Theoretical and experimental estimation of limiting input heat flux for thermoelectric power generators with passive cooling

Available online at www.sciencedirect.com

ScienceDirect Solar Energy 111 (2015) 201–217 www.elsevier.com/locate/solener

Theoretical and experimental estimation of limiting input heat flux for thermoelectric power generators with passive cooling Ashwin Date a,⇑, Abhijit Date a, Chris Dixon a, Randeep Singh b, Aliakbar Akbarzadeh a a

Energy Conservation and Renewable Energy, School of Aerospace Mechanical and Manufacturing Engineering, RMIT University, Bundoora East Campus, Australia b Fujikura Ltd., Thermal Engineering Division, 1-5-1 Koto-Ku, Kiba, Tokyo, Japan Received 25 May 2014; received in revised form 27 October 2014; accepted 30 October 2014

Communicated by: Associate Editor Yanjun Dai

Abstract This paper focuses on theoretical and experimental analysis used to establish the limiting heat flux for passively cooled thermoelectric generators (TEG). 2 commercially available TEG’s further referred as type A and type B with different allowable hot side temperatures (150 °C and 250 °C respectively) were investigated in this research. The thermal resistance of TEG was experimentally verified against the manufacturer’s specifications and used for theoretical analysis in this paper. A theoretical model is presented to determine the maximum theoretical heat flux capacity of both the TEG’s. The conventional methods are used for cooling of TEG’s and actual limiting heat flux is experimentally established for various cold end cooling configurations namely bare plate, finned block and heat pipe with finned condenser. Experiments were performed on an indoor setup and outdoor setup to validate the results from the theoretical model. The outdoor test setup consist of a fresnel lens solar concentrator with manual two axis solar tracking system for varying the heat flux, whereas the indoor setup uses electric heating elements to vary the heat flux and a low speed wind tunnel blows the ambient air past the device to simulate the outdoor breezes. It was observed that bare plate cooling can achieve a maximum heat flux of 18,125 W/m2 for type A and 31,195 W/m2 for type B at ambient wind speed of 5 m/s while maintaining respective allowable temperature over the hot side of TEG’s. Fin geometry was optimised for the finned block cooling by using the fin length and fin gap optimisation model presented in this paper. It was observed that an optimum finned block cooling arrangement can reach a maximum heat flux of 26,067 W/m2 for type A and 52,251 W/m2 for type B TEG at ambient wind speed of 5 m/s of ambient wind speed. The heat pipe with finned condenser used for cooling can reach 40,375 W/m2 for type A TEG and 76,781 W/m2 for type B TEG. Ó 2014 Elsevier Ltd. All rights reserved.

Keywords: Limiting heat flux; Conventional heat sink; Thermoelectric generator; Passive heat sink

1. Introduction Thermoelectric devices can be used as heat pumps using the Peltier effect or as heat engines for power generation ⇑ Corresponding author at: Energy Conservation and Renewable Energy Group, School of Aerospace, Mechanical and Manufacturing Engineering, RMIT University, PO Box: 71, Bundoora East Campus, Bundoora, Victoria 3083, Australia. Tel.: +61 425 819 090; fax: +61 3 9925 6108. E-mail address: [email protected] (A. Date).

http://dx.doi.org/10.1016/j.solener.2014.10.043 0038-092X/Ó 2014 Elsevier Ltd. All rights reserved.

using the Seebeck effect (Rowe, 2006; Gurevich and Logvinov, 2005). Thermoelectric power generators (Seebeck effect) have recently attracted many researchers because of their static operation, environmentally friendly nature, high reliability and potential for generating electricity from lower grade heat sources (Simons et al., 2005; Wang et al., 2012). A thermoelectric generator is a static heat engine that generates voltage when a temperature difference is created across its hot side and cold side. In 1961, the National Aeronautics and Space Administration

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A. Date et al. / Solar Energy 111 (2015) 201–217

Nomenclature Symbols A c h h* H I k l q00 q_ R th T V v v_ w W_ x

2

area (m ) fin gap (m) convection heat transfer coefficient (W/m2 K) modified convection heat transfer coefficient (W/m2 K) direct incident solar radiation flux on the surface (W/m2) current (A) thermal conductivity (W/m K) length (m) heat flux (W/m2) total rate of heat flow (W) thermal resistance (°C/W) thickness (m) temperature (K) voltage (V) velocity (m/s) volume flow rate (m3/s) width of the fin (m) power generated (W) height (m)

Greek symbols e emissivity of target and base surface g efficiency

was the first organisation to use thermoelectric technology in a real application, to supply electrical power to a spacecraft (Ewert et al., 1998). However the use of thermoelectric generators in mainstream power generation is restricted due to its low conversion efficiency of thermal energy to electricity. Many researches around the world are working in the field of materials to improve the conversion efficiency (figure of merit) of TEG’s such that they can compete with conventional heat engines (Dresselhaus et al., 2007; Snyder and Toberer, 2008; Hsu et al., 2004; Poudel et al., 2008). At the same time there have been various studies about the use of thermoelectric generators for power generation using different heat sources and cooling techniques. Champier et al. (2011, 2010) has discussed the possibility of generating power using heat sourced from a biomass stove and a wood stove in his paper, while Meng et al. (2011) has investigated the effect of irreversibility’s on the performance of thermoelectric generators. Baranowski et al. (2012) and Li et al. (2010) have done a study on potential use of concentrated solar thermal systems to be incorporated with thermoelectrics for power generation with active cooling methods. Most commonly used techniques for solar concentration are parabolic

Dimensionless numbers GC geometric solar concentration N quantity Nu Nusselt number Pr Prandlt number Re Reynolds number Subscripts a aperture b base gap gap between all fins convtar convection from target convHS convection from heat sink fin fin hs heat sink in input lens fresnel lens lostt lost from target t target teg thermoelectric generator radHS radiation from heat sink radtar radiation from target 1 ambient Constants   r Stefan Boltzmann constant 5:67  108 mW2 K 4

trough & dish, Fresnel lens reflectors and solar power towers (Price et al., 2002; Kritchman et al., 1979). Heat collected from the concentrated solar radiation over the target area results in high temperature heat source used to drive a thermoelectric generator. Heat is rejected to a cold reservoir or a heat sink. By lowering the temperature of the heat sink the efficiency of the heat engine improves. Yazawa et al. (2012) has discussed the thermal challenges in such systems and proposed the small scale residential system in his research. Fan et al. (2011) has done some work on concentrated solar thermal (CST) systems to be combined with thermoelectric generators for energy production with active water cooling heat exchanger. Auxiliary energy consumption by a cooling mechanism in all these systems is a very important component since the conversion efficiency of a commercially available thermoelectric generators is below 5% (Riffat and Ma, 2003). A few researchers such as Singh et al. (2011) and He et al. (2012) have incorporated passive cooling methods for thermoelectric power generation, however they have chosen low heat flux energy sources such as solar ponds or evacuated tube solar collectors. Previously Date et al. (2011) has presented a theoretical model to determine the limit of solar concentration for

