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Modeling and fabricating a prototype of a thermoelectric generator system of heat energy recovery from hot exhaust gases and evaluating the effects of important system parameters
Applied Thermal Engineering 132 (2018) 624–636
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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Research Paper
Modeling and fabricating a prototype of a thermoelectric generator system of heat energy recovery from hot exhaust gases and evaluating the effects of important system parameters Seyed Alireza Mostafavi ⇑, Mojtaba Mahmoudi Department of Mechanical Engineering, Faculty of Engineering, Arak University, Arak, Iran
h i g h l i g h t s A thermoelectric module with a low thermal conductivity is more effective. System efficiency could be improved by using liquids on the cold and hot side of TEG. The thermal conductivity of the heat sinks has no significant effect on efficiency. The good results have been yielded, especially at temperatures lower than 100 °C.
a r t i c l e
i n f o
Article history: Received 21 April 2017 Revised 10 November 2017 Accepted 4 January 2018 Available online 6 January 2018 Keywords: Thermoelectric Generator Energy recovery Smokestack Modeling
a b s t r a c t The heat lost through smokestacks has an adequate energy recovery capacity. A new and effective method of recovering this energy is the use of thermoelectric generators, which directly convert thermal energy to electricity. Some of the advantages of thermoelectric generators include their environmental friendliness and also their lack of moving or rotating parts, which makes them operate without noise and extends their service life. This paper deals with the general modeling of a thermoelectric generator system, including the modeling of the cooling system for the cold side of thermoelectric generator, system of heat transfer from smokestack to the hot side of thermoelectric generator and also the modeling of the thermoelectric modules themselves. In continuation, for validating the obtained equations, an experimental prototype of this thermoelectric generator is fabricated and the empirical results including the nominal voltage, current and power of the manufactured system are compared with the theoretical results. This comparison shows the validity of the presented modeling and the good agreement between the theoretical and practical results, especially at low temperatures. Based on the calculations, the highest error was 4.6 percent for a temperature difference of lower than 100 °C. Additionally, for the same temperature difference, the highest theoretical and practical output powers for this module were 3.4 W and 2.8 W, respectively. Considering the matching of these results, the effects of some important parameters on the output power of the considered thermoelectric generator are also investigated, and the significant influence of the thermal conduction coefficient of thermoelectric modules is demonstrated. Ó 2018 Elsevier Ltd. All rights reserved.
1. Introduction Petroleum-based and fossil fuels have been utilized extensively in transportation systems throughout the world; although for reasons such as the depletion of oil resources, environmental problems, and the regulations and limitations set by governments for reducing the consumption of fossil fuels, alternative fuels and vehi-
⇑ Corresponding author. E-mail address: [email protected] (S.A. Mostafavi). https://doi.org/10.1016/j.applthermaleng.2018.01.018 1359-4311/Ó 2018 Elsevier Ltd. All rights reserved.
cle powertrain systems are getting better in quality and more efficient [1]. Many of the existing commercial and environmental problems can be solved and socioeconomic benefits can be gained by improving the conditions of consumed fuels. Some of these issues are as follows: Despite the increase of energy efficiency in many developed countries these countries still depend on foreign countries for the fuel they need; and a substantial amount of this imported fuel (almost half of it) is utilized in vehicles and trucks [2].
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Nomenclature A b Cp D f h I K L _ m NuD n P Pr Q Rb Ri RL RhS ReD r T Tb TE TEG
area (m2 ) space between the fins (m) specific heat ðJ=kg KÞ diameter of a circular tube ðmÞ fanning friction factor heat transfer function (W=m2 K) current (A) thermal conductance (W=m K) length (mÞ mass flow rate (kg=s) Nusselt number number of fins electrical power (W) Prandtl number heat flow (W) thermal resistance of heat sink base (W=K) internal resistance (X) load resistance (X) heatsink thermal resistance (W=K) Reynolds number radius (m) temperature (K) bulk temperature of the exhaust gas thermoelectric thermoelectric generator
Almost one-third of carbon emission in the world is produced by various vehicles. Inefficient and fuel-guzzling vehicles are major causes of increased carbon production; and the increase of carbon dioxide along with other greenhouse gases is a key factor in global warming [3]. Equipped with systems such as accident. Navigation systems, future and next-generation vehicles should be able to produce on-demand power; which requires more fuel consumption. Almost all personal vehicles and light trucks are equipped with engines that run on gasoline or diesel. The energy consumption of a gasoline-burning internal combustion engine has been shown in Fig. 1 [4]. As is observed, 70% of the energy contained in fuel is lost, as heat, from the exhaust pipe or in the cooling process and the rest is converted to mechanical work and energy.
TC Th tb tf um VO Wf
cold junction temperature in a thermoelectric module hot junction temperature in a thermoelectric module heat sink base thickness fin thickness mean fluid velocity output voltage (v) fin width (m)
Greek symbols a seebeck coefficient DT temperature difference gf fins efficiency q density Subscripts b base c cold side f fins h hot side i input L load m mean o output
A portion of this produced work is used to overcome friction in the power transmission system of a vehicle and its other equipment such as cooling pump, fuel pump, etc. Consequently, only 20–25% of the initially produced energy is used to drive the vehicle. Moreover, this remaining energy has to overcome the following: inertia generated during the acceleration or uphill movement of vehicle, aerodynamic drag force friction between vehicle tires and road surface There are three major ways of reducing fuel consumption in vehicles [5]: Increasing the overall efficiency of power systems (engine, power transmission system, etc.) in order to produce more work from the consumed fuel, reducing the amount of work needed to move a vehicle by lowering its weight Reducing the friction between vehicle tires and road, etc and Recovering the energy dissipated from a vehicle. 1.1. Energy recovery from exhaust pipes
Fig. 1. Energy consumption of a gasoline-burning internal combustion engine.
A considerable amount of unused heat (about 40% according to Fig. 1) is dissipated via the exhaust pipe of a vehicle. Here, the notion of fuel consumption improvement means to increase the overall efficiency of a vehicle’s power transmission system which has lost a great deal of energy through the discharged exhaust gases. According to the book of ‘‘Vehicle Electronics and Electricity” published in 1999, the average electricity consumption of an automobile is 600 W [6]; which imposes an extra load on the engine to provide this power. If the heat lost through a vehicle’s exhaust pipe can be utilized to generate the electricity needed by the vehicle, a substantial amount of load can be removed from vehicle engine. One method of converting the dissipated heat to electricity is the use of thermoelectric (TE) converters.
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Thermoelectric converters work on the basis of thermoelectric law. Based on this law, when two conductors with different loads are connected together at different temperatures, an electrical load is induced in the connecting circuit. Each of the two currentcarrying conductors in this system is called a thermoelectric element, and each pair of these two conductors is called a thermoelectric couple [7]. A schematic view of these thermoelectric converters and the principles of their work have been depicted in Fig. 2. In an ordinary thermoelectric generator (TEG), the heat exchangers receive heat from a heat source and transfer it to thermocouple connections. A heat exchanger along with a thermoelectric couple is known as a thermoelectric generator. Thermoelectric generators have a solid-state technology; they have no moving parts and therefore have a very simple and reliable mechanism and a long service life. In view of the previous explanations, a thermoelectric generator system connected to an exhaust pipe should include the following components:
Exhaust system Cooling system Heat transfer system Thermoelectric modules
One of the earliest research works on thermoelectric generators was conducted by Richard H. Bauer [8] at Clarkson University during the years 1961–63. Bauer explored the possibility of designing a thermoelectric generator which could provide some supplemental electricity for a vehicle. The water used for cooling the engine was considered as the heat source and ambient air was used as the working fluid for the cold side of heat exchanger. Lead telluride was the only thermoelectric material used in Bauer’s study. His research showed the infeasibility of having a thermoelectric generator that uses the cooling water of vehicle engine as the heat source. This is due to the large volume and cross-sectional area of thermoelectric material necessary, needed to generate the required electricity. However, the research also indicated that if the temperature of heat source can be kept at about 600 K, a thermoelectric generator might be a feasible option. Concurrent with the work of Bauer, Anthony Joseph Tomarchio [9] at Clarkson University investigated the possibility of increasing a vehicle’s efficiency by replacing some of its equipment, such as dynamo, with a thermoelectric generator installed on the exhaust pipe of vehicle. In his research, he also used ambient air as the working fluid and lead telluride as the thermoelectric material, and he achieved the following results: At a vehicle speed of 50 mph, a maximum power of about 514 W with a voltage of 14.7 V is observed. A minimum vehicle speed of 20 mph is needed to get minimum output power from the battery and generator
Fig. 2. Schematic of a complete thermoelectric generator system.
