ME 381R Fall 2003

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ME 381R Fall 2003 Micro-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
78712 www.me.utexas.edu/lishi lishi_at_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
Cryogenic IR Night Vision
Beer Cooler
Thermally-Controlled Car Seat
Electronic Cooling
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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.

? lt0 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
? gt0 Positive Peltier coefficient High energy
holes move from left to right. Thermal current
and electric current flow in same direction.
q?j, where q is thermal current density and j
is electrical current density. ? ST (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.

is the Thomson coefficient in Volts/Kelvin
Seebeck coeff. S is temperature dependent
Relation given by Kelvin
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Thermoelectric Refrigeration
The rate of heat flow from one of the legs (i1
or 2)
(1)
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The rate of heat generation per unit length due
to Joule heating is given by
(2)
Eqn 2 is solved using the boundary conditions T
Tc at x0 and T Th at x l. Thus it is found
that
(3)
The total heat removed from source will be sum of
q1 and q2
qc (q1 q2 )x0
(4)
Eqs. 1, 3, 4?
K Thermal conductance of the two legs R
Electrical Resistance of the two legs
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The electrical power is given by
COP is given by heat removed per unit power
consumed
Differentiating w.r. to I we get max. value of COP
where
and Tm(ThTc)/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
When this condition is satisfied z becomes
Further, if S2-S1 S, k1 k2 K, s1 s2 s
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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 ZT1
• 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, S and s 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

where w is the power delivered to the external
load QH is the positive heat flow from
source to sink