A. Date et al. / Solar Energy 111 (2015) 201–217 Table 1 Properties of two thermoelectric generators (type A and type B) under test in this research. Properties

Type A thermoelectric generator

Type B thermoelectric generator

Contact surface

Polished ceramic plate

Dimensions Maximum hot side temperature Thermal resistance Maximum open circuit voltage Maximum short circuit current Maximum power output Number of junctions

40 mm  40 mm  3 mm 150 °C

Graphite thermal interface coating 40 mm  40 mm  3 mm 250 °C

1.2 °C/W

1.0 °C/W

3 V for DT of 100 °C

4 V for DT of 200 °C

0.60 A

1.25 A

1.8 W

5W

127

127

thermoelectric generators under passive cooling conditions. This paper focuses on investigating and establishing the limiting heat flux for 2 commercial TEG’s using conventional passive cooling methods. The theoretical model presented by Date et al. (2011) is further modified to estimate the maximum theoretical limiting heat flux for commercial TEG’s with conventional passive cooling methods. Two commercial TEG’s were chosen for this research and their thermal properties were measured experimentally to verify the manufacturers specifications. Concentrated solar thermal energy source was used as a high heat flux source for outdoor experiments in this research since it is easily accessible. Outdoor experiments were supported by indoor experiments to have flexibility for extensive testing. Indoor experiments were conducted under simulated conditions of Melbourne, Australia where the outdoor experiments were conducted. Average annual ambient wind speed in Melbourne, Australia varies in between 0 m/s and 5 m/s which were simulated using the wind tunnel. The concentrated solar thermal energy source is simulated using electric heating elements. Table 1 illustrates the manufacturer specifications and thermal properties of two commercial thermoelectric generators used in this research. 2. Thermoelectric generator characterization This section describes the test setup and test procedures for characterization of the thermoelectric generators that are used in this research. Bismuth telluride TEG’s are used in this research with properties as given in Table 1. Fig. 1 illustrates the schematic of the test setup used to determine the thermal resistance and power generation capacity of the TEG. The TEG is sandwiched between the electric heater block and the micro channel water cooled cold plate. The electric resistance heater

Regulated water Supply

Variable voltage power supply

Cold Water in

203

Micro Channel fin cold plate TEG Resisve Electric Heater

Warm Water out Data acquision system/ Data logger Electric load

Voltage & Current meters

Fig. 1. Schematic of a thermoelectric generator characterization test rig.

was supplied with regulated power using a variable voltage regulator. Digital voltage and current meters were used to record the power input readings. Water flowing through the micro channel cold plate is regulated using a flow control valve and the volume flow rate of water was measured using a stop watch and a volume measuring flask. An electronic load was used to load the thermoelectric generator to determine their maximum power generation capacity. An Agilent data acquisition system 349,070 A is used for measuring and recording the temperatures, DC voltage and DC current generated from thermoelectric generator. Two TEG’s were investigated to determine the following properties: thermal resistance, maximum open circuit voltage and power generation capacity. These properties of the thermoelectric generators were determined experimentally for varying heat flux. Fig. 2 shows a picture of the actual thermoelectric generator characterization test setup. An electric heater is mounted on Bakelite plate to act as both an electric and thermal insulator. Two cartridge electric heaters were inserted in the copper block. Each cartridge heater has a power rating of 100 W. K type thermocouples were used to measure the temperature on the hot and the cold side of thermoelectric generators. Inlet and outlet temperatures of the cooling water passing through the micro channel heat exchanger were recorded. The thermocouples were glued inside the grooves on the upper surface of the copper heater block and the lower surface of the cold plate to record the hot side and cold side temperatures. The size of the copper heater block is 40 mm  40 mm which matches with the size of TEG’s used in this research. Fig. 3 illustrates all the components of the testing system used for characterization of the thermoelectric generator. Voltage and current from the variable voltage power supply connected to the heater cartridge is measured using a digital voltmeter and ammeter as shown in Fig. 3. Uncertainty analysis is done for all the experimental results using the error propagation method defined by Drosg (2009). Accuracies of the measuring devices used in this research are given in Table 2. Fig. 4 compares the maximum power output at different input heat fluxes for type A and type B thermoelectric generators. With limiting hot side temperature of 150 °C the type A thermoelectric generator can produce 2.15 W at a heat flux of 60 kW/m2. For 60 kW/m2 of heat flux the temperature difference between hot and cold side was 95 °C.

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3. Fin optimisation

Micro channel cold plate

Thermoelectric generator Electric heater

Fig. 2. Picture of thermoelectric generator sandwiched between the electric heater and micro channel cold plate.

The type B thermoelectric generator that has a limiting hot side temperature of 250 °C and produce 3.95 W for a heat flux of 110 kW/m2 and the temperature difference between hot and cold side of 195 °C. Fig. 5 shows thermal resistance of type A and type B thermoelectric generators with change in applied heat flux. As specified by the manufacturers, the thermal resistance of the thermoelectric generators stays fairly constant with variation in applied heat flux. For type B thermoelectric generator the thermal resistance varies between 1.007 and 1.03 °C/W over heat flux variation of approximately 15–60 kW/m2. Whereas for type A thermoelectric generator with limiting hot side temperature of 250 °C, the thermal resistance varies from 1.10 to 1.16 °C/W over heat flux variation of 14–110 kW/m2. Experimental values of thermal resistances matches closely with the manufacturer’s specification and hence values from Table 1 are used in the further section for theoretical analysis.

