Thermoelectric effect and thermoelectric devices - MIT

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Thermal Radiaton: Planck’s Law

Inside the Cavity EM Wave In Equilibrium at Temperature T

Perfectly Reflecting Wall at T Frequency ν

Angular Frequency ω=2πν Wavelength λ Wavevector magnitude k=2π/λ

νλ=c

Wavevector k=(kx,ky,kz) 222 zyx kkkcck ++==ω

ω(k): Dispersion relation (linear)

k

x xx

x x

xx x

Lnk

nL

2 2

,...2

,...,2

2,2

π

λλλ

=

=

Basic Relations

How much energy in the cavity?

( )

( )

( )TfL

dk

L

dk

L

dk

TfL

dk

L

dk

L

dk

TfU

z

z

y

y

x

x

z

z

y

y

x

x

n n nx y z

,)/2()/2()/2(

2

,)2/2()2/2()2/2(

2

,2

000

1 1 1

ωωπππ

ωωπππ

ωω

h

h

h

∫∫∫

∫∫∫

∑∑∑

∞

∞−

∞

∞−

∞

∞−

∞∞∞

∞

=

∞

=

∞

=

=

==

Two polarization

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Thermal Radiaton: Planck’s Law ( )

( )

( )

( )

( ) ( )

( ) ωω

ωωωω

ωπ ωωω

ωωπωωπ

πωωπ

ωωπ

du

dDTf

d c

TfV

U

c d

c TfV

dkkTfV

dkdkdkTfVU zyx

∫

∫

∫

∫

∫

∫ ∫ ∫

∞

∞

∞

∞

∞

∞

∞−

∞

∞−

∞

∞−

=

=

=

⎟ ⎠

⎞⎜ ⎝

⎛⎟ ⎠

⎞⎜ ⎝

⎛ =

=

=

0

0

32

2

0

2

0 3

2

0 3

3

,

,

4,8 2

4,8 2

,8 2

h

h

h

h

h

D(ω)-density of states per unit volume per unit angular frequency interval

• Energy density per ω interval

( ) ( ) ( )

1exp

1 ,

32

3

−⎟⎟ ⎠

⎞ ⎜⎜ ⎝

⎛ =

=

Tk

c

DTfu

B

ωπ ω

ωωωω

h

h

h

Planck’s law

Solid Angle

dAp

2RdA

d p=Ω

whole space 4π

• Intensity: energy flux per unit solid angle

( ) ( )

exp

1 44 23

3

⎟ ⎠

⎞ ⎜⎜ ⎝

⎛ ==

Tk

c

cuI

B

ωπ ω

π ωω

h

h

Per unit wavelength interval

( ) ( ) 2 exp

14 5

⎜⎜ ⎝

⎛ ==

πλ π

λ ωωλ

Tk

c

d

dII

B

h

h

Planck’s law

⎟ −1

c ⎞

λ ⎟⎠⎟ −1

––WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MITWARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT

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Thermal Radiaton: Planck’s Law

( ) ( )

1exp

1 4 22

3

−⎟⎟ ⎠

⎞ ⎜⎜ ⎝

⎛ =

=

Tk

c A

IAQ

B

ωπ ω

λπλ

h

h

&

Q&

Total

( ) 4

0

TAdQQ σλλ == ∫ ∞

&&

10-1

100

101

102

103

104

0 2 4 6 8 10

EMIS

SIVE

PO

WER

(W/c

m2 μm

)

WAVELENGTH (μm)

5600 K

2800 K

1500 K

800 K

Emissive Power

Wien’s displacement law

mK2898max μλ =T

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Introduction to Thermoelectricity

Gang Chen

Mechanical Engineering Department Massachusetts Institute of Technology

URL: http://web.mit.edu/nanoengineering

––WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY,WARREN M. ROHS MITENOW HEAT AND MASS TRANSFER LABORATORY, MIT

97 Copyrig

.997 Dir

––WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MITWARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT

2.9

ht © Gang Chen, M

IT

For 2

ect Solar/T

hermal to

Electrical Energy C

onversion

Seebeck Effect

Seebeck effect: Discovered in 1821 Temperature difference generates voltage

http://www.sil.si.edu/silpublications/dibner-library-lectures/scientific-discoveries/text-lecture.htm

Thomas Johann Seebeck 1770-1831

Conductor 1 Conductor 2

Hot

Cold

Voltage

Copy

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Peltier Effect

Jean Charles Athanase Peltier 1785-1845 Peltier Effect: Discovered in 1834

An electrical current creates a cooling or heating effect at the junction depending on the direction of current flow.

Conductor 1 Conductor 2

Heating or Cooling

A

yr

––WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MITWARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT

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IT

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Thomson Effect

http://www.sil.si.edu/silpublications/dibner-library-lectures/scientific-discoveries/text-lecture.htm

Thomson effect predicted, 1855

William Thomson (Lord Kelvin) 1824 – 1907

ThotTcold current

heat release/absorption q(x)

anghe

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IT

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Current Density

Heat Flux

An Intuitive Picture of Thermoelectric Effects

• Current Flow in an Isothermal Conductor

• • •

• • •

•

•

•• •

•

•

• • • •

•

• • •

•

• • • • • •

• •

• •

•

• •

• •

• • •

•

•

•

• •

•

•

• • • •

•

•

•

•

•

•

•

• ••

• •

•

•

•

•

• •

ρσμ /εεεvJ ==== enene

Electron Charge [C]

Electron Density [1/m3]

Drift Velocity [m/s]

Mobility [m2/s.V]

Electrical Conductivity [1/Ωm]

Electrical Field [V/m]

eeq e

qqn JJvJ Π===

Heat Per Charge [J] Peltier Coefficient [J/A]

Electrical Resistivity [Ωm]

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onversion

Peltier Effect

Q (Peltier) = (Π 1−Π2)J

1

2

QQ

Je, Jq1

Je, Jq2

• Heating and cooling at junctions • Reversible with current direction

ang er•••••••

•

•• •

•• •

•• ••• •

•

•• •

•• •

•• • •

•• •• •

•

••

––WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MITWARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT

2.997 Copyright © G

Chen, MIT

For 2.997 Direct Solar/Th

mal to

Electrical Energy Conversio

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S = -ΔV/ΔT = -(Vhot-Vcold)/(Thot-Tcold)

S --- Seebeck Coefficient

Built-In Potential

Temp. Gradient

Vcold Tcold

Vhot Thot

Seebeck Effect

•• • ••• •

•

• • •

• • •

• • • • • •

•

• • •

• • •

• • • •

• • •• •

•

• •

• Charge diffusion under a temperature gradient • Built-in potential resisting diffusion

Ga he•••••••

•

•• •

•• •

•• ••• •

•

•• •

•• •

•• • •

•• •• •

•

•• ••

––WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MITWARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT

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ng Chen, M

IT

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rmal to

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onversion

Thomson Effect

ThotTcold

current

heat release/absorption q(x)

1 dq dT I dx dx

τ =Thomson Coefficient

• Kelvin Relations: Π = ST; T dS/ dTτ =• Kelvin Relations: Π = ST; T dS/ dTτ =

• • ••• •

•

• • •

• • •

• • • • •

•

• • •

• • •

• • • •

• • •• •

•

• •

2.997 Copyright ©

Gang Chen, MIT

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Properties are Temperature Dependent

Images removed due to copyright restrictions. Please see Fig. 2a,b in Poudel, Bed, et al. "High-ThermoelectricPerformance of Nanostructured Bismuth Antimony Telluride Bulk Alloys." Science 320 (May 2, 2008): 634-638.

––WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY,WARREN M. ROHS MITENOW HEAT AND MASS TRANSFER LABORATORY, MIT

997

For 2.997

trica

––WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MITWARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT

2. Copyrig

ht © Gang Chen, M

IT

Direct Solar/T

hermal to

Elec l Energy C

onversion

Thermoelectric Devices

COLD SIDE

HOT SIDE

-

I

+

N P

HOT SIDE

COLD SIDE

––WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MITWARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT

2.997 Copyright ©

Gang Chen, MIT

For 2.997 Direct Solar/T

hermal to

Electrical Energy C

onversionPerformance of Thermoelectric Devices

97r

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ht © Gang Chen, MIT

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Electrical Energy Conversio

n

Other Basic Relations: Heat Conduction

• Fourier Law for heat conductionTh

Tc

Tk∇−=q Thermal Conductivity [W/m.K]Heat Flux [W/m2]

Area AL • One-dimensional heat conduction

TKL

TTAkQ ch Δ= −

=

L

kAK =:eConductancThermal

p

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Device Analysis: Cooling • Ideal Devices

No Joule Heating, No Heat Conduction

Qc = (Πp -Πn)•Ι

QcTc

QhTh

p n • Real Devices:

Joule Heating & Heat Conduction

Qc= (Πp -Πn)•Ι − I2R/2 - K (Th-Tc

Electrical Resistance Thermal Conductance

p

pp

L

Ak K +=

n

nn

p

pp

A

L

A

L R

ρρ +=

)

kn An

Ln

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onversion

Refrigerator Performance QcTc

QhTh

Coefficient of Performance:

( ) ( )

( ) ( )

2 p n C H CC

2 p n H C

1S S IT K T T I RQ 2 W S S I T T I R

− − − − φ = =

− − +

( )

HM

C C max

H C M

T1 ZTT T

T T 1 ZT 1

+ −

φ = − + +

( ) ( )2 2 p n p n

p p p pn n n n

p n p

S S S S Z

KR L k AL k A A A L

− − = =

⎛ ⎞⎛ρ ρ+ +⎜ ⎟⎜⎜ ⎟⎜

⎝ ⎠⎝

Optimize Current:

.0MT =

Voltage Drop: ))(( chnp TTSSIRV −−+=

5(Th Tc+ )

⎞⎟⎟Ln ⎠

––WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY,WARREN M. ROHS MITENOW HEAT AND MASS TRANSFER LABORATORY, MIT

C

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For 2.997 Direct Solar/T

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onversion

Figure of Merit Z

p p p pn n n n

p n p n

L k AL k AKR A A L L

⎛ ⎞⎛ ⎞ρ ρ = + +⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟

⎝ ⎠⎝ ⎠

( ) ( )2 p p n nmin KR k k= ρ + ρ when

1/ 2 n p p n

p n n p

L A k L A k

⎛ ⎞ρ = ⎜⎜ ρ⎝

( ) ( )

2 p n

max 2 p p n n

S S Z

k k

− =

ρ + ρ For a single material: Z =

In a device, pn pairs are used:

(1) Areas of each type of legs need to be optimized (2) Two types of legs should have comparable properties (3) Current input to the device needs to be optimized

⎟⎟⎠

S2 σS2=

ρk k

––WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY,WARREN M. ROHS MITENOW HEAT AND MASS TRANSFER LABORATORY, MIT

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2.997 Copyright ©

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onversion

Typical Number

• Bi2Te3-based materials ~300 K

S=220 μV/K σ=105 Sm-1

k=1.5 W/mK

Power Factor: S2σ=48 μW/cm-K Figure of Merit: Z=3.2x10-3 1/K

ZT=1

• Device Leg: 1 mm x 1 mm x 2 mm

3

1 5 6 L 2 10R 0.02 A 10 10

−

−

× = = = Ω

σ ×

Legs are electrically in series but thermally in parallel

Image by michbich at Wikipedia.