At speeds below 20 mph, the needed power can only be provided by improving the semiconductors used in the thermoelectric material. Birkholz et al. [10] designed a thermoelectric generator that used FeSi2 as the thermoelectric material. They tested their generator on a Porsche 944 engine and obtained a maximum power of 58 W. By employing the thermoelectric modules made by the Hi-Z Company, Bass et al. [11] explored the recovery of dissipated heat from a diesel engine. They used different heat sources in their research and concluded that, because of the large temperature difference provided by the hot gases from the exhaust pipe, they have the best potential for use in thermoelectric generators. These researchers also used thermoelectric generators with various thermoelectric materials such as bismuth telluride (Bi2Te3), lead telluride, and silicone-germanium. Their studies showed that among these different thermoelectric materials, Bi2Te3 has the best performance, because its maximum working temperature is lower than that of other materials. Ikoma et al. [12] at Nissan Research Center used siliconegermanium as the thermoelectric material to fabricate a thermoelectric generator that consisted of 8 pairs of thermoelectric modules. This generator was installed in rectangular configuration on a 3000-CC automobile engine and achieved a better efficiency than its former counterpart. Vazequez et al. [13] compiled the results of the last 3 decades of research on the use of thermoelectric generators to generate electricity from the exhaust pipes of vehicles. They found out that the maximum amount of electrical power produced by thermoelectric generators varies from 43 to 193 W. The power production inefficiency was attributed to the thermoelectric generators whose working temperatures did not match the temperature of the outlet gases of exhaust pipes. For the purpose of minimizing fuel consumption in steam turbines, Yazawa et al. [14] presented a general model that used thermoelectric modules. They showed that the efficiency of a steam turbine increases by adding more thermoelectric modules. Dai et al. [15] presented a liquid–metal of a TEG system for energy recovery. When the heat source temperature was 195.9 °C, a maximum voltage of 34.7 V and a generator efficiency of 2% were obtained. Remeli et al. [16] presented a new method for recovering thermal energy and converting it to electricity by adding heat tubes to thermoelectric generators. Through this method, they were able to raise the generator efficiency by up to 2%. Nikolova et al. [17] proposed a specific system consisted of thermal power plants (TPPs), storage hydro power plants (HPPs), pumpedstorage hydro power plant (PSHPP) and wind power plant (WPP) to solve the generation scheduling problem, wind power plants are integrated into the system in order to minimize the total thermal unit fuel costs. Rezania et al. [18] compared a micro-structure plate-fin heat sink to a modified design of a cross-cut heat sink applied to a TEG device over a range of temperatures and thermal conductivities; they showed that the net power output of a TEG device can be significantly improved by optimal heat sink design. In addition, various new features have been added to traditional TEG devices to achieve better output. Modeling of an integrated cross flow heat exchanger with TEGs has also been studied by Crane and Jackson [19] with the aim to optimize the performance of the heat exchanger. This paper deals with the general modeling of a thermoelectric generator system, including the modeling of the cooling system for the cold side of thermoelectric generator, system of heat transfer from smokestack to the hot side of thermoelectric generator and also the modeling of the thermoelectric modules themselves. In continuation, for validating the obtained equations, an experimen-
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tal prototype of this thermoelectric generator is fabricated and the empirical results including the nominal voltage, current and power of the manufactured system are compared with the theoretical results. Considering the matching of these results, the effects of some important parameters on the output power of the considered thermoelectric generator are also investigated considering the matching of these results, the effects of some important parameters on the output power of the considered thermoelectric generator are also investigated 2. Modeling the thermoelectric generator A thermoelectric generator is studied in this section. In this investigation, first, the temperature distribution in the heat exchangers connected to the exhaust pipe outlet and the cooling system is explored and then the energy produced by the thermoelectric generator is calculated. Fig. 3 shows a general design of the examined thermoelectric generator system. Using a heat sink on the hot side of the thermoelectric is to increase the overall heat transfer area and thus improve the transfer of heat from the gases coming out of an exhaust pipe or smokestack to the hot surface of thermoelectric module. In fact, the use of a heat sink is one of the most effective mechanisms of increasing the amount of heat transfer. In view of Fig. 4 the examined thermoelectric generator system consists of 2 heat sinks on the cold side of thermoelectric modules and one heat sink on the hot side (which encounters the hot gases coming out of the exhaust pipe). This system also includes 8 thermoelectric modules between heat sinks; with 4 modules above the heat sink installed at the exhaust outlet and 4 modules below it. This thermoelectric generator system can be divided into 8 symmetric sections. Due to the symmetry of the 8 modules used in the system, each cross section has the same temperature profile; therefore, temperature distribution has been evaluated for just one module at each section. With this explanation, an appropriate control volume can now be chosen for each thermoelectric module (see Fig. 5). So by having the temperature distribution in each thermoelectric module, the temperature distribution in the whole heat converter can be computed. Finally, through this model, the power produced by all the 8 thermoelectric modules can be determined by using the temperature distribution for one module. Now the process of heat transfer in a thermoelectric module is explored and used in the modeling of a thermoelectric generator system. Fig. 5 shows the flow of heat in an isolated thermoelectric module from a thermoelectric generator system. The control volume has been selected according to Fig. 5. The energy obtained from exhaust gas is expressed as Eq. (1). [20].
Q 1 ¼ mh cph ðT hi T ho Þ
ð1Þ
Fig. 4. Arrangement of thermoelectric modules in the examined thermoelectric generator system.
Fig. 5. Each element of the thermoelectric generator system.
In Eq. (1), Q 1 is the energy obtained from exhaust pipe (as is shown in Fig. 5), mh is mass flow rate of gas in the exhaust pipe and cph is its specific heat capacity. T hi is the temperature of the gas entering each element in the heat sink installed at the exhaust pipe and T ho is the temperature of the outflowing gas of each element in the heat sink. The equation for convection heat transfer on the hot surface of thermoelectric module is expressed as Eq. (2), [20]:
Q1 ¼
Cold Side Heat Sink
Thermoelect ric Modules
Hot Side Heat Sink
Fig. 3. The examined thermoelectric generator system.
T hi þT ho 2
T hs
Rhs
ð2Þ
where Q 1 denotes the heat transfer (combination of convection and conduction heat transfers) over the hot surface of thermoelectric module, T hs is the temperature of the hot side of module, and Rhs is the thermal resistance, which is shown in Fig. 7. According to Fig. 7, this thermal resistance includes the resistance of fins and the resistance of heat sink base; which will be subsequently investigated. Also, the thermoelectric module’s inlet heat can also be expressed as Eq. (3) [21].
1 Q 1 ¼ K DT þ aT hs I I2 Ri 2
ð3Þ
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In Eq. (3), Q 1 , K, a and Ri are the input heat, conduction heat transfer coefficient, Seebeck coefficient and the internal resistance of the thermoelectric module, respectively, and I is the current flowing from each thermoelectric module. The convectional heat transfer equation for the cold surface of module can be defined as Eq. (4), [20].
Q2 ¼
co T cs T ci þT 2
ð4Þ
Rcs
Q 2 is the convectional heat transfer on the cold side (shown in Fig. 5), T cs is the temperature of the cold surface of thermoelectric module, T ci is the input temperature from the cooling fan and T co is the output temperature from the cold side of thermoelectric converter. Also, considering the material and arrangement of fins, Rcs is computed exactly like Rhs (illustrated in Fig. 7). The energy produced by the cooling fan is expressed as Eq. (5), [20].
Q 2 ¼ mc cpc ðT co T ci Þ
Fig. 6. Displaying a single element of the examined thermoelectric generator.
ð5Þ
In Eq. (5), Q 2 is the energy loss of the cooling fan, mc is the input mass flow rate into the element from the cooling side, and cpc is the specific heat capacity of fan air. The energy produced by the thermoelectric module is obtained from Eq. (6), [21].
P ¼ I 2 RL ¼
a2 ðT hs T cs Þ2 RL
ð6Þ
ðRi þ RL Þ2
By using Eqs. (1)–(6), the unknowns (including T co , T ho , T cs and T hs ) are obtained from Eqs. (7),
mh cph ðT hi T ho Þ mc cpc ðT co T ci Þ
T hi þT ho 2
T hs
Rhs
T hi þT ho 2
T hs
Rhs co T cs T ci þT 2
Rcs
Fig. 7. Thermal resistance of each heat sink.
¼0
ð7-aÞ Eq. (10), is used to compute Rf , which represents the resistance of fins and the surrounding air [22].
¼0
co ðT cs T ci þT Þ a2 ðT hs T cs Þ2 RL 2 ¼0 Rcs ðRi þ RL Þ2
ho ðT hi þT T hs Þ 1 2 K DT aT hs I þ I2 Ri ¼ 0 Rhs 2
ð7-bÞ Rf ¼ ð7-cÞ
ð7-dÞ
Eqs. (7) are general equations and they can be used for many thermoelectric generators. A thermoelectric module of the investigated thermoelectric generator has been depicted in Fig. 6. According to Fig. 7 thermal resistance can be used to compute the value of Rhs for each heat sink. Since the heat sinks used on both sides of the thermoelectric module are completely similar to each other, in this paper, the same Rhs value is considered for both heat sinks; the only difference is in the computations related to the fluids flowing in these heat sinks; which will be discussed later. Hence, according to Figs. 2–5, the value of Rhs is calculated from Eq. (8).
Rhs ¼ Rb þ Rf
ð8Þ
In Eq. (8), Rb represents the base resistance of each heat sink; which is determined by means of Eq. (9).
Rb ¼
tb kAb
ð9Þ
In Eq. (10), K is the conduction heat transfer coefficient of the metal used in the heat sink and tb , as is shown in Fig. 6 is the thickness of heat sink base, and Ab is the cross section area of heat sink base.
1 nhh W f ðtf þ 2gf Lf Þ
ð10Þ
As is shown in Fig. 6, W f is the fin width, tf is fin thickness, Lf is fin length, and n is the number of fins. hh denotes the convectional heat transfer coefficient of heat sink fluid. Also, Eq. (11) should be used to compute the value of gf in Eq. (10).
gf ¼
tanh mLc mLc
ð11Þ
And the value of mLc is determined from Eq. (12).
sffiffiffiffiffiffiffiffi 2hh Lf mLc ¼ ktf
ð12Þ
3. Measurement of parameters and the fabrication of the experimental prototype In this section, the parameters and inputs of Eqs. (7) are determined to find the unknown variables including T co , T ho , T cs and T hs . The thermoelectric modules used in this paper are of TEC12706 type; with a schematic of this module shown in Fig. 8. The Seebeck coefficient, internal resistance, and the thermal conduction coefficient of this module have been listed in the relevant specifications sheet of this thermoelectric module in Table 1. The objective here is to validate the equations used in the previous section for a thermoelectric generator; so the type and model of thermoelectric module is not important here; it should just be able to tolerate the temperature of exhaust gases. Once the equations are validated, thermoelectric modules of higher power can be used as
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S.A. Mostafavi, M. Mahmoudi / Applied Thermal Engineering 132 (2018) 624–636 Table 2 Geometrical dimensions of the studied heat sink. Specifications
Value
tb Ab
2 (mm) 1.806 102 (m2 ) 5.7 (mm) 62.5 (mm) 1.8 (mm) 15.7 (mm) 6 215 (W=K m)
b Wf tf Lf n k
Fig. 8. A schematic view of thermoelectric module TEC12706.
needed. Here, general equations, which govern all kinds of thermoelectric modules, are derived; and the main properties of thermoelectric module TEC12706 are used to confirm the accuracy of these equations. Therefore, the low-cost thermoelectric module TEC12706 can be appropriately used for recovering the heat energy dissipated by an exhaust pipe and also as a cooling system; however, the equipment it carries should be tolerant of exhaust pipe temperatures [23]. The geometrical dimensions of the examined heat sink (shown in Table 2) are according to the element depicted in Fig. 9. 3.1. Measuring the flow rate of exhaust gas The properties of smoke coming out of the exhaust pipe can be obtained from the composition of exhaust gases generated by gasoline-burning engines. Fig. 10 shows the tested gasoline engine whose exhaust gases have been used here. Table 3 contains the composition of exhaust gases produced by most gasoline-burning engines in which the fuel undergoes an almost complete combustion [24]. By knowing the composition of the exhaust gases flowing out of gasoline-burning engines the thermophysical properties of these gases can be obtained at different temperatures. The formula for gasoline combustion and the flow rate of fuel (gasoline) can be used to compute the flow rate of exhaust gas. Gasoline contains hydrocarbons of C5 to C11 or C12. Ordinary gasoline, which constitutes about 15% of crude oil, is known by chemical formula C8H16. The density of gasoline is normally 0.719 g/cm3 [25]. If gasoline (with a chemical formula of C8H16) is completely combusted, it decomposes according to Eq. (13), [26].
aC8 H16 þ ath ðO2 þ 3:76N2 Þ ! bCO2 þ cH2 O þ 3:76ath N2
Fig. 9. Three views of the examined element in the investigated thermoelectric generator.