An extensive research has been already been done on optimisation of the fin length and fin spacing for heat exchanger under natural cooling and forced cooling conditions (Yaziciog˘lu and Yu¨ncu¨, 2007). This section focuses on finding the optimum fin length and fin gap (or in other words number of fins) for the proposed configuration of the cooling end of thermoelectric generators, whose heated end is subjected to concentred solar radiation. To determine the thermal resistance of the heat exchanger under consideration, it is necessary to know the base temperature of the heat exchanger. This base temperature can be determined by using the information about the TEG’s hot side limiting temperature, the thermal resistance of TEG and the heat flux applied across the TEG. Rhs ¼

1 hhs  ðAgap þ N fin  gfin  Afin Þ

ð1Þ

The thermal resistance of the heat exchanger is dependent on the convection heat transfer coefficient and fin arrangement. Heat exchanger optimisation involves choosing the optimum number of fins and fin gap for certain air velocity along the length of the fins. c¼

w  N fin  thfin N fin  1

ð2Þ

c is the fin gap, w is the width of the heat exchanger and tf is the fin thickness as shown in Fig. 6. Their relation is illustrated in Eq. (2). The exposed surface area Agap of the base plate as defined in Eq. (3) Agap ¼ ðN fin  1Þ  c  l

ð3Þ

Total surface area Afin of one fin including both the sides as defined in Eq. (4) and neglecting the tip Afin ¼ 2  xfin  l

ð4Þ

Velocity v of air flowing over the fins can be calculated from Eq. (5) with known volume flow rate v_ . Variable Voltage power supply

Voltage and current read out

Insulated heater and heat sink with sample thermoelectric generator sandwiched in between

v¼

v_ ðN fin  1Þ  c  xfin

ð5Þ

Teertstra’s equation (Teertstra et al., 1999) to estimate the Nusselt number for determination of convection heat transfer coefficient is being used here as shown in Eq. (6). 2 30:33 6 1 Nu ¼ 4 3 þ h RePr 2

1 7 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffii3 5 pffiffiffiffiffiffi 0:33 3:65 ffi 0:644 Re  Pr  1 þ pffiffiffi Re

ð6Þ

Eq. (7) is used to calculate the fin efficiency that affects the performance of the heat exchanger while m is defined in Eq. (8) Fig. 3. Picture of experimental setup with data acquisition system, variable voltage power supply, and insulated heater with cooling block and thermoelectric generator.

gfin ¼

tanhðm  xfin Þ m  xfin

ð7Þ

A. Date et al. / Solar Energy 111 (2015) 201–217

205

Table 2 Accuracies of instruments. Instrument

Parameter measured

Instrument precision

Digital multimeter (AC) Digital multimeter (AC) K-type thermocouple Agilent data logger (34,972 A) Agilent data logger (34,972 A)

Voltage Current Temperature DC voltage

±1% of reading ±1.5% of reading ±1% of reading ±0.5% of reading

DC current

±0.13% of reading

Type A and B thermoelectric generator 4.5 4

Liming hot side temperature type A = 150°C Liming hot side temperature type B = 250°C Ambient Temperature = 17°C

TEG Power W

3.5 3

Type B TEG 2.5 2

Fig. 6. Schematic of the finned heat exchanger illustrating the nomenclature used for various dimensions.

Type A TEG

1.5 1 0.5 0 0

20

40

60

80

100

120

Heat Flux kW/m2

Fig. 4. Power generated from type A and type B TEG for different input heat flux.

Thermal resistance of type A and B thermoelectric generator

2

Thermal Resistance (°C/W)

1.8

Liming hot side temperature type A = 150°C Liming hot side temperature type B = 250°C Ambient Temperature = 17°C

1.6 1.4

Type A TEG

1.2 1 Type B TEG 0.8 0.6 0.4 0.2 0 0

20

40

60

80

100

120

Heat Flux kW/m2

Fig. 5. Thermal resistance of type A and type B thermoelectric generator with respect to applied heat flux.

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2h m¼ k fin  thfin

ð8Þ

Thermal conductivity of the fin material is stated as kfin. In this case the fin material is considered to be aluminium with thermal conductivity of 180 W/m K. The maximum surface area available for attaching the heat exchanger on the cold side of thermoelectric generator is equal to the target area of the solar thermal concentrator.

Fig. 7 also illustrates the relationship between the variation of heat exchanger thermal resistance and the change in number of fins at different ambient wind velocities. It can be observed from Fig. 7 that, increasing the number of fins on the heat exchanger will reduce its thermal resistance. This is due to the increase in the surface area for heat transfer from the heat exchanger. The range of air velocity considered for optimisation of the heat exchanger is selected by referring to the local average ambient air speed throughout the year (data acquired from the Bureau of Meteorology, Australia). It is observed that the thermal resistance reduces steeply as the number of fins increases from 0 to 4 irrespective of ambient wind velocity. The thermal resistance undergoes less steep reduction between 4 and 8 numbers of fins for all the ambient velocities. Beyond 8 fins the thermal resistance for velocities 3–5 m/s does not change much. This is a manifestation of the hyperbolic relation 1 of Ra hA . It can be concluded from above observation that increasing the number of fins beyond 8 fins will have very little advantage on reduction of thermal resistance of heat exchanger for ambient wind velocities in the range of 3–5 m/s. Thus the optimum number of fins is fixed as 8 to be used for the further optimisation analysis in the next section. Fin length plays an important role as well in having an optimum design for the heat exchanger. Fig. 8 illustrates the effect of increase in the fin length on the thermal resistance of the heat exchanger at various ambient wind velocities. For 1–3 m/s of ambient wind velocity a significant reduction in thermal resistance with increase in the fin length is observed; however for ambient wind velocity of 4 m/s and 5 m/s the thermal reduces does not decrease with increasing in the fin length. For higher ambient wind velocities the convection heat transfer coefficient is large and results in low thermal resistance even for the smaller

A. Date et al. / Solar Energy 111 (2015) 201–217

fin length and does not reduce drastically even when the fin length is increased. But for the smaller ambient wind velocities, the thermal resistance is large for smaller fin length and drastically reduces as the fin length increases. It can be observed from Fig. 8 that thermal resistance is already very low for ambient wind velocities of 4 m/s and 5 m/s and does not reduce much further with increasing fin length. The effect of fin length on the heat exchanger thermal resistance at low ambient wind velocities has a dominant effect on choosing the optimum fin length of the heat exchanger. It can be observed from Fig. 8 that the thermal resistance does not reduce drastically beyond the fin length of 0.1 m for any ambient wind velocity. For subsequent analysis fin length of the finned heat exchanger is varied from 0.06 m to 0.1 m for the purpose of this research. 4. Theoretical analysis Indoor testing facility was set-up to experimentally determine the limiting heat flux for type A and B TEG’s with conventional heat exchangers while maintaining the respective hot side temperature within the allowable limit. Solar heat flux is simulated in the indoor test setup by embedding the resistive heating elements inside the 100 mm long, 100 mm wide and 20 mm thick aluminium block attached to the hot side of the thermoelectric generator. This aluminium block is placed on the target plate and the cold side of the generator is covered with a 10 mm thick aluminium base plate. The amount of energy received by the heater plate is given by q_ in ¼ V  I ¼ Aa  H

