Thermoelectric Materials and Devices - Hierarchical Nanostructures for Energy Devices - page 133

Assuming that the temperature of each side is fixed, the maximum total
energy conversion eciency can be obtained by adjusting the ratio of the
load resistance to the internal resistance of the device, m ¼ R L /R. From
dZ/dm ¼ 0, the optimal resistance ratio that maximizes the eciency is
evaluated as

d n 3 r 4 n g | 7

r

1 þ S 2 sT avg
k

¼

p

m max Z ¼ 1 þ ZT avg

(6 : 16)

where T avg ¼ (T H þ T L )/2 is the average temperature of the hot and cold sides,
and ZT avg is the thermoelectric figure of merit of the material at the average
temperature. The resulting maximum total energy conversion eciency is
obtained by

p

1 þ ZT avg

p

1 þ ZT avg 1 1

Z max ¼ 1 T C ¼ Z C (6 : 17)

p

1 þ ZT avg

p

1 þ ZT avg þ T C

T H

þ T C
T H

T H

where Z C is the Carnot eciency, which is the theoretical maximum e-
ciency of an energy convertor between a heat sink and a heat source. The
thermoelectric figure of merit has a very important role in this equation: it is
an intrinsic index representing the performance of a device made from a
certain thermoelectric material. As for the maximum power output, the re-
sistance ratio m should satisfy dP/dm ¼ 0, which results in m ¼ 1. Then the
maximum power output is obtained as
P max ¼ S 2 DT 2
4R

(6 : 18)

.

6.5.2 Refrigeration
Thermoelectric refrigeration is operated by an external input power that
moves electrons and holes away from the target surface to cool down the
surface. For the thermoelectric refrigerator shown in Figure 6.17(b), the rate
of heat absorption (or the cooling power) at the cold side and input electric
power are expressed by eqn (6.19) and eqn (6.20), respectively:
Q in ¼ KDT þ SIT C 1

2 I 2 R

(6 : 19)

P ¼ SIDT þ I 2 R

(6.20)

The coecient of performance (COP) of the TE refrigerator is defined as
the cooling power divided by the input electric power such that

KDT þ SIT C 1

2 I 2 R

COP ¼ (6 : 21)

:

SIDT þ I 2 R