Engne
ð13Þ
Exhaust
Fig. 10. A schematic of the gasoline engine tested in this work.
Coefficients a, b, c and ath are obtained after balancing the combustion equation (Eq. (13)). Table 3 Composition of exhaust gases produced by gasoline-burning engines.
Table 1 Main specifications of the thermoelectric generator used. Specifications Volt
aM
K
RiM ðOhmsÞ K M Watts K
Value 0.0349 0.1290 2.3569
Name
% by volume
Nitrogen Carbon dioxide Water vapour Oxygen Nitrogen oxides Carbon monoxide Hydrocarbons Sulfur dioxide and other gases
71% 14% 13% 1% 6 0:25% 1% 6 0:25% 6 0:5%
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8a ¼ b 16a ¼ 2c
ð14Þ
Table 4 Volume flow rates of fuel obtained in three measurements.
2ath ¼ 2b þ c
Measurements
C8 H16 þ 12ðO2 þ 3:76N2 Þ ! 8CO2 þ 8H2 O þ ð3:76 12ÞN2
102
3.38 107
5
1.57 10
45
3.49 107
Third measurement
2.19 105
70
3.14 107
3.45 10
ð15Þ
The air-to-fuel ratio for the combustion Eq. (15) is expressed as Eq. (16).
mAir AF ¼ mfuel
Volume flow rate (m3 =s)
Second measurement
First measurement
By solving Eqs. (14), the balanced equation takes the form of Eq. (15).
Time (s)
5
Volume (m3 )
ð16Þ
Thus, the air-to-fuel ratio is obtained from Eq. (17).
kg ð12 4:76 kmolÞ 29 kmol AF ¼ kg kg þ ð8 kmolÞ 2 kmol ð8 kmolÞ 12 kmol
However, the objective is to get the flow rate of gases out of the exhaust pipe. For this purpose, the flow rate of consumed fuel should be added to the flow rate of air. Eqs. (16) and (18) and the flow rate of consumed fuel should be used to obtain the flow rate of air. These equations are expressed as Eq. (20-b).
_ exhaust gas ¼ ð1 þ AFÞ m _ fuel ¼ ð1 þ 14:79Þ 2:39 104 m ¼ 3:77 103 kg=s
¼ 14:79kg Air=kg fuel
ð20-bÞ
ð17Þ
Eq. (18), can be used to get the flow rate of air coming out of exhaust pipe.
_ fuel Þ _ Air ¼ ðAFÞðm m
ð18Þ
To calculate the flow rate of air, we need to measure the flow rate of utilized fuel for measuring the flow rate of consumed fuel, according to Fig. 11 a graded glass tube is installed in the fuel tank and used to measure the volume of consumed fuel per unit time. Through several measurements, the following values were obtained in Table 4. The measurements were taken at an average temperature of 125 °C. By averaging the flow rates in Table 4, the mean volume flow rate of consumed fuel is obtained according to Eq. (19).
Q ¼ 3:33 107 m3 =s
ð19Þ
To get the mass flow rate of fuel the volume flow rate should be multiplied by the density of gasoline, which has a mean value of 0.719 g/cm3 or 719 kg/m3. Thus, the mass flow rate of fuel is obtained from Eq. (20-a).
_ fuel ¼ qQ ¼ 719 3:33 107 ¼ 2:39 104 kg=s m
ð20-aÞ
3.2. Computing the convectional heat transfer coefficient [20] In this section, the coefficient of convectional heat transfer in the heat sink installed at exhaust pipe outlet is computed. In order to obtain this coefficient we should use the Nusselt number, which is defined as Eq. (21).
NuD ¼
hi D H K
ð21Þ
In Eq. (21), K is the conduction coefficient of fluid inside the conduit, hi is the internal convectional heat transfer coefficient and DH is the hydraulic diameter, which is expressed as Eq. (22), for non-circular conduits.
DH ¼
4A P
ð22Þ
In Eq. (22), A is the cross sectional area and P is the perimeter in contact with fluid. To find the Nusselt number in Eq. (21), empirical equations that depend on the type of flow have to be used. The type of flow can be determined with regards to the Reynolds number (which is defined as Eqs. (23)).
ReD ¼
qum DH l
ð23-aÞ
_ H mD lA
ð23-bÞ
or
ReD ¼
In Eqs. (23), q is the density of gases flowing inside the tube, um is the mean velocity of fluid at any cross section of tube, l is the _ is the mass flow rate of viscosity of the fluid in the tube and m gas in the tube. For Reynolds smaller than 2300, the flow is considered to be laminar; and if this flow is fully developed, the Nusselt number will have a constant value expressed by Eq. (24-a).
Graded Glass
NuD ¼ 4:36
Gasoline Ruler
And for Reynolds larger than 2300, the flow is considered to be turbulent; and if this flow is fully developed, the Nusselt number is defined according to Eq. (24-b). This equation is known as the Gnielinski equation and it is defined for the following range:
NuD ¼ Fig. 11. Graded glass tube used for measuring the volume flow rate of gasoline.
ð24-aÞ
f ðReD 8
1000ÞPr 12 2 pr3 1 1 þ 12:7 8f
ð24-bÞ
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In Eq. (24-b), f represents the friction coefficient, which is computed from Eq. (25).
f ¼ ½0:79 lnðReD Þ 1:64
2
ð25Þ
In Eq. (25) equation, Pr denotes the Prandtl number. The internal convectional heat transfer coefficient can be determined through Eqs. (21) and (24). Fluid properties are defined for an average temperature. Since these properties are obtained from empirical equations, they have an inherent error of 10%. Therefore, by knowing the properties of fluid and the flow rate of exhaust gases at the considered temperature, the value of h can be obtained by using the Nusselt number. 3.2.1. Computing the convectional heat transfer coefficient for the heat sink installed at exhaust pipe outlet [20] To compute the convectional heat transfer coefficient, Reynolds number should be determined first. By using the mass flow rate and the properties of exhaust gas in Table 5 and the geometrical properties of heat sink, the Reynolds number of the exhaust gas can be calculated by means of Eq. (23-b). Gas properties should be determined at an average temperature. So for an input temperature of 126 °C and output temperature of 101 °C, the mean temperature is calculated as 113.5 °C. Now by using Eq. (23-b) and the values of mass flow rate and hydraulic diameter, Reynolds number can be computed from Eq. (26).
ReD ¼ 903:7
ð26Þ
Since the Reynolds number is less than 2300, flow is laminar, and the Nusselt number is obtained from Eq. (24-a). And by using Eq. (21), the convectional heat transfer coefficient is determined from Eq. (27).
h¼
NuD k ¼ 13:77 DH
ð27Þ
3.2.2. Computing the convectional heat transfer coefficient for the heat sink installed on the cold side of thermoelectric module [20] The geometrical parameters and the materials of the heat sinks used on the cold and hot sides of thermoelectric module are exactly similar; so the specifications in Table 2 can also be used for the heat sink on the cold side. However, the fluid used in the cold side heat sink is air; and the procedure for calculating its convectional heat transfer coefficient has been explained below. The fan used in this system blows air at a velocity of about 6 m/ s into the heat sink installed on the cold side. The properties of air at a pressure of one atmosphere have been shown in Table 6. By having the geometrical specifications in Table 2 and air properties in Table 6, the Reynolds number can be calculated (Eq. (28)).
ReD ¼ 3578
ð28Þ
Since the Reynolds number is greater than 2300, the flow is considered as turbulent and it is assumed as a fully-developed flow. So Eq. (24-b) should be used to obtain the Nusselt number. Based on Eq. (21), the convectional heat transfer coefficient for the heat sink of the cold side is obtained from Eq. (29).
h ¼ 33:31
ð29Þ
Thus, all the parameters needed for determining the unknown variables of Eqs. (7) are obtained. By solving 4 equations and Eq. (6), five unknowns and also the values of output current, voltage and power are obtained and plotted versus the inlet temperature difference between the hot and cold sides of heat sinks (Figs. 12– 14). 4. Fabricating the experimental prototype The model explored in the previous sections of this paper has been fabricated according to Fig. 3, and care has been taken to comply with the details as much as possible. The heat sinks used in this experimental sample are according to Fig. 15, and the sizes and dimensions of these heat sinks are exactly the same as those selected in a previous section in Table 2. Also, thermoelectric modules of TEC12706 (which were shown in Fig. 8. and whose specifications were employed in designing the thermoelectric generator) have been used to manufacture the thermoelectric generator prototype. The fan depicted in Fig. 16 has been used to simulate the air flow over the heat sink on the cold side. The various components of the manufactured thermoelectric generator have been assembled by means of silicon glue and nuts and bolts and spacers. A view of the manufactured prototype of this thermoelectric generator is shown in Fig. 17. Ultimately, the outputs of this manufactured thermoelectric generator, including the voltage, current and generated electrical power, have been measured at a specific temperature and the results have been shown in Fig. 18. The measured results including the generated current, voltage and power output have been plotted versus input temperature difference in Figs. 19, 20 and 21, respectively. 5. Results and discussions The theoretical and experimental values obtained in diagram form have been compared in Figs. 22–24. Based on the calculations, the highest error was 4.6 percent for a temperature difference of lower than 100 °C. Some of the causes of discrepancy between theoretical and experimental results have been explained below: 1. In the performed modeling it has been assumed that the exterior surface and the area surrounding the heat converter and also the air gap between thermoelectric modules are completely isolated; while the heat lost from these surfaces and also through the nuts and bolts used to fasten the generator components could affect the output. 2. In the modeling, a uniform distribution of temperature is assumed for the exhaust gas at any cross section of exhaust pipe, in a direction parallel to flow; while the shape of rotor fins and other factors might nullify this assumption of uniform temperature distribution. 3. As was mentioned in Section 3.2, using the empirical equations for computing the Nusselt number to obtain the Reynolds number introduces an inherent error of 10%; which certainly affects the determination of the system’s output power. 4. There might be errors in the thermoelectric properties listed on the relevant data sheets.