ð9Þ

Heat sink Thermal Resistance °C/W

In this equation, V is the voltage supplied to the heating elements and I is the current flowing through them. In case of an actual solar concentrator the total energy received by the target plate is also expressed as product of aperture area Aa and direct incident solar radiation H. Fig. 9a and b illustrates the schematic of Fresnel lens solar concentrator and the detailed heat distribution in the whole system, 8

1.8

Heat sink Thermal Resistance °C/W

206

1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Fin Length (m) Velocity 1m/sec Velocity 4m/sec

Velocity 2m/sec Velocity 5m/sec

Velocity 3m/sec

Fig. 8. Effect of fin length on the thermal resistance of the heat exchanger for 8 numbers of fins at various air speeds.

treating the TEG as a thermal resistance for which heat in = heat out. This simplification is justified by the fact that currently for TEG’s the electric power output is very small compared to the input and output heat quantities. The geometric solar concentration can be calculated for outdoor Fresnel lens setup as follows GC ¼

Aa At

ð10Þ

Total energy supplied to the target plate will be equal to heat lost from target plate plus power extracted from thermoelectric generator plus heat dissipated from cold end of the TEG. Energy balance equation for such setup is given as q_ in ¼ q_ lostt þ q_ teg þ W_ TEG

ð11Þ

Since the conversion efficiency of TEG is less than 5%, power output W_ TEG from TEG is small and is neglected in the energy balance equation. q_ in ¼ q_ lostt þ q_ TEG

ð12Þ

Energy loss at the target plate will be via convection and radiation heat transfer to the ambient air. q_ lostt ¼ q_ convtar þ q_ radtar

ð13Þ

7

Energy lost due to convection is expressed as follows.

6

q_ convtar ¼ ht  At  ðT t  T 1 Þ

5

ð14Þ

4 3 2 1 0 0

4

8

12

16

20

24

28

32

Number of Fins Velocity 1m/sec Velocity 4m/sec

Velocity 2m/sec Velocity 5m/sec

Velocity 3m/sec

Fig. 7. Effect of number of fins on the thermal resistance of the fin heat exchanger at various air speeds.

Convection heat transfer coefficient ht is calculated using the heat transfer correlations. Energy loss due to radiation heat transfer from the target plate to the ambient air is expressed as follows. Here author would like to acknowledge that using the selective surface on the target area would improve the solar absorptance and would also reduce the amount of heat lost due to radiation at elevated temperatures.   ð15Þ q_ radtar ¼ r  e  At  T 4t  T 41

A. Date et al. / Solar Energy 111 (2015) 201–217

207

Incident Solar Radiation

a

Heat lost from top surface of target

Fresnel lens solar concentrator

Target Area Heat sink

b

Thermoelectric Generator

Thermoelectric generator

Heat conducted by Thermoelectric generator

c

RTEG

RTEG

RTEG

Rrad-tar

RTEG

Heat input to Thermoelectric generator

Rconv-tar

Thermoelectric Generator

Rconv-HS

Rrad-HS Heat sink Heat dissipated by Heat sink

Fig. 9. (a) Schematic of the Fresnel lens solar concentrator with finned heat exchanger. (b) Detailed description of heat distribution at target plate, thermoelectric generator and heat exchanger. (c) Equivalent thermal resistance circuit.

Here, r is Stefan Boltzmann constant and e is the surface emissivity. Rate of heat transfer through each thermoelectric generator is given by Eq. (16). q_ teg ¼

Tt  Tb Rteg

ð16Þ

Rteg is the thermal resistance offered by the thermoelectric generator, value of thermal resistance of TEG is provided by the manufacturer and experimentally verified in this research. Heat transfer gel is used to improve the heat transfer between the heater, TEG and base plate. The contact interface resistance is very small and is neglected for the purpose of theoretical analysis. Heat dissipated by the unfinned base plate via convection and radiation is stated in Eq. (17) where Ab is the base area and hb is the combined convection and radiation heat transfer coefficient calculated using the heat transfer correlations for corresponding geometry, temperatures and flow types (Incropera, 2007).   ð17Þ q_ base ¼ hb  Ab  ðT b  T 1 Þ þ r  e  Ab  T 4b  T 41 Similarly for the finned heat exchanger, heat will be dissipated from the fin surface by convection and radiation but since the fins are closely placed next to each other, the radiation from the fin surface will be a smaller part. Once again convection and radiation are being combined in a single heat transfer coefficient. A similar heat transfer model is used for heat pipe heat sink cooling by considering the thermal resistance of each heat pipe being 0.35 °C/W as provided by the heat pipe heat sink manufacturers. q_ fin ¼ hfin  Afin  ðT b  T 1 Þ

ð18Þ

Theoretical results of limiting heat flux for type A and type B thermoelectric generator are illustrated in Fig. 10. The maximum hot side temperature is 150 °C and 250 °C for type A and type B TEG’s respectively and the ambient temperature is assumed to be 18 °C with ambient wind velocity varying between 0 m/s to 5 m/s. Theoretical limiting heat flux for type A and type B thermoelectric generators is established for various configurations of cooling heat exchanger including bare plate heat exchanger and finned heat exchanger. Fin lengths for the finned heat exchanger are varied taking into account the heat exchanger optimisation as discussed in earlier section. It is observed that there is a considerable improvement in the limiting heat flux when the bare plate is replaced with a 60 mm finned block for both the TEG’s. It is observed that the limiting heat flux further enhances by 12% when the fin length is increased from 60 mm to 80 mm, however it only increases by 7% when fin length is increased from 80 mm to 100 mm at lower velocities. At higher velocities the improvement is even lower and drops to 5% for increase in fin length from 80 mm to 100 mm. This trend is similar for the type B thermoelectric generators as well. 4.1. Maximum theoretical limiting heat flux A maximum theoretical limiting heat flux analysis for both the TEG’s is presented in this section. The theoretical model is presented where the hot side temperature is limited to 150 °C and 250 °C for type A and type B TEG’s respectively. To estimate the theoretical limit of the heat input flux, the cooling method is not restricted to passive cooling and heat transfer coefficient and heat exchangers surface area are increased from zero to infinity, that is