––WARREN M. ROHSENOW HEAT AND WARREN M. ROHSENOW HEAT AND

2.997 Copyright © Gang Chen, MIT

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mal to

Electrical Energy Conve

Ceramics plate for electrical insulation

Two Tcthermocouples soldered intodrilled holes

Copper blocks (T )

One Ththermocouple soldered into drilled holes

MASS TRANSFER LABORATORY, MITMASS TRANSFER LABORATORY, MIT

er

rsion

Current (A) 0 2 4 6 8 10

Tem

pera

ture

Diff

eren

ce (o C

)

0

20

40

60

80

100

120 Experimental data Theoretical prediction

An Example

Th = 100 °C

hh

Ceramics plate for electrical insulation

Two Tc thermocouples soldered into drilled holes

Copper blocks (T )

One Th thermocouple soldered into drilled holes

• Match two leg size • Minimize contact

resistance • Optimize current

––WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MITWARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT

2.997 Copyright ©

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For 2.997 Direct Solar/T

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onversion

Temperature Dependence of Properties

Images removed due to copyright restrictions. Please see Fig. 2a,b,d,e in Poudel, Bed, et al.

"High-Thermoelectric Performance of Nanostructured Bismuth Antimony Telluride Bulk Alloys." Science 320 (May 2, 2008): 634-638.

––WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MITWARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT

2.997 Copyright ©

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For 2.997 Direct Solar/T

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Differential Analysis

x

2 2

d dT dS dTk JT J 0 dx dT dxdx

⎛ ⎞ − + ρ =⎜ ⎟⎝ ⎠

Thomson Effect, Usually Neglected Joule Heating

Boundary Conditions (Cooling):

O

L x=0: c dT dT q k J k ST dx dx

= − + Π = − +Tc given or Jc

.997 Copyright © Gang Chen, MI

or 2.997 Direct Solar/Thermal to

2

T

FElectri

cal Energy Conversion

Thermoelectric Power Generation

ALKALI METAL THERMAL TO

AL

RCIEL LLE

TH

TEC

0.1

0.2

0.3

0.4

CARNOT CYCLE 10

7

ZT m

1

TNAPLERWPOMER

SEINGENEVIOTOMAUT

SC

ALKALI METALTHERMALTOALKALI METALTHERMALTO

IED LES ALP NT

4

ERENONII C

RO

0.1

0.2

0.3

0.4

0.1

0.2

0.3

0.4

0.1

0.2

0.3

0.4

CARNOT CYCLE 10

7

2

T

50.

ZTm

SRTOARENEGERWPOCITRELECOMERTH

AERENGGNILRIST

SROTAGMERTH

ave

Constant Properties

0.60.0.0.666Efficiency

POW

ER G

ENER

ATI

ON

EFF

ICIE

NC

Y

POW

ERG

ENER

ATI

ON

EFFI

CIE

NC

Y

0.50.0.0.555⎛ T ⎞ 1 + ZT −1⎜⎜ c ave

Th ⎟⎟

Tc

η = 1 −⎝ ⎠ 1 + ZTave + 4THTHERMALERMAL

POPOWERWERPLPLANTANT

Th

Tc + ThT 2= DIESEL PLANT

2 STIRLINGELELECTRIC CELLSECTRIC CELLSGENERATORTPV 1

THERMIONIC AUTAUTOMOTIVEOMOTIVEGENERATORS 0.5 ENENGINESGINES

THERMOELECTRICPOWER GENERATORS

00001 2 3 4 5 6 7 8 9 111 2 3 4 5 6 7 8 9 10111000TEMPERATURE RATIO (T /T )TEMPERATURE RATIO (T /T )hot coldhot cold

––WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY,WARREN M. ROHS MITENOW HEAT AND MASS TRANSFER LABORATORY, MIT

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2.997 Copyright © Gang Chen, MIT

For 2.997 Direct Solar/Thermal to

Electrical Energy Conversio

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Thermoelectric Refrigeration