Table 5 Properties of gases coming out of the tested gasoline engine’s exhaust pipe. T (K)
q (kg/m3 )
cp (kJ/kgK)
l 107 (Ns/m2 )
k 103 (W/mK)
386
0.9180
1.0886
206.364
30.7488
632
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Table 6 Properties of air at a pressure of one atm and temperature of 303 K. T (K)
q (kg=m3 )
cp (kJ/kgK)
l 107 (Ns/m2 )
k 103 (W/mK)
303.15
1.1509
1.007
186.08
26.5
Fig. 12. Output current versus the input temperature difference between the hot and cold sides of heat sinks obtained theoretically.
Fig. 15. A schematic of the heat sinks used in the experimental prototype.
Fig. 13. Potential difference between two outlets versus the input temperature difference between the hot and cold sides of heat sinks obtained theoretically.
Fig. 16. The fan used in the fabrication of experimental prototype to simulate the flow of air over the heat sink installed on the cold side.
Fig. 14. Output power of thermoelectric generator versus the input temperature difference between the hot and cold sides of heat sinks obtained theoretically.
5. The properties of exhaust gas compositions are obtained at an average temperature, and using an average temperature throughout the heat sink connected to exhaust pipe might affect the output values.
6. The compositions of exhaust gases and the percentage of each one cannot be measured exactly and they might be different from the original compositions; and this could be an important source of error in the computation of thermophysical properties and fluid flow rates. 7. Laboratory instruments such as multimeters, thermometers, calipers, etc. could be out of calibration, and human error in using these devices may also introduce some inaccuracies. 8. Pressure drop along the flow path of exhaust gases causes the temperature of the hot sides of thermoelectric modules, which are farther away from generator inlet, to be less than the temperature of modules that are closer to generator inlet; this can also cause a discrepancy in the theoretical and experimental results.
633
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Fan
Cold side heatsink TEG modules
Fig. 17. A view of the fabricated experimental prototype.
Input temperature to the cold side heatsink Difference potential
Potenal Difference (V)
Fig. 19. Generated current versus the input temperature difference between the hot and cold sides of heat sinks obtained experimentally.
Hot side heatsink
10 9 8 7 6 5 4 3 2 1 0 20
45
70
95
120
Input Temperatue Difference ( ) Fig. 20. Potential difference between two outlets versus the input temperature difference between the hot and cold sides of heat sinks obtained experimentally.
Input temperature to the hot side heatsink
TEG System
Fig. 18. Laboratory measurements obtained from the fabricated prototype.
5.1. Analysis of some important parameters In the previous section it was demonstrated that the theoretical and experimental results have an adequate agreement, especially at a temperature difference of less than 100 °C. Therefore, the theoretical results could be used to analyze the effects of some important parameters, with the hope of designing a better prototype with a higher output power in the future. In the following analyses, the output powers of the thermoelectric generator versus some generator system parameters have been shown at a constant temperature difference of 50 °C. The temperatures of the cold and hot surfaces are 300 and 350 K, respectively. Hence, the thermal properties have been investigated at these tem-
Fig. 21. Output power of thermoelectric generator versus the input temperature difference between the hot and cold sides of heat sinks obtained experimentally.
peratures, and the same physical properties as before have been considered in the analyses. Fig. 25 shows the output power of the fabricated thermoelectric generator versus the Seebeck coefficient of thermoelectric module. According to Fig. 25, using a thermoelectric generator with a higher Seebeck coefficient causes an increase in output power; which is predictable, because the Seebeck coefficient is actually the ratio of output voltage to the temperature difference between the two sides of a thermoelectric module; thus by increasing the Seebeck coefficient, the total voltage and, consequently, the output power of the thermoelectric generator increases.
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Fig. 22. Comparing the generated currents with respect to the input temperature difference between hot and cold sides of heat sink in theoretical and experimental investigations.
Fig. 25. Output power versus the Seebeck coefficient of thermoelectric module.
Fig. 26. Output power versus the internal resistance of thermoelectric modules. Fig. 23. Comparing the potential differences between two outlets with respect to the input temperature difference between hot and cold sides of heat sink in theoretical and experimental investigations.
Fig. 27. Output power versus the heat conductivity coefficient of thermoelectric modules. Fig. 24. Comparing the output powers with respect to the input temperature difference between hot and cold sides of heat sink in theoretical and experimental investigations.
Fig. 26 shows the output power versus the internal resistance of thermoelectric modules. As is observed in Fig. 26, with the increase in the internal resistance of thermoelectric modules the output power diminishes; which is obvious, because by increasing the internal resistance of thermoelectric modules, the amount of electrical current decreases, resulting in the drop of output power. The output power versus the heat conduction coefficient of thermoelectric modules has been illustrated in Fig. 27. As Fig. 27 shows, by increasing the heat conduction coefficient of thermoelectric modules, the generator’s output power dimin-
ishes. As the diagram shows, this is one of the most important factors affecting the output of thermoelectric generator. The increase of heat conduction coefficient leads to the transfer of more heat from the hot side of a thermoelectric module to its cold side; this raises the temperature of the cold side and reduces the temperature difference between the hot and cold sides of thermoelectric module; which itself is the main cause of power generation. According to Fig. 27, increasing the heat conductivity coefficient of thermoelectric modules by more than 4 W/K reduces the generated power to zero; because, due to the small thickness of thermoelectric modules, with this increase in the heat conduction coefficient, practically there is no temperature difference between the hot and cold surfaces of a module. In fact, one of the most important factors in the fabrication of thermoelectric modules is to choose materials with a low heat conduction coefficient.
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Fig. 28 shows the output power versus the rate of gas flow into the heat sink installed at exhaust pipe outlet. As is observed in Fig. 28, the increase in the flow rate of gas flowing into the heat sink at exhaust pipe outlet leads to the increase in the output power of thermoelectric generator. As is evident, and in view of Eq. (1), this increased flow rate increases the amount of heat transfer, which causes the heat of the exhaust gases to be more effectively transferred to the hot surfaces of thermoelectric modules and thereby raises the temperature of the hot sides and increases the generated power of the thermoelectric generator. Fig. 29 shows the output power of the thermoelectric generator versus the flow rate of gas entering the heat sink installed on the cold side of thermoelectric module. As is observed in Fig. 29, with the increase in the flow rate of gas entering the heat sink installed on the cold side of thermoelectric module, the output power increases considerably. The reason is that the increase of flow rate increases the heat transfer from the cold surface of a thermoelectric module to the surrounding atmosphere and makes the surface cooler, thereby increasing the temperature difference between the hot and cold sides of the thermoelectric module; and this increase of temperature difference leads to more output power from the thermoelectric generator. Therefore, if liquids are used on the cold side of thermoelectric modules, the overall efficiency of a thermoelectric generator can be significantly increased; because by using liquids, a greater flow rate can be produced. Fig. 30 shows the output power versus heat conduction coefficient for the heat sink installed at exhaust pipe outlet. According to Fig. 30, as was expected, the heat conduction coefficient of the heat sink installed at exhaust pipe outlet has no significant impact on output power. Of course, the diagram in Fig. 29 relates to the heat conduction range of metals; which, at heat conduction coefficients of less than 100, the effect could be significant. So if a metal with a relatively good conduction is used in the making of heat sinks installed in a thermoelectric generator, even the heat conduction effect of the heat sinks can be ignored. The reason for the negligible influence of heat conduction is the small thickness (tb in Fig. 9) through which heat is transferred by conduction. In fact, the effect of conduction heat transfer is much less than that of convection heat transfer. Fig. 31 shows the behavior of output power with respect to the heat conduction coefficient of the heat sink installed on the cold surface of thermoelectric module. In view of Fig. 31 with the increase in the heat conduction coefficient of the heat sink installed on the cold side of thermoelectric module, the output power increases very slightly; and this is due to
635
Fig. 29. Output power versus the flow rate of gas entering the heat sink installed on the cold side of thermoelectric module.
Fig. 30. Output power versus heat conduction coefficient for the heat sink installed at exhaust pipe outlet.
Fig. 31. Output power versus heat conduction coefficient for the heat sink installed on the cold surface of thermoelectric module.
the same reasons mentioned for the heat sink installed at exhaust pipe outlet. 6. Conclusions
Fig. 28. Output power versus the flow rate of gas entering the heat sink installed at exhaust pipe outlet.
In this paper, first, a thermoelectric generator has been designed and modelled. By having the temperatures and the rates of flow into the heat sink installed at exhaust pipe outlet and the heat sinks installed on the cold side of thermoelectric modules as the equation inputs, the output power of the deigned generator has been computed. Moreover, an experimental prototype of the designed model has been manufactured in Section 4 and its output
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power has been measured against the input temperature difference between hot and cold sides. The theoretical and experimental values obtained in diagram form have been compared in Section 5. These comparisons show that the results agree with each other to a large extent, especially at temperatures lower than 100 °C. Considering the matching of these results, the effects of some important parameters on the output power of the considered thermoelectric generator are also investigated, and the significant influence of the thermal conduction coefficient of thermoelectric significant impact on output power and the heat conduction coefficient of the heat sink installed at exhaust pipe outlet and on the cold side of thermoelectric module has no significant impact on output power.
