Page 420 - Mechanical Engineers' Handbook (Volume 4)

3 Thermal Control Techniques 409

P 0.489 2 A v m 2 v 2 1 (1 K )
2
G v
v
1
2
2
c
2g (1 K ) ƒ A v 1 v 1 c v 1
c
(107)
(h) Compare
P with specified
P. If comparison fails select a different surface
or adjust the dimensions and begin again with step 1.
If the cold plate is loaded on one side only, an identical procedure is followed except
in steps 8 and 9. For single-side loading and for double and triple stacks, use must be made
of the cascade and cluster algorithms for the combination of fins described in Section 3.1.
Detailed examples of both of the foregoing cases may be found in Kraus and Bar-Cohen. 11

3.3 Thermoelectric Coolers

Two thermoelectric effects are traditionally considered in the design and performance eval-
uation of a thermoelectric cooler:
The Seebeck effect concerns the net conversion of thermal energy into electrical energy
under zero current conditions when two dissimilar materials are brought into contact. When
the junction temperature differs from a reference temperature, the effect is measured as a
voltage called the Seebeck voltage E .
s
The Peltier effect concerns the reversible evolution or absorption of heat that occurs
when an electric current traverses the junction between two dissimilar materials. The Peltier
heat absorbed or rejected depends on and is proportional to the current flow. There is an
additional thermoelectric effect known as the Thomson effect, which concerns the reversible
evolution or absorption of heat that occurs when an electric current traverses a single ho-
mogeneous material in the presence of a temperature gradient. This effect, however, is a
negligible one and is neglected in considerations of thermoelectric coolers operating over
moderate temperature differentials.

Equations for Thermoelectric Effects
Given a pair of thermoelectric materials, A and B, with each having a thermoelectric power
42
and , the Seebeck coefficient is
B
A

(108)
A
B
The Seebeck coefficient is the proportionality constant between the Seebeck voltage and
the junction temperature with respect to some reference temperature
dE dT
s
and it is seen that

dE
s
dt
The Peltier heat is proportional to the current flow and the proportionality constant is
, the Peltier voltage

q I (109)
p