thermoelectric generation is becoming very interesting field of studying. Gratuity of waste heat and its great presence in numerous applications overcome low efficiency values, that TEGs present; however, until to date not many applications have been materialized. Initial investment and payback time (due to low efficiency) are deterrents for the development of this technology. This is the reason why computational models are playing very important role in the development of thermoelectric power generation. Due to complicated physical phenomena, that take place in TEGs, knowledge of TEG-based systems' behavior in different conditions is crucial to evaluate their potential, as well as to improve their performance, basing on both thermoelectric material properties and properties and dimensions of heat exchangers located on both sides of TEMs.
Modeling of each component of TEG is essential to perform accurate simulation of behavior of TEG-based systems. TEG is formed by TEMs (which present thermoelectric material, ceramic plates, joints…), the heat exchangers that are located on both sides of thermoelectric modules, as well as by any elementary component for correct assembly of the whole system; consequently, everything needs to be included into the model [41,42]. Moreover, each thermoelectric phenomenon (Seebeck effect, Thomson effect, Peltier effect and Joule effect) needs to be taken into account, especially in thermoelectric generation due to significant temperature difference between hot and cold sides of TEMs, to obtain accurate results [43][44][45]; likewise, thermoelectric properties need to be defined as function of temperature not to commit big errors [46]. Furthermore, resolution has to bear in mind transient state of operation [47,48], especially if trying to model combustion systems with permanent changes in per-formance and, thus, permanent changes in temperature and mass flow, as vehicles or combustion stoves. The latest applications are very precious due to gratuity of waste heat.
Computational model developed to optimize any thermoelectric application, especially TEGs, which harvest waste heat to produce electricity, includes each thermoelectric phenomenon, each component of the system, temperature dependence of thermoelectric properties and transient state of operation. Moreover, it includes novel parameters, such as occupancy ratio, that is, the ratio between area covered by thermoelectric modules and dissipative base area (Eq. (1)), mass flow of refrigerants and temperature decrease in flue gases when flowing along TEG. Previously mentioned parameters are determinant of net thermoelectric power generation (Eq. (2)), the main parameter to optimize in any application.
Computational methodology uses finite differences approach to solve behavior of the system. It solves each thermoelectric phenomenon, Seebeck effect Eq. (3), Peltier effect Eq. (4), Thomson effect Eq. (5) and Joule effect Eq. (6), and it includes Fourier law of heat conduction used in one-dimensional form, when heat power generation Eq. (7) takes place: , Resolution methodology is based on previously published and validated computational model [26,49].
Temperature decrease in flue gases is achieved by discretizing pipe, where flue gases circulate. Within each block, thermoelectric phenomenon is solved. To that objective, temperature of flue gases must be known. Temperature of heat source in each block    is selected as the mean temperature between entry    and exit    temperatures of each block,   Exit temperature is obtained using heat power extracted from flue gases by TEG in that block, Eq. (8). As blocks are located sequentially, exit temperature of previous block coincides with entry temperature of the following block,    + 1 =    :  Figure 2 presents block "i" of pipe and discretization of that block in order to apply finite differences method to solve thermoelectric phenomena. There are totally 16 nodes, which represent the whole TEG: node 1 is heat source, while node 16 is heat sink; nodes 2 and 15 are hot side and cold side heat exchangers, respectively; and nodes 3-14 represent TEM, where nodes 3 and 14 are hot and cold sides and from node 4 to node 13 thermoelectric material is represented. Electrical analogy is composed by thermal resistances, thermal capacities and absorbed or generated heat fluxes.   and   stand for resistances of hot side and cold side heat dissipators, respectively,   are contact resistances and   and   stand for two alternative ways for heat power to reach heat sink. The best scenario would be where the total amount of heat power circulates through thermoelectric modules, but in real application there are parasitic heats that circulate along other elements. In this case, heat power that reaches cold sink directly from hot source is born in mind through   , and heat power that flows through assembling screws attaching cold and hot dissipators is represented by   . Particularly, this model considers temperature loss of flue gases, while they circulate along TEG, occupancy ratio and mass flow of refrigerants. Methodology used can be seen in Figure 3. The first step is to choose the number of blocks, in which the pipe is discretized, . Once this parameter is selected and information of application is introduced into the model, resolution starts from the first block, where the mean temperature of the block is supposed to be entry temperature of the block, in the case of first block's temperature is that of flue gases. The next step is to suppose heat power that needs to be dissipated by heat exchangers,    , parameter that determines thermal resistance of dissipation systems, as it will be seen in the next section. Thermal resistances of dissipation systems are now determined, so the finite differences method can be used to solve thermoelectric phenomena, obtaining heat power to dissipate and closing the most interior iteration loop. As heat dissipators are function of heat power to dissipate, and at the same time, they define amount of heat that TEG is extracting from flue gases, this issue is solved through an iteration process, which obtains the heat power to dissipate. Once known, the mean temperature of the block needs to be obtained. The mean temperature is computed as the mean value between entry and exit temperatures of flue gases, and exit temperature is obtained using Eq. (8), so new iteration loop solves this situation. Finally, when everything has converged, thermoelectric generation is saved and resolution follows to the next block. This procedure keeps on until each block has been solved and the total power generation has been computed. Figure 3 presents schematic of the methodology used to obtain thermoelectric power generation. Net power generation, Eq. (2), is afterward obtained, giving power consumption of auxiliary equipment, determined by the test conducted to thermally characterize the different types of heat exchangers studied, finned dissipator, cold plate, heat pipe and thermosiphon. Experimental thermal characterization of these systems is explained in the next section, very important data that are essential to include into the computational model in order to calculate accurate results about thermoelectric power generation from any application.