[11]
[12]
[13]
[14]
[15]
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Contents lists available at ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Research Paper
Modeling and fabricating a prototype of a thermoelectric generator system of heat energy recovery from hot exhaust gases and evaluating the effects of important system parameters Seyed Alireza Mostafavi ⇑, Mojtaba Mahmoudi Department of Mechanical Engineering, Faculty of Engineering, Arak University, Arak, Iran
h i g h l i g h t s A thermoelectric module with a low thermal conductivity is more effective. System efficiency could be improved by using liquids on the cold and hot side of TEG. The thermal conductivity of the heat sinks has no significant effect on efficiency. The good results have been yielded, especially at temperatures lower than 100 °C.
a r t i c l e
i n f o
Article history: Received 21 April 2017 Revised 10 November 2017 Accepted 4 January 2018 Available online 6 January 2018 Keywords: Thermoelectric Generator Energy recovery Smokestack Modeling
a b s t r a c t The heat lost through smokestacks has an adequate energy recovery capacity. A new and effective method of recovering this energy is the use of thermoelectric generators, which directly convert thermal energy to electricity. Some of the advantages of thermoelectric generators include their environmental friendliness and also their lack of moving or rotating parts, which makes them operate without noise and extends their service life. This paper deals with the general modeling of a thermoelectric generator system, including the modeling of the cooling system for the cold side of thermoelectric generator, system of heat transfer from smokestack to the hot side of thermoelectric generator and also the modeling of the thermoelectric modules themselves. In continuation, for validating the obtained equations, an experimental prototype of this thermoelectric generator is fabricated and the empirical results including the nominal voltage, current and power of the manufactured system are compared with the theoretical results. This comparison shows the validity of the presented modeling and the good agreement between the theoretical and practical results, especially at low temperatures. Based on the calculations, the highest error was 4.6 percent for a temperature difference of lower than 100 °C. Additionally, for the same temperature difference, the highest theoretical and practical output powers for this module were 3.4 W and 2.8 W, respectively. Considering the matching of these results, the effects of some important parameters on the output power of the considered thermoelectric generator are also investigated, and the significant influence of the thermal conduction coefficient of thermoelectric modules is demonstrated. Ó 2018 Elsevier Ltd. All rights reserved.
1. Introduction Petroleum-based and fossil fuels have been utilized extensively in transportation systems throughout the world; although for reasons such as the depletion of oil resources, environmental problems, and the regulations and limitations set by governments for reducing the consumption of fossil fuels, alternative fuels and vehi-
⇑ Corresponding author. E-mail address: [email protected] (S.A. Mostafavi). https://doi.org/10.1016/j.applthermaleng.2018.01.018 1359-4311/Ó 2018 Elsevier Ltd. All rights reserved.
cle powertrain systems are getting better in quality and more efficient [1]. Many of the existing commercial and environmental problems can be solved and socioeconomic benefits can be gained by improving the conditions of consumed fuels. Some of these issues are as follows: Despite the increase of energy efficiency in many developed countries these countries still depend on foreign countries for the fuel they need; and a substantial amount of this imported fuel (almost half of it) is utilized in vehicles and trucks [2].
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Nomenclature A b Cp D f h I K L _ m NuD n P Pr Q Rb Ri RL RhS ReD r T Tb TE TEG
area (m2 ) space between the fins (m) specific heat ðJ=kg KÞ diameter of a circular tube ðmÞ fanning friction factor heat transfer function (W=m2 K) current (A) thermal conductance (W=m K) length (mÞ mass flow rate (kg=s) Nusselt number number of fins electrical power (W) Prandtl number heat flow (W) thermal resistance of heat sink base (W=K) internal resistance (X) load resistance (X) heatsink thermal resistance (W=K) Reynolds number radius (m) temperature (K) bulk temperature of the exhaust gas thermoelectric thermoelectric generator
Almost one-third of carbon emission in the world is produced by various vehicles. Inefficient and fuel-guzzling vehicles are major causes of increased carbon production; and the increase of carbon dioxide along with other greenhouse gases is a key factor in global warming [3]. Equipped with systems such as accident. Navigation systems, future and next-generation vehicles should be able to produce on-demand power; which requires more fuel consumption. Almost all personal vehicles and light trucks are equipped with engines that run on gasoline or diesel. The energy consumption of a gasoline-burning internal combustion engine has been shown in Fig. 1 [4]. As is observed, 70% of the energy contained in fuel is lost, as heat, from the exhaust pipe or in the cooling process and the rest is converted to mechanical work and energy.
TC Th tb tf um VO Wf
cold junction temperature in a thermoelectric module hot junction temperature in a thermoelectric module heat sink base thickness fin thickness mean fluid velocity output voltage (v) fin width (m)
Greek symbols a seebeck coefficient DT temperature difference gf fins efficiency q density Subscripts b base c cold side f fins h hot side i input L load m mean o output
A portion of this produced work is used to overcome friction in the power transmission system of a vehicle and its other equipment such as cooling pump, fuel pump, etc. Consequently, only 20–25% of the initially produced energy is used to drive the vehicle. Moreover, this remaining energy has to overcome the following: inertia generated during the acceleration or uphill movement of vehicle, aerodynamic drag force friction between vehicle tires and road surface There are three major ways of reducing fuel consumption in vehicles [5]: Increasing the overall efficiency of power systems (engine, power transmission system, etc.) in order to produce more work from the consumed fuel, reducing the amount of work needed to move a vehicle by lowering its weight Reducing the friction between vehicle tires and road, etc and Recovering the energy dissipated from a vehicle. 1.1. Energy recovery from exhaust pipes
Fig. 1. Energy consumption of a gasoline-burning internal combustion engine.
A considerable amount of unused heat (about 40% according to Fig. 1) is dissipated via the exhaust pipe of a vehicle. Here, the notion of fuel consumption improvement means to increase the overall efficiency of a vehicle’s power transmission system which has lost a great deal of energy through the discharged exhaust gases. According to the book of ‘‘Vehicle Electronics and Electricity” published in 1999, the average electricity consumption of an automobile is 600 W [6]; which imposes an extra load on the engine to provide this power. If the heat lost through a vehicle’s exhaust pipe can be utilized to generate the electricity needed by the vehicle, a substantial amount of load can be removed from vehicle engine. One method of converting the dissipated heat to electricity is the use of thermoelectric (TE) converters.
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Thermoelectric converters work on the basis of thermoelectric law. Based on this law, when two conductors with different loads are connected together at different temperatures, an electrical load is induced in the connecting circuit. Each of the two currentcarrying conductors in this system is called a thermoelectric element, and each pair of these two conductors is called a thermoelectric couple [7]. A schematic view of these thermoelectric converters and the principles of their work have been depicted in Fig. 2. In an ordinary thermoelectric generator (TEG), the heat exchangers receive heat from a heat source and transfer it to thermocouple connections. A heat exchanger along with a thermoelectric couple is known as a thermoelectric generator. Thermoelectric generators have a solid-state technology; they have no moving parts and therefore have a very simple and reliable mechanism and a long service life. In view of the previous explanations, a thermoelectric generator system connected to an exhaust pipe should include the following components:
Exhaust system Cooling system Heat transfer system Thermoelectric modules
One of the earliest research works on thermoelectric generators was conducted by Richard H. Bauer [8] at Clarkson University during the years 1961–63. Bauer explored the possibility of designing a thermoelectric generator which could provide some supplemental electricity for a vehicle. The water used for cooling the engine was considered as the heat source and ambient air was used as the working fluid for the cold side of heat exchanger. Lead telluride was the only thermoelectric material used in Bauer’s study. His research showed the infeasibility of having a thermoelectric generator that uses the cooling water of vehicle engine as the heat source. This is due to the large volume and cross-sectional area of thermoelectric material necessary, needed to generate the required electricity. However, the research also indicated that if the temperature of heat source can be kept at about 600 K, a thermoelectric generator might be a feasible option. Concurrent with the work of Bauer, Anthony Joseph Tomarchio [9] at Clarkson University investigated the possibility of increasing a vehicle’s efficiency by replacing some of its equipment, such as dynamo, with a thermoelectric generator installed on the exhaust pipe of vehicle. In his research, he also used ambient air as the working fluid and lead telluride as the thermoelectric material, and he achieved the following results: At a vehicle speed of 50 mph, a maximum power of about 514 W with a voltage of 14.7 V is observed. A minimum vehicle speed of 20 mph is needed to get minimum output power from the battery and generator
Fig. 2. Schematic of a complete thermoelectric generator system.
