AME  60634    Int.  Heat  Trans.  

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Thermoelectric Effect & Thermoelectric Devices

*borrowed heavily from presentation by G. Chen, MIT

AME  60634    Int.  Heat  Trans.  

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Seebeck Effect

cold  

hot  

Seebeck Effect: Temperature difference generates a voltage between two different materials

Thomas Johann Seebeck 1821, Germany

Conductor 1 Conductor 2

AME  60634    Int.  Heat  Trans.  

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Seebeck Effect

Thot Tcold

electrons diffuse from hot to cold

electric potential builds up that resists diffusion

S = −ΔVΔT

= −Vhot −VcoldThot −Tcold

Seebeck coefficient: S [V/K]

AME  60634    Int.  Heat  Trans.  

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Peltier Effect

Peltier Effect: Current flow can induce a temperature gradient depending on direction of current flow

hot  

Conductor 1 Conductor 2

A

Jean Charles Athanase Peltier 1834, France

AME  60634    Int.  Heat  Trans.  

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Current and Heat Flow

€

F = −q

E − m* v

τ= m* d v

dt

Newton’s 2nd Law

Coulombic force drag due to collisions

The steady-state solution gives the average electron “drift” velocity

€

v = − qτm*

E

€

µe =qτm* ≡ electron mobility

The current density is the rate of charge transport per unit area (like heat flux)

jelec = −nelecqv = nelecq

2τm*

E =σ

∇Φ compare to Ohm’s law!

But the electrons carry heat with them!

jheat = nelecuv = u

qjelec =Πjelec

Peltier coefficient: Π [J/A]

AME  60634    Int.  Heat  Trans.  

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Peltier Effect

q q 1

2

jelec, jheat

jelec, jheat

q (Peltier): (Π1-Π2)×j

-  Induced heating and cooling at the two junctions due to mismatch -  Reversible by reversing the direction of current flow -  A refrigerator! (current is “work” to drive “heat”)

AME  60634    Int.  Heat  Trans.  

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Thomson Effect

William Thomson, Lord Kelvin 1855, Ireland

Thot Tcold

current

heat release/adsorption

Thomson Effect: Current flow through a temperature gradient will generate/absorb heat because thermoelectric properties are temperature dependant

AME  60634    Int.  Heat  Trans.  

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Thomson Effect

Thot Tcold

electrons diffuse from hot to cold

current

heat release/absorption needed for energy balance

Thomson coefficient: τ = (1/i)×(dq/dx)/(dT/dx)

q(x)

i

Kelvin Relations:

Π = ST; τ = T dSdT

AME  60634    Int.  Heat  Trans.  

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Thermocouples & The Thermoelectric Effect

Thermocouples operate under the principle that a circuit made by connecting two dissimilar metals produces a measurable voltage when a temperature gradient is imposed between one end and the other.

AME  60634    Int.  Heat  Trans.  

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Thermoelectric Devices

http://www.energybandgap.com

AME  60634    Int.  Heat  Trans.  

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Peltier Coolers

Ideal Device: •  No conduction (hot to cold) •  No Joule heating

Tc, qc

Th, qh

qc = Π p −Πn( )× i

Real Device: •  conduction (hot to cold) •  Joule heating

qc = Π p −Πn( )i− i2R 2−σ cond Th −Tc( )

electrical resistance thermal conductance

R =Lp

Apσ p

+LnAnσ n

σ cond =ApkpLp

+AnknLn

AME  60634    Int.  Heat  Trans.  

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Peltier Coolers: Refrigeration Performance Voltage Drop:

V = iR+Sp − SnTh −Tc

Real Device: •  conduction (hot to cold) •  Joule heating

Tm =12Th +Tc( )

Coefficient of Performance:

COP = qcW

=Sp − Sn( )iTc − i2R 2−σ cond Th −Tc( )

Sp − Sn( )i Th −Tc( )+ i2R

Optimal Current to Maximize COP:

COPmax =Tc

Th −Tc( )1+ ZTM −Th Tc1+ ZTM +1

AME  60634    Int.  Heat  Trans.  

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The Z Parameter

Z =Sp − Sn( )

2

Rσ cond

=Sp − Sn( )

2

Lp

Apσ p

+LnAnσ n

"

#$$

%

&''ApkpLp

+AnknLn

"

#$$

%

&''

To Maximize Z:

Rσ cond( )min =kpσ p

+kpσ p

!

"##

$

%&&

2LnAp

LpAn=

σ nknσ pkp

!

"##

$

%&&

12

when

Leading to Z:

Zmax =Sp − Sn( )

2

kp σ p + kn σ n( )2

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Figure of Merit: ZT

ZT = σS2Tk

For a Single Material:

increase electrical conductivity decrease thermal losses (conduction)

http://chemgroups.northwestern.edu/kanatzidis/greatthermo.html

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Superlattice

ZT = σS2Tk

increase electrical conductivity decrease thermal losses (conduction)

kσT

=π 2kB

2

3q2constrained by

Widemann-Franz

ZT = σS2Tkelec + kphonon

http://lucidthoughts.com.au/

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http://www.kickstarter.com/projects/flamestower/flamestower-charge-your-gear-with-fire

http://www.customthermoelectric.com/

http://energyblog.nationalgeographic.com/2013/09/24/google-science-fair-winner-makes-flashlight-powered-by-body-heat/