A. Date et al. / Solar Energy 111 (2015) 201–217

(a)

Limiting Heat Flux (kW/m2)

80

Maximum hot side liming temperature = 150°C Direct incedent solar radiaon = 900 W/m2 Ambient Temperature = 18°C

70

90 80 70

60

60 50 50 40

40

30

30

20

20

10

10 0

0 0

1

2

3

4

5

Number of Suns (Solar concentration)

Type A: thermoelectic generator -Theoretical results 90

6

Similarly by combining Eqs. (9)–(19) and solving for the maximum theoretical limiting input heat of q_ in q_ in ¼ h

i ðT t  T 1 Þ þ ht  At ðT t  T 1 Þ þ hb1Ab   þ reAt T 4t  T 41

100 mm Fin

Heat pipe

Rteg Ab 4

Limiting Heat Flux (kW/m2)

80

90 80

70

70

60

60 50 50 40

40

30

30

20

20

Maximum hot side liming temperature = 250°C Direct incedent solar radiaon = 900 W/m2 Ambient Temperature = 18°C

10 0 0

1

2

3

4

10 0 5

Number of Suns (Solar concentration)

(b)

6

Wind Velocity (m/sec) 60 mm Fin

80 mm Fin

100 mm Fin

Heat pipe

þ h1b

i ðT t  T 1 Þ þ ht ðT t  T 1 Þ

  þ re T 4t  T 41

Bare plate

Type B: thermoelectic generator -Theoretical results 90

1

H ¼h

Bare plate

Fig. 10. (a) Theoretical results of limiting heat flux for type A thermoelectric generators [solar flux (W/m2) vs. velocity (m/s), hot side temperature = 150 °C ambient temp: 18 °C, velocity of air range from 0 m/s to 5 m/s]. (b) Theoretical results of limiting heat flux for type B thermoelectric generators [solar flux (W/m2) vs. velocity (m/s), hot side temperature = 250 °C ambient temp: 18 °C, velocity of air range from 0 m/s to 5 m/s].

the resistance between the cold bases and ambient in the limit is zero. Total heat reaching the surface of the target plate in case of an outdoor solar concentrating system is the product of incident direct solar heat flux radiation and target area as mentioned in Eq. (12). Some of this heat is lost to the surroundings by convection and radiation as per Eqs. (14) and (15). Neglecting the small work output from TEG, the remaining heat passes through the thermoelectric generators attached to the target plate and finally through the base plate and heat exchanger to be dissipated to ambient air. The target area of the test setup is such that 4 thermoelectric generators can be accommodated for each test. The individual thermal resistance of each thermoelectric generator is known and all 4 thermoelectric generators are connected in a parallel thermal circuit. Total heat flowing through these 4 thermoelectric generators is stated as

ð21Þ

Thermal resistance of the TEG’s are known from the earlier section. Fig. 11 shows the maximum allowable heat flux curve with respect to the change in modified convection heat transfer coefficient. Modified convection heat transfer coefficient is a product of convection heat transfer coefficient and a ratio of total heat transfer surface area to the cold side surface area of the TEG h ¼ hb 

Atotal

HT surface

ð22Þ

Ateg

It is observed that the maximum allowable heat flux increases as the convection heat transfer coefficient increases although the slope of this curve starts to reduce and eventually will reach the maximum limit. Fig. 11 illustrates the maximum possible limiting heat flux for two thermoelectric generators under test. Term modified convection heat transfer coefficient hb used in this analysis represents the enhancement in the cooling methods used on the cold side of the thermoelectric generators to allow more heat dissipation. It can be seen from above figure that there is steep rise in the allowable heat flux while the required convection heat transfer coefficient increases from 0 to 6000 W/m2 K. From 0 to 1000 W/m2 K the slope of the limiting heat flux curve reduces and then flattens with further increase in required convection heat transfer coefficient. The approximate value of maximum allowable Maximum Allowable Heat Flux (kW/m2)

80 mm Fin

ð20Þ

This can be expressed in terms of incident solar radiation as follows.

Wind Velocity (m/sec) 60 mm Fin

1

Rteg 4

120 120 109 kW/m2

100

Type B TEG Maximum hot side temperature = 250°C

80

68 kW/m2

100 80

60 Type A TEG Maximum hot side temperature = 150 °C

40

60 40

20

20

Direct incedent solar radiaon = 900 W/m2 Ambient Temperature = 16°C

0

0 0

1000

2000

3000

4000

5000

Number of Suns (Solar Concentration)

208

6000

Modified heat transfer coefficient (hb) W/m2.K

q_ teg ¼

Tt  Tb Rteg 4

ð19Þ

Fig. 11. Maximum allowable heat flux for type A and type B thermoelectric generator with limiting hot side temperature of 150 °C and 250 °C respectively.

A. Date et al. / Solar Energy 111 (2015) 201–217

209

heat flux of type A thermoelectric generator is 68,000 W/ m2 while that for type B thermoelectric generator is 109,000 W/m2.

Wind tunnel speed controller

Wind tunnel

5. Experimental results and discussion Outdoor and indoor experimental test setups were designed and built at RMIT university research facility to assist in testing of thermoelectric generator with variable heat flux input and different conventional passive heat exchangers. The outdoor experimental setup consisted of a manual dual solar tracking system with a Fresnel lens solar concentrator. Indoor test setup consisted of an electric heater for simulating solar concentration and wind tunnel for simulating the ambient wind condition. 5.1. Indoor experimental setup and results Fig. 12 shows a schematic diagram of the indoor testing setup used for testing thermoelectric generators to determine their limiting heat flux. As mentioned earlier solar concentration was simulated using resistive electric heating elements embedded in the aluminium heater block for the indoor test setup. The heater block and its design are explained in the further section. A variable voltage transformer was used to control the power input to the heater block. A digital voltmeter and ammeter were used to measure voltage and current input to the heater block. The test setup with solar concentration simulator and heat exchanger is placed inside the previously mentioned wind tunnel. The speed of air inside the wind tunnel is controlled using the fan speed controller. A Pitot tube was inserted inside the wind tunnel with total pressure and static pressure tappings that were connected to an inclined manometer to measure the dynamic pressure of air inside the wind tunnel from which the velocity may be deduced. A hand held anemometer was also used to validate the air velocity in the indoor setup. A data acquisition system was configured with a computer to measure and record different parameters such as temperature, voltage and current from the test setup. Fig. 13 illustrates the complete indoor testing setup being placed inside the wind tunnel. A data taker was used Stac pressure connecon