At speeds below 20 mph, the needed power can only be provided by improving the semiconductors used in the thermoelectric material. Birkholz et al. [10] designed a thermoelectric generator that used FeSi2 as the thermoelectric material. They tested their generator on a Porsche 944 engine and obtained a maximum power of 58 W. By employing the thermoelectric modules made by the Hi-Z Company, Bass et al. [11] explored the recovery of dissipated heat from a diesel engine. They used different heat sources in their research and concluded that, because of the large temperature difference provided by the hot gases from the exhaust pipe, they have the best potential for use in thermoelectric generators. These researchers also used thermoelectric generators with various thermoelectric materials such as bismuth telluride (Bi2Te3), lead telluride, and silicone-germanium. Their studies showed that among these different thermoelectric materials, Bi2Te3 has the best performance, because its maximum working temperature is lower than that of other materials. Ikoma et al. [12] at Nissan Research Center used siliconegermanium as the thermoelectric material to fabricate a thermoelectric generator that consisted of 8 pairs of thermoelectric modules. This generator was installed in rectangular configuration on a 3000-CC automobile engine and achieved a better efficiency than its former counterpart. Vazequez et al. [13] compiled the results of the last 3 decades of research on the use of thermoelectric generators to generate electricity from the exhaust pipes of vehicles. They found out that the maximum amount of electrical power produced by thermoelectric generators varies from 43 to 193 W. The power production inefficiency was attributed to the thermoelectric generators whose working temperatures did not match the temperature of the outlet gases of exhaust pipes. For the purpose of minimizing fuel consumption in steam turbines, Yazawa et al. [14] presented a general model that used thermoelectric modules. They showed that the efficiency of a steam turbine increases by adding more thermoelectric modules. Dai et al. [15] presented a liquid–metal of a TEG system for energy recovery. When the heat source temperature was 195.9 °C, a maximum voltage of 34.7 V and a generator efficiency of 2% were obtained. Remeli et al. [16] presented a new method for recovering thermal energy and converting it to electricity by adding heat tubes to thermoelectric generators. Through this method, they were able to raise the generator efficiency by up to 2%. Nikolova et al. [17] proposed a specific system consisted of thermal power plants (TPPs), storage hydro power plants (HPPs), pumpedstorage hydro power plant (PSHPP) and wind power plant (WPP) to solve the generation scheduling problem, wind power plants are integrated into the system in order to minimize the total thermal unit fuel costs. Rezania et al. [18] compared a micro-structure plate-fin heat sink to a modified design of a cross-cut heat sink applied to a TEG device over a range of temperatures and thermal conductivities; they showed that the net power output of a TEG device can be significantly improved by optimal heat sink design. In addition, various new features have been added to traditional TEG devices to achieve better output. Modeling of an integrated cross flow heat exchanger with TEGs has also been studied by Crane and Jackson [19] with the aim to optimize the performance of the heat exchanger. This paper deals with the general modeling of a thermoelectric generator system, including the modeling of the cooling system for the cold side of thermoelectric generator, system of heat transfer from smokestack to the hot side of thermoelectric generator and also the modeling of the thermoelectric modules themselves. In continuation, for validating the obtained equations, an experimen-
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tal prototype of this thermoelectric generator is fabricated and the empirical results including the nominal voltage, current and power of the manufactured system are compared with the theoretical results. Considering the matching of these results, the effects of some important parameters on the output power of the considered thermoelectric generator are also investigated considering the matching of these results, the effects of some important parameters on the output power of the considered thermoelectric generator are also investigated 2. Modeling the thermoelectric generator A thermoelectric generator is studied in this section. In this investigation, first, the temperature distribution in the heat exchangers connected to the exhaust pipe outlet and the cooling system is explored and then the energy produced by the thermoelectric generator is calculated. Fig. 3 shows a general design of the examined thermoelectric generator system. Using a heat sink on the hot side of the thermoelectric is to increase the overall heat transfer area and thus improve the transfer of heat from the gases coming out of an exhaust pipe or smokestack to the hot surface of thermoelectric module. In fact, the use of a heat sink is one of the most effective mechanisms of increasing the amount of heat transfer. In view of Fig. 4 the examined thermoelectric generator system consists of 2 heat sinks on the cold side of thermoelectric modules and one heat sink on the hot side (which encounters the hot gases coming out of the exhaust pipe). This system also includes 8 thermoelectric modules between heat sinks; with 4 modules above the heat sink installed at the exhaust outlet and 4 modules below it. This thermoelectric generator system can be divided into 8 symmetric sections. Due to the symmetry of the 8 modules used in the system, each cross section has the same temperature profile; therefore, temperature distribution has been evaluated for just one module at each section. With this explanation, an appropriate control volume can now be chosen for each thermoelectric module (see Fig. 5). So by having the temperature distribution in each thermoelectric module, the temperature distribution in the whole heat converter can be computed. Finally, through this model, the power produced by all the 8 thermoelectric modules can be determined by using the temperature distribution for one module. Now the process of heat transfer in a thermoelectric module is explored and used in the modeling of a thermoelectric generator system. Fig. 5 shows the flow of heat in an isolated thermoelectric module from a thermoelectric generator system. The control volume has been selected according to Fig. 5. The energy obtained from exhaust gas is expressed as Eq. (1). [20].
Q 1 ¼ mh cph ðT hi T ho Þ
ð1Þ
Fig. 4. Arrangement of thermoelectric modules in the examined thermoelectric generator system.
Fig. 5. Each element of the thermoelectric generator system.
In Eq. (1), Q 1 is the energy obtained from exhaust pipe (as is shown in Fig. 5), mh is mass flow rate of gas in the exhaust pipe and cph is its specific heat capacity. T hi is the temperature of the gas entering each element in the heat sink installed at the exhaust pipe and T ho is the temperature of the outflowing gas of each element in the heat sink. The equation for convection heat transfer on the hot surface of thermoelectric module is expressed as Eq. (2), [20]:
Q1 ¼
Cold Side Heat Sink
Thermoelect ric Modules
Hot Side Heat Sink
Fig. 3. The examined thermoelectric generator system.
T hi þT ho 2
T hs
Rhs
ð2Þ
where Q 1 denotes the heat transfer (combination of convection and conduction heat transfers) over the hot surface of thermoelectric module, T hs is the temperature of the hot side of module, and Rhs is the thermal resistance, which is shown in Fig. 7. According to Fig. 7, this thermal resistance includes the resistance of fins and the resistance of heat sink base; which will be subsequently investigated. Also, the thermoelectric module’s inlet heat can also be expressed as Eq. (3) [21].
1 Q 1 ¼ K DT þ aT hs I I2 Ri 2
ð3Þ
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In Eq. (3), Q 1 , K, a and Ri are the input heat, conduction heat transfer coefficient, Seebeck coefficient and the internal resistance of the thermoelectric module, respectively, and I is the current flowing from each thermoelectric module. The convectional heat transfer equation for the cold surface of module can be defined as Eq. (4), [20].
Q2 ¼
co T cs T ci þT 2
ð4Þ
Rcs
Q 2 is the convectional heat transfer on the cold side (shown in Fig. 5), T cs is the temperature of the cold surface of thermoelectric module, T ci is the input temperature from the cooling fan and T co is the output temperature from the cold side of thermoelectric converter. Also, considering the material and arrangement of fins, Rcs is computed exactly like Rhs (illustrated in Fig. 7). The energy produced by the cooling fan is expressed as Eq. (5), [20].
Q 2 ¼ mc cpc ðT co T ci Þ
Fig. 6. Displaying a single element of the examined thermoelectric generator.
ð5Þ
In Eq. (5), Q 2 is the energy loss of the cooling fan, mc is the input mass flow rate into the element from the cooling side, and cpc is the specific heat capacity of fan air. The energy produced by the thermoelectric module is obtained from Eq. (6), [21].
P ¼ I 2 RL ¼
a2 ðT hs T cs Þ2 RL
ð6Þ
ðRi þ RL Þ2
By using Eqs. (1)–(6), the unknowns (including T co , T ho , T cs and T hs ) are obtained from Eqs. (7),
mh cph ðT hi T ho Þ mc cpc ðT co T ci Þ
T hi þT ho 2
T hs
Rhs
T hi þT ho 2
T hs
Rhs co T cs T ci þT 2
Rcs
Fig. 7. Thermal resistance of each heat sink.
¼0
ð7-aÞ Eq. (10), is used to compute Rf , which represents the resistance of fins and the surrounding air [22].
¼0
co ðT cs T ci þT Þ a2 ðT hs T cs Þ2 RL 2 ¼0 Rcs ðRi þ RL Þ2
ho ðT hi þT T hs Þ 1 2 K DT aT hs I þ I2 Ri ¼ 0 Rhs 2
ð7-bÞ Rf ¼ ð7-cÞ
ð7-dÞ
Eqs. (7) are general equations and they can be used for many thermoelectric generators. A thermoelectric module of the investigated thermoelectric generator has been depicted in Fig. 6. According to Fig. 7 thermal resistance can be used to compute the value of Rhs for each heat sink. Since the heat sinks used on both sides of the thermoelectric module are completely similar to each other, in this paper, the same Rhs value is considered for both heat sinks; the only difference is in the computations related to the fluids flowing in these heat sinks; which will be discussed later. Hence, according to Figs. 2–5, the value of Rhs is calculated from Eq. (8).
Rhs ¼ Rb þ Rf
ð8Þ
In Eq. (8), Rb represents the base resistance of each heat sink; which is determined by means of Eq. (9).
Rb ¼
tb kAb
ð9Þ
In Eq. (10), K is the conduction heat transfer coefficient of the metal used in the heat sink and tb , as is shown in Fig. 6 is the thickness of heat sink base, and Ab is the cross section area of heat sink base.
1 nhh W f ðtf þ 2gf Lf Þ
ð10Þ
As is shown in Fig. 6, W f is the fin width, tf is fin thickness, Lf is fin length, and n is the number of fins. hh denotes the convectional heat transfer coefficient of heat sink fluid. Also, Eq. (11) should be used to compute the value of gf in Eq. (10).
gf ¼
tanh mLc mLc
ð11Þ
And the value of mLc is determined from Eq. (12).
sffiffiffiffiffiffiffiffi 2hh Lf mLc ¼ ktf
ð12Þ
3. Measurement of parameters and the fabrication of the experimental prototype In this section, the parameters and inputs of Eqs. (7) are determined to find the unknown variables including T co , T ho , T cs and T hs . The thermoelectric modules used in this paper are of TEC12706 type; with a schematic of this module shown in Fig. 8. The Seebeck coefficient, internal resistance, and the thermal conduction coefficient of this module have been listed in the relevant specifications sheet of this thermoelectric module in Table 1. The objective here is to validate the equations used in the previous section for a thermoelectric generator; so the type and model of thermoelectric module is not important here; it should just be able to tolerate the temperature of exhaust gases. Once the equations are validated, thermoelectric modules of higher power can be used as
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Value
tb Ab
2 (mm) 1.806 102 (m2 ) 5.7 (mm) 62.5 (mm) 1.8 (mm) 15.7 (mm) 6 215 (W=K m)
b Wf tf Lf n k
Fig. 8. A schematic view of thermoelectric module TEC12706.
needed. Here, general equations, which govern all kinds of thermoelectric modules, are derived; and the main properties of thermoelectric module TEC12706 are used to confirm the accuracy of these equations. Therefore, the low-cost thermoelectric module TEC12706 can be appropriately used for recovering the heat energy dissipated by an exhaust pipe and also as a cooling system; however, the equipment it carries should be tolerant of exhaust pipe temperatures [23]. The geometrical dimensions of the examined heat sink (shown in Table 2) are according to the element depicted in Fig. 9. 3.1. Measuring the flow rate of exhaust gas The properties of smoke coming out of the exhaust pipe can be obtained from the composition of exhaust gases generated by gasoline-burning engines. Fig. 10 shows the tested gasoline engine whose exhaust gases have been used here. Table 3 contains the composition of exhaust gases produced by most gasoline-burning engines in which the fuel undergoes an almost complete combustion [24]. By knowing the composition of the exhaust gases flowing out of gasoline-burning engines the thermophysical properties of these gases can be obtained at different temperatures. The formula for gasoline combustion and the flow rate of fuel (gasoline) can be used to compute the flow rate of exhaust gas. Gasoline contains hydrocarbons of C5 to C11 or C12. Ordinary gasoline, which constitutes about 15% of crude oil, is known by chemical formula C8H16. The density of gasoline is normally 0.719 g/cm3 [25]. If gasoline (with a chemical formula of C8H16) is completely combusted, it decomposes according to Eq. (13), [26].
aC8 H16 þ ath ðO2 þ 3:76N2 Þ ! bCO2 þ cH2 O þ 3:76ath N2
Fig. 9. Three views of the examined element in the investigated thermoelectric generator.
