ETJOURNALOFENGINEERING&TECHNOLOGY

Autumn 2010coNcoLO,0)NNNZC/)C/)ANALYSIS OF

THERMOELECTRIC GENERATORSWITH INTERNAL

IRREVERSIBILITIESS. Sharma I

Abstract

Abstract- The thermoelectric generators available

in our country are of lower wattage and cannot be

used commercially for electrical power generation.

In this work, a model of thermoelectric generator is

analyzed. The entropy generation method is used

to calculate the second law efficiency. Entropy

generation, power and efficiency with respect to

current are also studied and analyzed.

'Department of Mechanical EngineeringNI.E.T., Gr. Noidasudhanshu.shr@gmail.com

'Department of Mechanical EngineeringAmity University, Noida

P.K.s. Nain2

Introduction

The use of Peltier and Seebeck effect in

thermocouples to produce refrigeration and electricpower generation is well known. In recent years theimproved performance available through the use ofsemiconductors rather than the metals in suchthermocouples has been recognized. The response ofthe device when it is used as a Seebeck effect heatengine and as a Peltier effect heat pump was investigatedby Gupta et. al. (1984)[1].

The formulation and analysis of thermoelectricgenerators in many texts neglect the external and internalirreversibilities, assuming the generator is exoreversible[2,3].

The thermoelectric generator describes a system inwhich two dissimilar materials are joined electrically andthermally for the purpose of producing power output.These will be preferred as a power source due to theirsmall size, simplicity, quietness and reliability.

From the second law of thermodynamics it can be shownthat no system can ever be 100% efficient. Whencalculating the energy efficiency of a system, the figurefound gives no indication of how the system compares toa thermodynamically perfect one operating under thesame conditions. In comparison, the rational efficiency ofa system can reach 100% because the work output iscompared to the potential ofthe inputto do work.

Theoretical Modeling

The thermoelectric generator can be modeledthermodynamically as a cyclic, irreversible heat enginekvl~""[4]. This system contains two nand p type •..•..•L.L..:;lLJ

semiconductor legs and hot and cold junctions.The heat source and the heat sink reservoirs areshown in fig 1. The thermoelectric generatorrepresents a typical example of an inherentlyirreversible, direct energy conversion device andentails interesting electrical as well as thermalphenomena.

(i)Efficiency of an internally irreversible model

I II~,,

_________ L _,,,,,

o.si- ~ cxITH,

\l------7-~powerJ

o .si- i

I

,,,,,,,---------,---- ----------,

2

I TCI

Fig 1. Schematic diagram of thermoelectricgenerator

The generator is modeled as internallyirreversible. The heat transfer to the generatorQH and heat rejected QC are:

QH = aITH + K(TH Te) 0.512 R (1)

(2)

The Joule heat has been split evenly between thetwo sides ofthe generator.

Work output

W = QH Qe= aI(TH Te) /2R

TeWy = QH(l T)

H

(3)

(4)

The entropy generation is, as usualn Q

Sgen= -L -j=1 T

(5)

Where it refers to the exchangelocation(node).So for this apparently two node case:

Qe QHSgen = - -

Te TH (6)

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After substitutions and rearranging themathematical terms, the above equationsimplifies to

S = TH -Te [K(TH -Te)+ 0.512

R(TH -TYrHTe)lgen THTe J

The irreversibility in the thermoelectric generatoris clearly due to the conduction of heat and to thedissipation of joule heat as the Seebeck & Peltiereffects do not give rise to entropy creation sincethey are reversible effects. Moreover, theconduction heat given K (TH -TC) 2

~TH -Te)generates entropy in the amount --l THTe

and Joule heat I 2R generates entropy in

amount /2R(TH +Te )2THTe

Actual workoutput from generators

~ctunl = w;. - TeS gen (8)

First Law Efficiency is work output out of heat suppliedW

11/=-QH (9)

Second Law Efficiency

't1 _ Wac/unl'Ill - TV.