Thermal characterization of heat exchangers
Thermal characterization of heat dissipation systems is crucial to obtain accurate results using computational model presented in the above section. Four different heat dissipation systems (cold plate, finned dissipator, heat pipe and thermosiphon) have been experimentally tested in order to obtain their thermal resistances as function of influential parameters in thermoelectric power generation: occupancy ratio, mass flow of refrigerants and heat power to dissipate.

Cold plate
Use of fluids as heat carrier enhances thermal transfer. In the case of tested system, water has been used in order to characterize heat dissipation system thermally and to analyze results, if net thermoelectric generation increases. Heat dissipation system is formed by cold plate (cold side heat exchanger), fan-coil composed by core and fans to make air circulate through its fins (the secondary heat exchanger in charge of reducing temperature of heat carrier fluid), pump, necessary elements to direct fluid flow and secure safe performance of dissipation system and sensors to obtain the data, as shown in Figure 4 [51]. Cold plate has 26 transversal channels with diameter 6.2 mm and two manifolds to distribute water coolant along the channels. Plate exterior dimensions are 190 mm × 230 mm. The fan-coil presents core formed by two 8 mm diameter pipes with total number of 12 passes. It is provided with wind tunnel, which presents three fans to make air circulate through its fins. Pump used in the system has been specially chosen, and pumping level can be chosen from one to four using switch. Test bench used to obtain experimentally thermal resistance of cold plate system [51]. Power consumption of pump and fans of fan-coil as function of water and air mass flows, respectively, is shown in Figure 8, which represents all relations between mass flows and consumption of auxiliary equipment used for different heat exchangers.
Thermal characterization has been performed using experimental data and validated computational model, enabling to obtain thermal resistances on test bench. Description of the model and validation details can be found in publications, Aranguren et al. [40,51]. Thermal resistance of cold plate is not function of heat power to dissipate due to small influence of this parameter on temperature of water coolant, the term that could influence on thermal resistance. Figure 5a depicts influence of heat power for specific water mass flow. Figure 5b presents the influence of occupancy ratio on thermal resistance per thermoelectric module for fixed heat power and water mass flow. As ratio grows, implying that number of TEMs grows, thermal resistance worsens due to the reduction in dissipative area per thermoelectric module. Figure 5c presents dependence of thermal resistance air and water mass flows at different occupancy ratio. Occupancy ratio has a great influence on thermal resistance, showing that increasing number of modules harms thermal resistance. Within the same occupancy ratio, water and air mass flow show influence on thermal resistance, most notable for high occupancy ratios, where dissipative area is reduced and any improvement in convective coefficients procures important benefits to thermal resistance.

