Page 421 - Mechanical Engineers' Handbook (Volume 4)

410 Cooling Electronic Equipment

The Thomson heat is proportional to a temperature difference dT and the proportionality
constant is , the Thomson coefficient. With dq IdT, it is observed that dT is a
T
voltage and the Thomson voltage is defined by
T 2
E dT
T
T 1
Considerations of the second laws of thermodynamics and the Kirchhoff voltage laws
show that the Peltier voltage is related to the Seebeck coefficient 42

T (110)
and if the Seebeck coefficient is represented as a polynomial 42
a bT
then
2
aT bT
Design Equations
In Fig. 17, which shows a pair of materials arranged as a thermoelectric cooler, there is a
cold junction at T and a hot junction at T . The materials possess a thermal conductivity k
c h
and an electrical resistivity . A voltage is provided so that a current I flows through the
cold junction from B to A and through the hot junction from A to B. This current direction
is selected to guarantee that T T .
c h
The net heat absorbed at the cold junction is the Peltier heat
q T IT (111a)
p c c
2
minus one-half of the I R loss (known as the Joule heat or Joule effect)

Figure 17 Thermoelectric cooler.