Page 423 - Mechanical Engineers' Handbook (Volume 4)

412 Cooling Electronic Equipment

1
T/
T
COP m (120)
m
2(1
T/T )
c
The current that optimizes or maximizes the coefficient of performance can be shown
to be

T
I (121)
0
R[(1 zT ) 1/2 1]
a
where T ⁄2(T T ). In this case, the optimum coefficient of performance will be
1
c
h
a
COP (T /T )
T
c
c
h
0

T 1 (122)
where
1
[1 ⁄2z (T T )] 1/2 (123)
c
h
Analysis of Thermoelectric Coolers
In the event that a manufactured thermoelectric cooling module is being considered for a
particular application, the designer will need to specify the number of junctions required. A
detailed procedure for the selection of the number of junctions is as follows:
1. Design specifications
(a) Total cooling load, q , W
T
(b) Cold-side temperature, T ,K
c
(c) Hot-side temperature, T ,K
h
(d) Cooler specifications
i. Materials A and B
ii. and ,V/ C
A
B
iii. and , ohm cm
A
B
iv. k and k , W/cm C
B
A
v. A and A ,cm 2
B
A
vi. L,cm
2. Cooler calculations
(a) Establish

.
A
B
(b) Calculate R from Eq. (113).
(c) Calculate K from Eq. (114).
(d) Form
T T T ,Kor C.
h
c
(e) Obtain z from Eq. (118), 1/ C.
3. For maximum heat pumping per couple
(a) Calculate I from Eq. (119), A.
m
(b) Calculate the heat absorbed by each couple q, from Eq. (112), W.
(c) Calculate
T from Eq. (117), K or C.
m
(d) Determine COP from Eq. (120).
m
(e) The power required per couple will be p q/COP ,W.
m