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to monitor and record the hot and cold side temperature and open circuit voltage readings of thermoelectric generator. A voltage transformer was used to vary the input power to the electric heating elements. A speed controller was used to vary and control the wind velocity flowing through the wind tunnel. Fig. 14 shows the actual test setup to simulate the solar concentration using the electric heating elements. A 100 mm long, 100 mm wide and 20 mm thick aluminium plate was used as the heat target/spreader plate for the indoor test setup. Two resistive heating elements were inserted in the target plate as a heat source in the setup. A 80 mm long, 80 mm wide and 2 mm deep slot is machined on the top of the target plate to mount 4 TEG’s (each 40 mm long, 40 mm wide and 3 mm thick). Silicon based thermal conducting compound with thermal conductivity of 3.6 W/m K was used to reduce the contact resistance between the target plate and the thermoelectric generators. K type thermocouples were used measure the temperature of hot and cold side of TEG’s. Fig. 15 a shows the bare base plate placed over the thermoelectric generators for heat spreading and dissipation. Fig. 15b shows the fins attached over the base plate for increasing the surface area which will increase the total heat transfer rate over the cold side of thermoelectric generator. The heat transfer rate was further enhanced by using the heat pipe heat exchanger over the cold side of thermoelectric generator as shown in Fig. 15c. Fig. 16 shows three different fin length heat exchangers that are used for this research to determine the limiting heat flux for type A and type B thermoelectric generator. The surface area of the base plate is 100 cm2 which can occupy 4 thermoelectric generators that are 40 mm long and 40 mm wide (i.e. 16 cm2). The base plate is added with the extended vertical fins to enhance the heat transfer which will allow us to reach higher solar heat flux while maintaining the temperature of the hot side of the thermoelectric generator within its working limit. Three different fin length configurations have been examined in this research. All the three configurations have 8 fins that are separated by 10 mm from each other. The first configuration has fin length of 60 mm from the base plate with a

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0.18 m2 which is 3 times greater than that for a simple finned heat exchanger attached directly to target area as illustrated in Fig. 16. Experimental limiting heat flux for bare plate, 60 mm fin, 80 mm fin and 100 mm fin heat exchanger for type A and type B thermoelectric generator is compared with the theoretical predictions of the heat flux limit at various air speeds representing local ambient wind speed in Fig. 17 below. The limiting heat flux is based on the maximum hot temperature that a thermoelectric generator can handle. Theoretical estimation using heat transfer correlations (Incropera, 2007) predict that the allowable heat flux for type A thermoelectric generator with bare plate heat exchanger and natural convection cooling will be 5500 W/m2 and can reach up to 17,000 W/m2 for wind speed of 5 m/s. Experimentally it is observed that the allowable heat flux for bare plate heat exchanger is 4000 W/m2 under natural convection condition and can reach up to 16,300 W/m2 for wind speed of 5 m/s. Predicted allowable heat fluxes for 60 mm, 80 mm and 100 mm fin connected to base plate of type A under natural

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Fig. 14. Indoor resistive heating solar concentrator simulator with thermoelectric generators mounted on the target plate.

total surface area of 768 cm2. The second configuration has fins length of 80 mm from the base plate with a total surface area of 1024 cm2. And the last fin has fin length of 100 mm from the base plate having a total surface area of 1280 cm2. An off the shelf heat pipe heat exchanger (shown in Fig. 15c) that is commonly used for electronics cooling is chosen for cooling of thermoelectric generator in this research. The heat exchanger has 4 U-shaped heat pipes with diameter of 6 mm and total length of 200 mm. Heat pipes at the base of U shape are flattened and attached to an aluminium heat spreader to allow maximum surface contact with the heat source. The U-shape helps to attach fins across all the heat pipes together. The 4 U-shaped heat pipes are partially flattened at the evaporator and have 36 fins along the vertical length which acts as the condenser for dissipating heat. Each fin is 100 mm in length and 50 mm in width and separated from each other with a distance of 4 mm. These fins are placed closely in the heat exchanger since it is designed to be used for processor cooling and is restricted by small space inside the desktop computer. The overall surface area of the heat pipe condenser is

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convection cooling are 10,700 W/m2, 11,400 W/m2 and 13,900 W/m2 respectively. Experimental results show that under similar conditions the allowable heat fluxes will be 8100 W/m2, 9700 W/m2 and 10,600 W/m2 for 60 mm, 80 mm and 100 mm fin respectively. Similarly at the maximum wind speed of 5 m/s heat transfer correlations predict that allowable heat fluxes for 60 mm, 80 mm and 100 mm fin connected to base plate under natural convection cooling are 22,200 W/m2, 23,700 W/m2 and 25,600 W/m2 respectively. While experimental results show that under similar conditions the allowable heat fluxes will be 21,400 W/m2, 22,100 W/m2 and 23,400 W/m2 for 60 mm, 80 mm and 100 mm fin respectively. Fig. 17 also compares the estimated and measured limiting heat flux for type B thermoelectric generator at various wind speeds. It is observed that for type B thermoelectric generators the allowable heat flux for bare plate heat exchanger is 8300 W/m2 under natural convection condition and can reach up to 30,000 W/m2 for wind speed of 5 m/s. While the allowable heat fluxes will be 15,300 W/m2, 18,100 W/m2 and 19,500 W/m2 for 60 mm, 80 mm and 100 mm fin respectively with natural convection cooling and can reach 48,900 W/m2, 50,300 W/m2 and 52,200 W/m2 for the wind speed of 5 m/s for 60 mm, 80 mm and 100 mm fin heat exchanger respectively.