Engne
ð13Þ
Exhaust
Fig. 10. A schematic of the gasoline engine tested in this work.
Coefficients a, b, c and ath are obtained after balancing the combustion equation (Eq. (13)). Table 3 Composition of exhaust gases produced by gasoline-burning engines.
Table 1 Main specifications of the thermoelectric generator used. Specifications Volt
aM
K
RiM ðOhmsÞ K M Watts K
Value 0.0349 0.1290 2.3569
Name
% by volume
Nitrogen Carbon dioxide Water vapour Oxygen Nitrogen oxides Carbon monoxide Hydrocarbons Sulfur dioxide and other gases
71% 14% 13% 1% 6 0:25% 1% 6 0:25% 6 0:5%
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8a ¼ b 16a ¼ 2c
ð14Þ
Table 4 Volume flow rates of fuel obtained in three measurements.
2ath ¼ 2b þ c
Measurements
C8 H16 þ 12ðO2 þ 3:76N2 Þ ! 8CO2 þ 8H2 O þ ð3:76 12ÞN2
102
3.38 107
5
1.57 10
45
3.49 107
Third measurement
2.19 105
70
3.14 107
3.45 10
ð15Þ
The air-to-fuel ratio for the combustion Eq. (15) is expressed as Eq. (16).
mAir AF ¼ mfuel
Volume flow rate (m3 =s)
Second measurement
First measurement
By solving Eqs. (14), the balanced equation takes the form of Eq. (15).
Time (s)
5
Volume (m3 )
ð16Þ
Thus, the air-to-fuel ratio is obtained from Eq. (17).
kg ð12 4:76 kmolÞ 29 kmol AF ¼ kg kg þ ð8 kmolÞ 2 kmol ð8 kmolÞ 12 kmol
However, the objective is to get the flow rate of gases out of the exhaust pipe. For this purpose, the flow rate of consumed fuel should be added to the flow rate of air. Eqs. (16) and (18) and the flow rate of consumed fuel should be used to obtain the flow rate of air. These equations are expressed as Eq. (20-b).
_ exhaust gas ¼ ð1 þ AFÞ m _ fuel ¼ ð1 þ 14:79Þ 2:39 104 m ¼ 3:77 103 kg=s
¼ 14:79kg Air=kg fuel
ð20-bÞ
ð17Þ
Eq. (18), can be used to get the flow rate of air coming out of exhaust pipe.
_ fuel Þ _ Air ¼ ðAFÞðm m
ð18Þ
To calculate the flow rate of air, we need to measure the flow rate of utilized fuel for measuring the flow rate of consumed fuel, according to Fig. 11 a graded glass tube is installed in the fuel tank and used to measure the volume of consumed fuel per unit time. Through several measurements, the following values were obtained in Table 4. The measurements were taken at an average temperature of 125 °C. By averaging the flow rates in Table 4, the mean volume flow rate of consumed fuel is obtained according to Eq. (19).
Q ¼ 3:33 107 m3 =s
ð19Þ
To get the mass flow rate of fuel the volume flow rate should be multiplied by the density of gasoline, which has a mean value of 0.719 g/cm3 or 719 kg/m3. Thus, the mass flow rate of fuel is obtained from Eq. (20-a).
_ fuel ¼ qQ ¼ 719 3:33 107 ¼ 2:39 104 kg=s m
ð20-aÞ
3.2. Computing the convectional heat transfer coefficient [20] In this section, the coefficient of convectional heat transfer in the heat sink installed at exhaust pipe outlet is computed. In order to obtain this coefficient we should use the Nusselt number, which is defined as Eq. (21).
NuD ¼
hi D H K
ð21Þ
In Eq. (21), K is the conduction coefficient of fluid inside the conduit, hi is the internal convectional heat transfer coefficient and DH is the hydraulic diameter, which is expressed as Eq. (22), for non-circular conduits.
DH ¼
4A P
ð22Þ
In Eq. (22), A is the cross sectional area and P is the perimeter in contact with fluid. To find the Nusselt number in Eq. (21), empirical equations that depend on the type of flow have to be used. The type of flow can be determined with regards to the Reynolds number (which is defined as Eqs. (23)).
ReD ¼
qum DH l
ð23-aÞ
_ H mD lA
ð23-bÞ
or
ReD ¼
In Eqs. (23), q is the density of gases flowing inside the tube, um is the mean velocity of fluid at any cross section of tube, l is the _ is the mass flow rate of viscosity of the fluid in the tube and m gas in the tube. For Reynolds smaller than 2300, the flow is considered to be laminar; and if this flow is fully developed, the Nusselt number will have a constant value expressed by Eq. (24-a).
Graded Glass
NuD ¼ 4:36
Gasoline Ruler
And for Reynolds larger than 2300, the flow is considered to be turbulent; and if this flow is fully developed, the Nusselt number is defined according to Eq. (24-b). This equation is known as the Gnielinski equation and it is defined for the following range:
NuD ¼ Fig. 11. Graded glass tube used for measuring the volume flow rate of gasoline.
ð24-aÞ
f ðReD 8
1000ÞPr 12 2 pr3 1 1 þ 12:7 8f
ð24-bÞ
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In Eq. (24-b), f represents the friction coefficient, which is computed from Eq. (25).
f ¼ ½0:79 lnðReD Þ 1:64
2
ð25Þ
In Eq. (25) equation, Pr denotes the Prandtl number. The internal convectional heat transfer coefficient can be determined through Eqs. (21) and (24). Fluid properties are defined for an average temperature. Since these properties are obtained from empirical equations, they have an inherent error of 10%. Therefore, by knowing the properties of fluid and the flow rate of exhaust gases at the considered temperature, the value of h can be obtained by using the Nusselt number. 3.2.1. Computing the convectional heat transfer coefficient for the heat sink installed at exhaust pipe outlet [20] To compute the convectional heat transfer coefficient, Reynolds number should be determined first. By using the mass flow rate and the properties of exhaust gas in Table 5 and the geometrical properties of heat sink, the Reynolds number of the exhaust gas can be calculated by means of Eq. (23-b). Gas properties should be determined at an average temperature. So for an input temperature of 126 °C and output temperature of 101 °C, the mean temperature is calculated as 113.5 °C. Now by using Eq. (23-b) and the values of mass flow rate and hydraulic diameter, Reynolds number can be computed from Eq. (26).
ReD ¼ 903:7
ð26Þ
Since the Reynolds number is less than 2300, flow is laminar, and the Nusselt number is obtained from Eq. (24-a). And by using Eq. (21), the convectional heat transfer coefficient is determined from Eq. (27).
h¼
NuD k ¼ 13:77 DH
ð27Þ
3.2.2. Computing the convectional heat transfer coefficient for the heat sink installed on the cold side of thermoelectric module [20] The geometrical parameters and the materials of the heat sinks used on the cold and hot sides of thermoelectric module are exactly similar; so the specifications in Table 2 can also be used for the heat sink on the cold side. However, the fluid used in the cold side heat sink is air; and the procedure for calculating its convectional heat transfer coefficient has been explained below. The fan used in this system blows air at a velocity of about 6 m/ s into the heat sink installed on the cold side. The properties of air at a pressure of one atmosphere have been shown in Table 6. By having the geometrical specifications in Table 2 and air properties in Table 6, the Reynolds number can be calculated (Eq. (28)).
ReD ¼ 3578
ð28Þ
Since the Reynolds number is greater than 2300, the flow is considered as turbulent and it is assumed as a fully-developed flow. So Eq. (24-b) should be used to obtain the Nusselt number. Based on Eq. (21), the convectional heat transfer coefficient for the heat sink of the cold side is obtained from Eq. (29).
h ¼ 33:31
ð29Þ
Thus, all the parameters needed for determining the unknown variables of Eqs. (7) are obtained. By solving 4 equations and Eq. (6), five unknowns and also the values of output current, voltage and power are obtained and plotted versus the inlet temperature difference between the hot and cold sides of heat sinks (Figs. 12– 14). 4. Fabricating the experimental prototype The model explored in the previous sections of this paper has been fabricated according to Fig. 3, and care has been taken to comply with the details as much as possible. The heat sinks used in this experimental sample are according to Fig. 15, and the sizes and dimensions of these heat sinks are exactly the same as those selected in a previous section in Table 2. Also, thermoelectric modules of TEC12706 (which were shown in Fig. 8. and whose specifications were employed in designing the thermoelectric generator) have been used to manufacture the thermoelectric generator prototype. The fan depicted in Fig. 16 has been used to simulate the air flow over the heat sink on the cold side. The various components of the manufactured thermoelectric generator have been assembled by means of silicon glue and nuts and bolts and spacers. A view of the manufactured prototype of this thermoelectric generator is shown in Fig. 17. Ultimately, the outputs of this manufactured thermoelectric generator, including the voltage, current and generated electrical power, have been measured at a specific temperature and the results have been shown in Fig. 18. The measured results including the generated current, voltage and power output have been plotted versus input temperature difference in Figs. 19, 20 and 21, respectively. 5. Results and discussions The theoretical and experimental values obtained in diagram form have been compared in Figs. 22–24. Based on the calculations, the highest error was 4.6 percent for a temperature difference of lower than 100 °C. Some of the causes of discrepancy between theoretical and experimental results have been explained below: 1. In the performed modeling it has been assumed that the exterior surface and the area surrounding the heat converter and also the air gap between thermoelectric modules are completely isolated; while the heat lost from these surfaces and also through the nuts and bolts used to fasten the generator components could affect the output. 2. In the modeling, a uniform distribution of temperature is assumed for the exhaust gas at any cross section of exhaust pipe, in a direction parallel to flow; while the shape of rotor fins and other factors might nullify this assumption of uniform temperature distribution. 3. As was mentioned in Section 3.2, using the empirical equations for computing the Nusselt number to obtain the Reynolds number introduces an inherent error of 10%; which certainly affects the determination of the system’s output power. 4. There might be errors in the thermoelectric properties listed on the relevant data sheets.