Finned dissipator
Finned dissipators up to date have been the most used heat exchangers in thermoelectricity due to their simplicity. Studied finned dissipator has external dimensions of 190 mm × 230 mm, base thickness of 14.5 mm and height, thickness and spacing of fins of 39.5, 1.5 and 3.3 mm, respectively. It is provided with wind tunnel, which includes two fans to make air circulate along its fins. The finned dissipator is shown in Figure 7a. Relation between power consumption of fans and air mass flow is presented in Figure 8. Figure 6 presents thermal resistance of finned dissipator as function of heat power to dissipate, occupancy ratio and mass flow of air. Heat power to dissipate does not determine thermal resistance, as (shown in Figure 6a and b). Each panel of Figure 6 presents thermal resistance of finned dissipator as function of heat power to dissipate, the first one for fixed air mass flow of ṁ ai = 0.024 kg/s and the second one for ṁ ai = 0.060 kg/s. Occupancy ratio influences highly thermal resistance, and higher occupancy ratios procure higher thermal resistances per thermoelectric module, due to the reduction in dissipative area per TEM, as presented in Figure 6. Figure 6d shows the influence of air mass flow, and for high occupancy ratios, influence is more remarkable than for low ones, due to the higher benefits that improvement in convection coefficients has for small convective areas. The expanded uncertainty of thermal resistance R TEM is equal to ±10.80%.

Heat pipe
Heat pipes are passive devices able to transfer great amount of heat with small temperature differences. Heat pipes present sealed volumes provided with porous media and divided into three regions: evaporator, where heat is absorbed; condenser, where heat is emitted; and adiabatic region. Working fluid evaporates due to heat gained and flows into the condenser, where it condensates and returns to evaporator due to capillary lift. Tested heat pipe is composed by 10 8 mm diameter pipes with length of 350 mm and spaced 7 mm. Base external dimension of heat pipe is 90 × 192.5 mm 2 , and pipes are inserted, being the region, where heat arrives. To help condensation of working fluid water, heat pipe includes wind tunnel provided with fan, as Figure 7b presents. Air mass flow as function of power consumption is shown in Figure 8.  Thermal resistance of heat pipe is function of heat power to dissipate. Condensation and boiling coefficients depend on temperature of fluid and walls, and, therefore, thermal resistance is function of heat power that has to be dissipated, as shown Figure 9a. Occupancy ratio and air mass flow present the same tendency as in previous cases, as shown in Figure 9b, c and d. The expanded uncertainty of thermal resistance R TEM is equal to ±7.88%.

Thermosiphon
Thermosiphons with phase change present the same physical phenomena, than heat pipes, but they do not present porous media. Hence, they need gravitational forces to ensure that condensate heat carrier returns to evaporator. Tested thermosiphon has vessel of 160 × 200 mm 2 and 22 mm diameter pipe that connects the circuit. Pipe is divided into six channels with diameter of 10 mm. Condenser area is composed by seven levels extended along 850 mm with width of 240 mm and depth of 500 mm. This area has 8 mm spaced fins in order to help working fluid, R134a, to condensate. Thermosiphon does not present auxiliary equipment as previous heat exchangers presented. Figure 10 shows heat dissipation system. Thermosiphon test does not present any fans to help working fluid to condensate, so thermal resistance depends only on heat power to dissipate and occupancy ratio, as displayed in Figure 11. Due to natural convection to exterior space and boiling and condensation coefficients, thermal resistance depends on calorific power to a higher extent to dissipate. Higher heat power to dissipate procures higher temperatures, which benefit transfer coefficients involved, and procuring lower thermal resistances, especially high occupancy ratios, is more affected due to high occupation, as presented in Figure 11b. The expanded uncertainty of thermal resistance  is equal to ±8.42%.

