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ME 381R Fall 2003Micro-Nano Scale Thermal-Fluid Science and Technology

Lecture 15:

Introduction to Thermoelectric Energy Conversion(Reading: Handout)

Dr. Li Shi

Department of Mechanical Engineering The University of Texas at Austin

Austin, TX 78712www.me.utexas.edu/~lishi

lishi@mail.utexas.edu

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References

Thermo-electrics: Basic principles and New Materials Development by Nolas, Sharp and Goldsmid

Thermoelectric Refrigeration by Goldsmid

Thermodynamics by Callen. Sections 17-1 to 17-5

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Outline

• Thermoelectric Effects

• Thermoelectric Refrigeration

• Figure of Merit (Z)

• Direct Thermal to Electric Power Generation

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Applications

Beer Cooler

Thermally-Controlled Car Seat

Electronic Cooling

Cryogenic IR Night Vision

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Basic Thermoelectric Effects

• Seebeck effect

• Peltier Effect

• Thomson effect

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Seebeck Effect• In 1821, Thomas Seebeck found that an electric current

would flow continuously in a closed circuit made up of two dissimilar metals, if the junctions of the metals were maintained at two different temperatures.

S= dV / dT;

S is the Seebeck Coefficient with units of Volts per Kelvin

S is positive when the direction of electric current is same as the direction of thermal current

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Peltier Effect

• In 1834, a French watchmaker and part time physicist, Jean Peltier found that an electrical current would produce a temperature gradient at the junction of two dissimilar metals.

П <0 ; Negative Peltier coefficient

High energy electrons move from right to left.

Thermal current and electric current flow in opposite directions.

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Peltier Cooling

П >0 ; Positive Peltier coefficient

High energy holes move from left to right.

Thermal current and electric current flow in same direction.

q=П*j, where q is thermal current density and j is electrical current density.

П= S*T (Volts)

T is the Absolute Temperature

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Thomson Effect

• Discovered by William Thomson (Lord Kelvin)

• When an electric current flows through a conductor, the ends of which are maintained at different temperatures, heat is evolved at a rate approximately proportional to the product of the current and the temperature gradient.

dx

dTI

dx

dQ

is the Thomson coefficient in Volts/Kelvin

Seebeck coeff. S is temperature dependent

dT

dSTRelation given by Kelvin:

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Thermoelectric Refrigeration

The rate of heat flow from one of the legs (i=1 or 2) :

00

xiiixi dx

dTAkITSq (1)

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The rate of heat generation per unit length due to Joule heating is given by:

2

22

dx

TdAk

A

Iii

ii

(2)

Eqn 2 is solved using the boundary conditions T= Tc at x=0 and T= Th at x= l. Thus it is found that:

l

TTAk

A

lxI

dx

dTAk chii

iiii

)(]2/[2

The total heat removed from source will be sum of q1 and q2qc= (q1 + q2 )|x=0

(3)

(4)

Eqs. 1, 3, 4

RITKITSSq cc2

12 5.0)(

K: Thermal conductance of the two legs

R: Electrical Resistance of the two legs

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The electrical power is given by:

RITISSw 212 )(

COP is given by heat removed per unit power consumed

])[(

5.0)(

12

212

IRTSSI

RITKITSS

w

q cc

11

/1max

m

chm

ch

c

zT

TTzT

TT

T

Differentiating w.r. to I we get max. value of COP

where KR

SSz

212 )(

and Tm=(Th+Tc)/2

A similar approach can be used to obtain the maximum degree of cooling and maximum cooling power.

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It is obvious that z will be maximum when RK will have minimum value. This occurs when:

11

22

22

11

/

/

k

k

lA

lA

When this condition is satisfied z becomes:

22/122

2/111

212

])/()/[(

)(

kk

SSZ

Further, if S2=-S1 = S, k1 = k2 = K, 1 =2 =

k

SZ

2

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ZTm vs. COP

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Criteria

• For greatest cooling efficiency we need a material that:

• conducts electricity well (like metal)

• conducts heat poorly (like glass)

• Bismuth telluride is the best bulk TE material with ZT=1

• To match a refrigerator, ZT= 4 - 5 is needed

• To efficiently recover waste heat from car, ZT = 2 is needed

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Progress in ZT Fundamental limitations:

k and , S and are coupled.

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Thermoelectric Power Generation

• Used in Space shuttles and rockets for compact source of power.

• Diffusive heat flow and Peltier effect are additive i.e. both reduce the temperature gradient.

• The efficiency of power generation is given by:

RITkITSS

IRTSSI

q

w

cH2

12

12

5.0)(

])[(

where: w is the power delivered to the external load

QH is the positive heat flow from source to sink