Thermoelectric Materials and Devices - Hierarchical Nanostructures for Energy Devices - page 132

d n 3 r 4 n g | 7

Figure 6.17 Two modes of thermoelectric device operation. (a) Power generation,
(b) refrigeration.

practical use generally consists of multiple pairs of elements to meet the
specific performance requirement. A thermoelectric device works as a power
generator when a temperature gradient is applied across the device, i.e.
vertically from the top to the bottom in Figure 6.17(a), and the resulting
Seebeck voltage is applied to an external load resistance producing electric
power. If the temperatures of the hot and cold sides are stabilized and
reached at the steady-state, the net heat input and power output are ex-
pressed by eqn (6.12) and eqn (6.13), respectively, as

.

Q in ¼ KDT þ SIT H 1

2 I 2 R

(6 : 12)

P ¼ I 2 R L (6.13)

where K is the total thermal conductance of the TE device, DT ¼ T H T C is
the temperature difference across the device, I is the net current flowing in
the electric circuit, and R and R L are the internal resistance of the device and
the load resistance, respectively. S ¼ S p S n is the total Seebeck coe cient.
Note that the Seebeck coecient of the p-type element S p has a positive sign,
while that of the n-type element S n has a negative sign, so that they are added
up in magnitude for S. The net current I is obtained by the ohmic law in the
electric circuit with the total Seebeck voltage SDT as

I ¼ R þ R L
SDT

(6 : 14)

The energy conversion e ciency is expressed as
Z ¼ P

I 2 R L
KDT þ SIT H 1

Q in ¼

(6 : 15)

2 I 2 R