Initial experiments for cooling using this heat pipes were performed under air velocity of 0 m/s or in other words under natural convection cooling conditions. It was observed that the cold side temperature of the thermoelectric generator was maintained at lower value than that was achieved while using the bare plate or simple finned heat exchanger. However contrary to what might be expected the limiting heat flux value was also lower than that achieved with the other heat exchanger configurations. The reason for limiting heat flux did not have any improvement under natural convection condition can be attributed to the smaller fin gap that restricts convection heat transfer which is dominant at lower temperature. Due to this reason it was decided that for further testing the heat pipe heat exchanger will be tested under air velocity ranging from 1 m/s to 5 m/s. Fig. 18 shows the comparison between theoretical and experimental results for limiting heat flux of type A thermoelectric generator cooled by the heat pipe with finned condenser. Good agreement between theoretical and experimental results is observed in the above figure. Experimental results show that at 1 m/s air velocity the heat pipe with finned condenser has limiting heat flux for type A thermoelectric generator is 32.7 kW/m2. Limiting heat flux increases to 40.3 kW/m2 as the air velocity increases and

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Fig. 17. (a) Comparison between calculated and experimental values for maximum allowable heat flux for type A and type B thermoelectric generators for bare plate heat exchanger at wind speed ranging from 0 m/s to 5 m/s. (b) Comparison between calculated and experimental values for maximum allowable heat flux for type A and type B thermoelectric generator for 60 mm fins heat exchanger at wind speed ranging from 0 m/s to 5 m/s. (c) Comparison between calculated and experimental values for maximum allowable heat flux for type A and type B thermoelectric generators for 80 mm fins heat exchanger at wind speed ranging from 0 m/s to 5 m/s. (d) Comparison between calculated and experimental values for maximum allowable heat flux for type A and type B thermoelectric generators for 100 mm fins heat exchanger at wind speed ranging from 0 m/s to 5 m/s.

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reaches 5 m/s of air velocity which is 23% improvement from limiting heat flux at air velocity of 1 m/s. Fig. 19a shows the comparison between the limiting heat flux for type A thermoelectric generator cooled with a bare plate, finned heat block (60 mm length fin, 80 mm length fin, 100 mm length fin) and heat pipe with finned condenser. It is evident from Fig. 19 that the limiting heat flux for type A thermoelectric generator increases in achievable heat flux from when cooled with bare plate to finned block and further increases as we move on to being cooled by heat pipe with finned condenser. Limiting heat flux at air velocity of 0 m/s with bare plate heat exchanger is 4 kW/m2. However for finned block with 60 mm fin length, the limiting heat flux increases by 100% to 8 kW/ m2. Further increasing the length of the fins to 80 mm shows the increase in the limiting heat flux for type A thermoelectric generator by 25% to 10 kW/m2. Rise in the limiting heat flux with increase in the length of the fin length goes on, but with diminishing returns with increase in fin length and for fin length of 100 mm the improvement is only 6% going to 10.6 kW/m2. The limiting heat flux for the type A thermoelectric generator at an air velocity of 1 m/s with bare plate heat is 8.8 kW/m2, for finned block with 60 mm fin length is 13 kW/m2, for 80 mm long fin is 14.2 kW/m2 and that for 100 mm long fin is 14.7 kW/m2. A similar trend of diminishing improvement of limiting heat flux is seen. At 1 m/s the limiting heat flux with heat pipe with finned condenser is 32.7 kW/m2 which is 2.17 times more than that for finned block with 100 mm fin length. A similar trend is seen over the whole range of variation in air velocity for type A thermoelectric generator. At 5 m/s air velocity the limiting heat flux for bare plate is observed to be 16 kW/m2 that for finned block of 100 fin length is 23.4 kW/m2 while that for heat pipe with finned condenser is 40.3 kW/m2. There is a significant rise in the limiting heat flux for heat pipe heat sink. This significant rise in the limiting heat flux can be attributed to following factors. As compared to solid copper or aluminium, heat pipes

have very high thermal conductivity and hence the rate of heat transfer is enhanced. Heat pipes provide lower thermal resistance for the flow of heat as compared to the finned aluminium heat sink. Heat pipe allows us to efficiently carry the heat away from the target area and hence allows us to have longer condenser length. This increases the number of fins that can be attached for cooling which increases the surface area available for heat transfer. Considering that there is no significant improvement in the heat transfer by increasing the fin length beyond 100 mm, it can be said that the limiting heat flux for type A thermoelectric generator with finned block is 23,400 W/m2 at air velocity of 5 m/s while that for heat pipe with finned condenser is 40,300 W/m2. Limiting heat flux can be expressed in terms of limiting number of suns when subjected to actual solar concentrator as seen on the secondary Y-axis considering the direct solar radiation over the aperture of solar concentrator to be 900 W/m2. Similar to the earlier comparison, Fig. 19b shows the comparison between the limiting heat fluxes for type B thermoelectric generator with bare plate, 60 mm length fin, 80 mm length fin and 100 mm length fin for velocity varying from 0 m/s to 5 m/s. Limiting heat flux for bare plate with air velocity of 0 m/s is 9250 W/m2, while that for 5 m/s air velocity is 34,600 W/m2. An improvement of 65% is seen in the limiting heat flux from bare plate to 60 mm finned block at 0 m/s air velocity reaching 15,350 W/m2. However for 5 m/s air velocity the improvement is only 41% from bare plate to 60 mm length finned block reaching 48,900 W/m2. Thereafter a similar trend is seen in improvement of limiting heat flux was observed that seen with the type A thermoelectric generator. Very insignificant improvement is seen with increase in length of fin from 60 mm to 80 mm and further to 100 mm. Maximum limiting heat flux for the type B thermoelectric generator with 100 mm length fin and 5 m/s air velocity is 52,000 W/m2 which is equivalent to 58 suns solar concentration under the constant direct solar of 900 W/m2 over the solar concentrator surface. Fig. 20a and b shows the experimental results for electric power generation from type A and type B thermoelectric generators under test in this research. Similar behaviour of power output is observed for type A and type B thermoelectric generators. Drastic rise in power generation capacity can be observed when changing cooling from bare plate to having 60 mm finned block, which further increases, but slightly as the fin length is increased from 60 mm to 80 mm and further to 100 mm. With natural convection over the bare plate (0 m/s air velocity) type B thermoelectric generator produce 0.02 W, however that increases to 0.2 W showing improvement of more than 10 times when cooling is changed to the 60 mm finned block. It is observed that the increase in the power generation for type B thermoelectric generator from bare plate to 60 mm fin heat exchanger is better than that for type A thermoelectric generator. This is because the limiting temperature of the type B thermoelectric generator is 100 °C higher than that for the type