0

1

2

3

4

5

6

1 1.2 1.4 1.6 1.8

CO

EFFI

CIE

NT

OF

PER

FOR

MA

NC

E

TEMPERATURE RATIO (Thot

/Tcold

) 2.0

0.51 2 4 710 ZT

m

CARNOT CYCLE STIRLING REFRIGERATORS HOUSEHOLD REFRIGERATORS & AIR-CONDITIONERS

THERMOELECTRIC REFRIGERATORS

STIRLING CRYOCOOLERS

Coefficient of Performance

11 /1

++

−+

− =

ave

chave

ch

c

ZT

TTZT

TT

TCOP

––WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MITWARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT

2.997 Copyright ©

Gang Chen, MIT

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hermal to

Electrical Energy C

onversion

Current and Potential Applications

2.997 Copyright ©

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For 2.997 Direct Solar/T

hermal to

Electrical Energy C

onversion

Commercial Thermoelectric Devices

Power Generators from Hi-Z

Coolers from Marlow Industries

Images removed due to copyright restrictions. Please see http://www.hi-z.com/index.php http://www.marlow.com/thermoelectric-modules/

––WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY,WARREN M. ROHS MITENOW HEAT AND MASS TRANSFER LABORATORY, MIT

2.997 Copyright ©

Gang Chen, MIT

For 2.997 Direct Solar/T

hermal to

Electrical Energy C

onversion

Current Applications in Refrigeration

.

Images removed due to copyright restrictions. Please see: http://www.roadtrucker.com/12-volt-coolers-accessories/ 12-volt-coolers-products/igloo-40-quart-kool-mate-40-12-volt-thermo-electric-cooler-6402.jpg http://image.made-in-china.com/2f0j00kvZEKWVPgtlu/Refrigerator-BC-65A-.jpg http://www.newdavincis.com/images/wc-1682%2016%20bottles.jpg http://www.rmtltd.ru/datasheets/TO812.4MD04116xx.pdf http://www.medsystechnology.com/images/gem4000_w32a.jpg http://amerigon.com/ccs_works.php

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For 2.997 Direct Solar/T

hermal to

Current Applications in Power Generation

http://www.research.philips.com/newscenter/pictures/downloads/misc-sustainability_05-0_h.jpg

Electrical Ener

Conversion

Images removed due to copyright restrictions. Please see: http://thermoelectrics.caltech.edu/images/mhw-rtg.gif

http://www.roachman.com/thermic/thermic1.jpg

––WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY,WARREN M. ROHS MITENOW HEAT AND MASS TRANSFER LABORATORY, MIT

http://globalte.com/pdf/teg_5120_spec.pdf

2.997 C

MIT

For 2.

Object being cooled

N NP PTE Element

Ceramicsubstrate

Carriers moving heat

Electricalinterconnect

+_

DC Power source

Heat sink

TobjectTcold

Thot

TambientT

Tte

Ele Figure by MIT OpenCourseWare.c

System Consideration

Sometimes, thermal systems more expansive ––WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY,WARREN M. ROHS MITENOW HEAT AND MASS TRANSFER LABORATORY, MIT

––WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MITWARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT

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Heat to Electricity Recovery from Gas Stream

Hot Gas m, Th,i

Hot Gas Th,o

Heat Transfer Surfaces

Coolant

Insulation Hot Side TemperatureTH

Cold Side TemperatureTc

• For thermoelectric devices, TH higher is better • However, maximum heat intercepted from hot

gas stream, mcp(Th,i-TH), decreases with TH

––WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MITWARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT

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Vehicle Systems

Gasoline 100 kJ

10kJ 30kJ 35kJ

Parasitic heat losses Coolant Exhaust

9kJ 10kJ

6kJ Auxiliary

Driving

Mechanical losses

Main AC: TE Local cooling of seats: TE

Catalytic converter: TE

Radiator: TE

In US, transportation uses ~26% of total energy.

––WARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MITWARREN M. ROHSENOW HEAT AND MASS TRANSFER LABORATORY, MIT

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Prototypes

http://cache.gawker.com/

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2.997 Direct Solar/Thermal to Electrical Energy Conversion Technologies Fall 2009

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