Table 5 Properties of gases coming out of the tested gasoline engine’s exhaust pipe. T (K)
q (kg/m3 )
cp (kJ/kgK)
l 107 (Ns/m2 )
k 103 (W/mK)
386
0.9180
1.0886
206.364
30.7488
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Table 6 Properties of air at a pressure of one atm and temperature of 303 K. T (K)
q (kg=m3 )
cp (kJ/kgK)
l 107 (Ns/m2 )
k 103 (W/mK)
303.15
1.1509
1.007
186.08
26.5
Fig. 12. Output current versus the input temperature difference between the hot and cold sides of heat sinks obtained theoretically.
Fig. 15. A schematic of the heat sinks used in the experimental prototype.
Fig. 13. Potential difference between two outlets versus the input temperature difference between the hot and cold sides of heat sinks obtained theoretically.
Fig. 16. The fan used in the fabrication of experimental prototype to simulate the flow of air over the heat sink installed on the cold side.
Fig. 14. Output power of thermoelectric generator versus the input temperature difference between the hot and cold sides of heat sinks obtained theoretically.
5. The properties of exhaust gas compositions are obtained at an average temperature, and using an average temperature throughout the heat sink connected to exhaust pipe might affect the output values.
6. The compositions of exhaust gases and the percentage of each one cannot be measured exactly and they might be different from the original compositions; and this could be an important source of error in the computation of thermophysical properties and fluid flow rates. 7. Laboratory instruments such as multimeters, thermometers, calipers, etc. could be out of calibration, and human error in using these devices may also introduce some inaccuracies. 8. Pressure drop along the flow path of exhaust gases causes the temperature of the hot sides of thermoelectric modules, which are farther away from generator inlet, to be less than the temperature of modules that are closer to generator inlet; this can also cause a discrepancy in the theoretical and experimental results.
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Fan
Cold side heatsink TEG modules
Fig. 17. A view of the fabricated experimental prototype.
Input temperature to the cold side heatsink Difference potential
Potenal Difference (V)
Fig. 19. Generated current versus the input temperature difference between the hot and cold sides of heat sinks obtained experimentally.
Hot side heatsink
10 9 8 7 6 5 4 3 2 1 0 20
45
70
95
120
Input Temperatue Difference ( ) Fig. 20. Potential difference between two outlets versus the input temperature difference between the hot and cold sides of heat sinks obtained experimentally.
Input temperature to the hot side heatsink
TEG System
Fig. 18. Laboratory measurements obtained from the fabricated prototype.
5.1. Analysis of some important parameters In the previous section it was demonstrated that the theoretical and experimental results have an adequate agreement, especially at a temperature difference of less than 100 °C. Therefore, the theoretical results could be used to analyze the effects of some important parameters, with the hope of designing a better prototype with a higher output power in the future. In the following analyses, the output powers of the thermoelectric generator versus some generator system parameters have been shown at a constant temperature difference of 50 °C. The temperatures of the cold and hot surfaces are 300 and 350 K, respectively. Hence, the thermal properties have been investigated at these tem-
Fig. 21. Output power of thermoelectric generator versus the input temperature difference between the hot and cold sides of heat sinks obtained experimentally.
peratures, and the same physical properties as before have been considered in the analyses. Fig. 25 shows the output power of the fabricated thermoelectric generator versus the Seebeck coefficient of thermoelectric module. According to Fig. 25, using a thermoelectric generator with a higher Seebeck coefficient causes an increase in output power; which is predictable, because the Seebeck coefficient is actually the ratio of output voltage to the temperature difference between the two sides of a thermoelectric module; thus by increasing the Seebeck coefficient, the total voltage and, consequently, the output power of the thermoelectric generator increases.
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Fig. 22. Comparing the generated currents with respect to the input temperature difference between hot and cold sides of heat sink in theoretical and experimental investigations.
Fig. 25. Output power versus the Seebeck coefficient of thermoelectric module.
Fig. 26. Output power versus the internal resistance of thermoelectric modules. Fig. 23. Comparing the potential differences between two outlets with respect to the input temperature difference between hot and cold sides of heat sink in theoretical and experimental investigations.
Fig. 27. Output power versus the heat conductivity coefficient of thermoelectric modules. Fig. 24. Comparing the output powers with respect to the input temperature difference between hot and cold sides of heat sink in theoretical and experimental investigations.
Fig. 26 shows the output power versus the internal resistance of thermoelectric modules. As is observed in Fig. 26, with the increase in the internal resistance of thermoelectric modules the output power diminishes; which is obvious, because by increasing the internal resistance of thermoelectric modules, the amount of electrical current decreases, resulting in the drop of output power. The output power versus the heat conduction coefficient of thermoelectric modules has been illustrated in Fig. 27. As Fig. 27 shows, by increasing the heat conduction coefficient of thermoelectric modules, the generator’s output power dimin-
ishes. As the diagram shows, this is one of the most important factors affecting the output of thermoelectric generator. The increase of heat conduction coefficient leads to the transfer of more heat from the hot side of a thermoelectric module to its cold side; this raises the temperature of the cold side and reduces the temperature difference between the hot and cold sides of thermoelectric module; which itself is the main cause of power generation. According to Fig. 27, increasing the heat conductivity coefficient of thermoelectric modules by more than 4 W/K reduces the generated power to zero; because, due to the small thickness of thermoelectric modules, with this increase in the heat conduction coefficient, practically there is no temperature difference between the hot and cold surfaces of a module. In fact, one of the most important factors in the fabrication of thermoelectric modules is to choose materials with a low heat conduction coefficient.
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Fig. 28 shows the output power versus the rate of gas flow into the heat sink installed at exhaust pipe outlet. As is observed in Fig. 28, the increase in the flow rate of gas flowing into the heat sink at exhaust pipe outlet leads to the increase in the output power of thermoelectric generator. As is evident, and in view of Eq. (1), this increased flow rate increases the amount of heat transfer, which causes the heat of the exhaust gases to be more effectively transferred to the hot surfaces of thermoelectric modules and thereby raises the temperature of the hot sides and increases the generated power of the thermoelectric generator. Fig. 29 shows the output power of the thermoelectric generator versus the flow rate of gas entering the heat sink installed on the cold side of thermoelectric module. As is observed in Fig. 29, with the increase in the flow rate of gas entering the heat sink installed on the cold side of thermoelectric module, the output power increases considerably. The reason is that the increase of flow rate increases the heat transfer from the cold surface of a thermoelectric module to the surrounding atmosphere and makes the surface cooler, thereby increasing the temperature difference between the hot and cold sides of the thermoelectric module; and this increase of temperature difference leads to more output power from the thermoelectric generator. Therefore, if liquids are used on the cold side of thermoelectric modules, the overall efficiency of a thermoelectric generator can be significantly increased; because by using liquids, a greater flow rate can be produced. Fig. 30 shows the output power versus heat conduction coefficient for the heat sink installed at exhaust pipe outlet. According to Fig. 30, as was expected, the heat conduction coefficient of the heat sink installed at exhaust pipe outlet has no significant impact on output power. Of course, the diagram in Fig. 29 relates to the heat conduction range of metals; which, at heat conduction coefficients of less than 100, the effect could be significant. So if a metal with a relatively good conduction is used in the making of heat sinks installed in a thermoelectric generator, even the heat conduction effect of the heat sinks can be ignored. The reason for the negligible influence of heat conduction is the small thickness (tb in Fig. 9) through which heat is transferred by conduction. In fact, the effect of conduction heat transfer is much less than that of convection heat transfer. Fig. 31 shows the behavior of output power with respect to the heat conduction coefficient of the heat sink installed on the cold surface of thermoelectric module. In view of Fig. 31 with the increase in the heat conduction coefficient of the heat sink installed on the cold side of thermoelectric module, the output power increases very slightly; and this is due to
635
Fig. 29. Output power versus the flow rate of gas entering the heat sink installed on the cold side of thermoelectric module.
Fig. 30. Output power versus heat conduction coefficient for the heat sink installed at exhaust pipe outlet.
Fig. 31. Output power versus heat conduction coefficient for the heat sink installed on the cold surface of thermoelectric module.
the same reasons mentioned for the heat sink installed at exhaust pipe outlet. 6. Conclusions
Fig. 28. Output power versus the flow rate of gas entering the heat sink installed at exhaust pipe outlet.
In this paper, first, a thermoelectric generator has been designed and modelled. By having the temperatures and the rates of flow into the heat sink installed at exhaust pipe outlet and the heat sinks installed on the cold side of thermoelectric modules as the equation inputs, the output power of the deigned generator has been computed. Moreover, an experimental prototype of the designed model has been manufactured in Section 4 and its output
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power has been measured against the input temperature difference between hot and cold sides. The theoretical and experimental values obtained in diagram form have been compared in Section 5. These comparisons show that the results agree with each other to a large extent, especially at temperatures lower than 100 °C. Considering the matching of these results, the effects of some important parameters on the output power of the considered thermoelectric generator are also investigated, and the significant influence of the thermal conduction coefficient of thermoelectric significant impact on output power and the heat conduction coefficient of the heat sink installed at exhaust pipe outlet and on the cold side of thermoelectric module has no significant impact on output power.
[11]
[12]
[13]
[14]
[15]
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