(10)

Results and Discussion

Seeing the equation of entropy generation, itcan be analyzed that the irreversibility inthermoelectric device is due to conduction ofheat between TH and TC as well as joule heat.The value of entropy generation is 0.15 in fig. 2even if the current is zero. It shows even if nocurrent flows in the circuit it will give rise toentropy generation. This is due to heatconduction between temperature reservoirs.

---~----

ETJOURNALOFENGINEERING&TECHNOLOGY

0.15

0.17

~ 0.165c:~!ii~ 0.16C)

~e'E 0.155w

0.145 -"-~-"-----,--~-~~-~~-~---'o 100 200 300 400 500 600 700 800 900 1000

Current (A)

fig.2: Entropy generation vs current inthermoelectric generator

Fig.3 shows the reversible work output betweenthe two temperature limits. It shows themaximum work potential of the heat supplied tothe high temperature reservoir of thethermoelectric generator.

70 ////

//./

//,./

45 v'a 100 200 300 400 500 600 700 800 900 1000

Current (A)

65

50

Fig.3: Reversible work output vs current inthermoelectric generator.

The curve between actual work output andcurrent shows that the curvatures of entropygeneration curve and power output curve are inopposite direction. This shows that the entropygeneration reduces the power output and poweroutput will be low at the points where entropygeneration is high. The actual power outputdoes not depend upon the conductivity ofmaterial. The objective of operating athermoelectric generator is to get power output.By putting the equation of actual work outputequal to zero to values of current supplied can

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be calculated on which workoutput will be zero.

I=Oand J = a(TH - TcJR

20,'-~-~---~-~ __ -~-T __~.~~~

18

116 r

14 >

12l

~ 10 f

: r4 l2 l

100 200 300 400 500 600 700 800 900 1000Current (A)

Fig.4: Actual power out put vs current inthermoelectric generator

This is the theoretical operating range ofthermoelectric generator. Since the equation isquadratic, there will be a particular value ofcurrent supplied between these two criticalvalued at which power output is maximum.

First law efficiency also follows the pattern ofactual power output. It gives the power outputout of the heat supplied to the high temperaturereservoir. Second law efficiency shown in fig. 6gives the ratio of actual power output toreversible power output. This value is higherbecause reversible work is itself the availablepart of the supplied heat.

0.12

0.1

fU 0.08~~-: 0.06~ii:

0.04

0.02

oL-~--~-~-~~-~~~~~.o 100 200 300 400 500 600 700 800 900 1000

Current (A)

Fig. 5. First law efficiency vs current in11"'I'Tr"-:-1

thermoelectric generator

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The low thermodynamic efficiency ofthermoelectric generators results mainly fromthe irreversible character of the heat transport,in~~ •••.•..••.•.-

0.05

0.25

i 0.2

~~ 0.15.'l"c8~ 0.1

./

//

oL-~-~~_~_~~_~~_~~o ~ ~ ~ ~ ~ ~ ~ ~ ~ 1~

Current (A)

Fig. 6: Second law efficiency vs current inthermoelectric generator

The study provided useful thermodynamicsreasoning as applied to low maintenance devicewhich is under-used in a world of bulky pollutiongenerating monsters.

Conclusion & Scope of Future Work

In this work TEG are modeled with internalirreversibilities. The newer materials are

increasing efficiency so TEG are devices offuture. The characteristic equations aredeveloped & simulation curves are analysedand give useful insight into behaviour of TEG,materials control a and thus actual power outputof TEG. However the model presented hererequire incorporation of external irreversibilitiesand work in this direction will throw a usefulinsiqht to researchers working in area of TEG .

DO

References

1. Gupta VK, Shanker G, Saraf B and Sharma NK(1984) Experiment to verify the second law ofthermodynamics using a thermoelectric device.Am.J.Phys.52(7}: 625-27

2. B.D. Wood, Application of thermodynamics.Addison-esley, Reading, Mass. (1982).

3. S.w. Angrist, Direct Energy Conversion. Allyn &Bacon, Boston, Mass.(1982}.

4. J.M. Gordon, Am. J. Physics. 59,551 (1991).

ODD

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