Thermoelectric computational optimization of waste heat energy harvesting from real application
Computational model, which enables determining behavior of any TEG and thermal characterization of four different types of studied heat exchangers used to optimize net thermoelectric power generation of real application, is tested on furnace located in Spain. Computational model computes thermoelectric power generation, including calculation power consumption of auxiliary equipment shown in Figure 8, and net power generation can be computed (Eq. 2) as well, which is a real target of optimization in any application.
Total consumption of auxiliary equipment is essential to obtain net thermoelectric power generation, the goal of this optimization. Consumption of auxiliary equipment is obtained as function of mass flow presented in Figure 8 and with accounting for number of TEM units necessary to cover the whole available surface of the chimney, totally 769 units. Cold plate, finned dissipator and heat pipe present auxiliary consumption, while thermosyphon does not, as explained in previous section. As it can be seen in Figures 5, 6 and 9, increment in mass flow of refrigerants, with simultaneous increment in auxiliary equipment consumption, causes improvement in thermal resistances. This fact leads to higher thermoelectric power generation, due to improvement in heat transfer on both sides of the TEMs, obtaining higher difference of temperature between their sides and consequently higher thermoelectric power generation. Nevertheless, consumption of auxiliary equipment grows, so it is not so clear as in the case, when increasing mass flow of refrigerants leads to increase in net power generation. Figure 12 shows thermoelectric and net power generation as function of occupancy ratio, when finned dissipators are located on cold side of TEG. It can be seen, that higher air mass flow produces higher thermoelectric power generation; however, net power generation has optimum near the second smallest mass flow simulated, and after this value, net power generation decreases significantly, even obtaining negative values for small occupancy ratios and high mass flow of the air. Occupancy ratio is also determined for thermoelectric power generation. Higher occupancy ratio leads to higher thermal resistances per thermoelectric module and, therefore, less power generation per module unit; however, number of units to produce electricity is higher. Once more, it is necessary to elaborate optimization to get the maximum net power generation point. Figure 12 presents the influence of this parameter, when finned dissipators are simulated on cold side. Occupation ratio value that provides maximum power generation is equal to δ ≈ 0.4, that is, optimum is reached, when approximately 40% of available surface is covered by TEMs only. This optimization is crucial to obtain the highest thermoelectric power generation and to optimize initial investment as well, because reduction in number of TEMs, which is necessary to install, reduces the cost of the application.  Figure 13 shows that the best cold side heat exchanger for this case is thermosiphon, obtaining up to 16280 W from waste heat of the furnace. The optimum occupancy ratio that provides this value equals to  = 0.32. The number of TEMs necessary to cover 32% of chimney surface is 6720, and the smallest TEMs number is required, if compared with other optimum values as function of occupancy ratio. Therefore, thermosiphons are heat exchangers that not only provide the highest net thermoelectric power generation, but also the ones that require the smallest initial investment. Moreover, these systems have no moving parts, so they are completely robust and lack of maintenance.
Thermosiphons produce 30% more net optimal power than the second best option, heat pipes. Besides, occupancy ratio to maximize net power generation for heat pipes is higher, so the initial investment has to be approximately 30% higher to obtain the maximum electrical energy. If optimal heat exchangers are compared with cold plates and finned dissipators, electrical energy production is 72 and 86% higher. Cold plates present optimum values of higher than thermosiphons, while finned dissipators present approximately the same occupancy ratio, so the same initial investment. Consumption of auxiliary equipment is deterrent, and small thermal resistances that cold plate presents produce higher thermoelectric power generation, but large consumption of auxiliary equipment negatively influences on net power generation, as Figure 13 shows, even when auxiliary equipment consumption has been optimized to obtain the maximum net power generation for each occupancy ratio.

Conclusions
Harvesting of waste heat to produce electrical energy via TEGs is a promising technology to help mitigate environmental issues that nowadays society is facing. TEGs are solid-state systems, which barely present moving parts, and, therefore, they are very robust, reliable, silent and long-lasting.
Developed general computational model allows predicting behavior of any TEG. It does not include the most common simplifications that the rest of models from publications have and besides it includes new parameters, such as occupancy ratio, mass flow of refrigerants and temperature reduction in flue gases, while they flow along the system. The latter parameters are determinant for thermoelectric power generation and, therefore, very important to bear in mind for optimization study.
Thermal resistances of different heat exchange systems are function of novel parameter, occupancy ratio, included in computational model. Occupancy ratio has negative influence on thermal resistance per thermoelectric module, if it increases, due to the reduction in available dissipative area per TEM. Calorific power to dissipate influences just heat exchangers, where phase change is involved and mass flow of refrigerants determines thermal resistance, but in greater extent, when occupancy ratio has high values.
Thermosiphon with phase change is a dissipation system that provides the highest net thermoelectric power generation, 137 MWh/year, which is equivalent to supply 40 Spanish dwellings, when 32% of chimney surface is covered by TEMs. This production is 30, 72 and 87% higher than optimal productions of heat pipe, cold plate and finned dissipators, respectively. Moreover, the number of TEMs required for use in TEG with thermosiphons is lower or similar to that for the rest of heat dissipation systems, so not only power generation is optimum, but initial investment also.
The absence of moving parts for TEG built with thermosiphon procures really robust, reliable and silent power generation system that can produce electrical energy from waste heat of any system, improving their efficiency and, therefore, collaborating to satisfy demand for electrical energy in green manner.