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A thermoelectric generator. Higher hot side temperature means higher temperature difference between the hot and cold side of type B thermoelectric generator and thus a more effective heat engine. Further increasing the fin length to 80 mm the power generation from type B thermoelectric generator rises to 0.25 W which is just 1.25 times greater. For 100 mm finned block power output from type B thermoelectric generator increases only by 1.12 times to 0.28 W. Increase in the air velocity gradual raises the maximum power produced by each type B thermoelectric generator. Type B thermoelectric generator with bare plate produces maximum power of 0.25 W at air speed of 5 m/s. At the same air velocity and 60 mm fin heat power production of type B thermoelectric generator is increased by 3.36 times to 0.84 W. However further increasing the fin length to 80 mm improves the power production of type B thermoelectric generator only by 1.09 times to 0.92 W. Maximum power output from type A thermoelectric generator with 100 mm fin length at heat flux of 52.2 kW/m2 and 5 m/s air velocity is 0.98 W which is only 1.06 times that with 80 mm fin length.

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Fig. 22. Variation of solar concentration for outdoor test rig.

focal length of the target area is variable to adjust to the solar concentration. As shown in Fig. 22, the Fresnel lens solar concentrator used for the outdoor testing rig has a fixed surface area of 1.4 m2 with 1350 mm length and 1040 mm width. Hence a simple way was devised to change the aperture area of the Fresnel lens on the outdoor testing rig such that the amount of incident solar radiation reaching the target area could be varied. Thin concentric sheets of plywood were cut to the shape of Fresnel lens as shown in Fig. 22 to vary the heat flux reaching the target. Outdoor experiments were conducted in natural wind conditions and hence only single data points were collected for each heat exchanger configuration and the actual

outdoor wind velocity was measured using a handheld anemometer across the heat exchanger at the target. Fig. 23a shows the comparison between the indoor and outdoor results for type A and type B thermoelectric generator with the bare plate. While testing the type A thermoelectric generator the average ambient wind speed was measured to be 3.5 m/s. Heat flux at the target was calculated by measuring the surface area of Fresnel lens that is open to the direct solar radiation and measuring the direct incident solar radiation over the Fresnel lens surface. Outdoor results are found to have a very good agreement with the indoor measurements. Outdoor measurements suggest that the limiting heat flux for the type A thermoelectric generator at 3.5 m/s of air velocity is 14.2 kW/m2, while limiting heat

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with 60 mm fin length for type A thermoelectric generator is 14.1 kW/m2, while that for type B is 23.6 kW/m2 and that for type A and type B thermoelectric generator with 80 mm length fin 15.2 kW/m2 and 27.2 kW/m2 respectively and with 100 mm fin length for type A and type B thermoelectric generator is 16.4 kW/m2 and 36.8 kW/m2 respectively. Fig. 24 shows the comparison between indoor and outdoor measurements for limiting heat flux for type A and type B thermoelectric generator cooled with the heat pipe with finned condenser. Outdoor limiting heat fluxes for type A and type B thermoelectric generators are measured as 32.8 kW/m2 and 60.6 kW/m2 respectively.

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flux for type B thermoelectric generator at 1 m/s measured ambient air velocity is 15.1 kW/m2. Fig. 23b–d also shows the comparison between indoor and outdoor limiting heat flux for type A and type B with 60 mm, 80 mm and 100 mm length fin heat exchanger respectively. All the fin configurations have shown a good agreement between indoor and outdoor experimental results. The limiting heat flux with outdoor measurements

6. Conclusion The comparison between the thermal performances of two commercially available thermoelectric generators is presented in this paper with their cold sides cooled by either bare plate, 60 mm fin, 80 mm fin and 100 mm fin or heat pipe heat exchanger at wind speed ranging from 0 m/s to 5 m/s for. Maximum allowable heat flux that can be reached keeping the hot side temperature to the maximum permitted operating level for type A and type B thermoelectric generators is also explained in this paper. This allowable heat flux is separately determined for wind velocity of 0–5 m/s and for different heat exchanger configurations.

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Type A thermoelectric generator can reach a maximum of 16,300 W/m2 for bare plate heat exchanger and 5 m/s velocity and generate 0.1 W power. With 100 mm finned heat exchanger it can reach 23,400 W/m2 at 5 m/s air velocity and produce 0.53 W power. The type A thermoelectric generator is restricted to its permissible hot side temperature of 150 °C. Type B thermoelectric generator shows higher allowable heat flux than type A thermoelectric generator since its permissible hot side temperature is 250 °C. At wind speed of 5 m/s and bare plate heat exchanger type B thermoelectric generator’s allowable heat flux reaches 31,100 W/m2 and produce 0.25 W of electric power. Allowable heat flux increases to 52,200 W/m2 for 100 mm finned heat exchanger at wind speeds of 5 m/s and produce 0.98 W electric power. It can also be concluded from the optimisation of the cooling heat exchanger, and experimental analysis of limiting heat flux and power generation from type A and type B thermoelectric generators, that having fins on the heat exchanger has a drastic effect on the power production capacity of the thermoelectric generators. However increasing the fin length from 60 mm to 100 mm does not have as much effect on the cooling capacity of the heat exchanger and similarly does not have as much effect on power generation capacity from thermoelectric generators and their allowable heat flux limits as changing from bare plate to .mm long fins. Thus it is suggested that 100 mm fin length would be the useful limit to the size of the fins, beyond which further increase in fin length is unlikely to be economic. This research establishes the limits of heat flux for commercially available thermoelectric generators and presents their power generation capacity over a range of wind speeds representing common local ambient wind conditions. This critical information about the limiting heat flux provides a helpful insight on the use of these thermoelectric generators under solar concentration and can provide information on the limiting number of suns that these individual generator can withstand while still being operational. This information can also be used for combining the thermoelectric generators with waste heat recovery systems and designing the cooling system and designing the stand alone power generation systems. Finally this research shows the great potential of thermoelectric generators to be combined either with concentrated solar thermal systems, industrial heat recovery systems or any other available heat source together with passively cooling to become a feasible technology for medium to large scale power generation with the attraction of minimal moving parts. However basic TEG’s need to become more efficient if they are to replace the use fossil fuels fired systems for power generation to a large extent. References Baranowski, L.L., Snyder, G.J., Toberer, E.S., 2012. Concentrated solar thermoelectric generators. Energy Environ. Sci. 5 (10), 9055–9067.

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