Modern Engineering Thermodynamics

19.4 Thermoelectric Coupling 769
This discovery was originally thought to be independent of the Seebeck effect and gave rise to a new parameter
called the relative Peltier coefficient, π AB , defined as
Q
π AB = π A − π B =
_ P
(19.16)
I
where _Q P is the Peltier heating or cooling rate, and π A and π B are the absolute Peltier coefficients for the pure
conductors. Later (see Eq. (19.33)), it was discovered that the Peltier and Seebeck coefficients are related by
π AB = Tα AB (or π A = Tα A ), where T is the absolute temperature of the junction.
19.4.3 The Kelvin Effect 5
When an electric current passes through a single homogeneous conductor along which a temperature difference
exists, heating or cooling of the conductor occurs, depending on the direction of the current flow relative to the
temperature difference (see Figure 19.4).
The Kelvin effect can be demonstrated by heating the center of a uniform wire while cooling its ends and passing
a current through it. If we measure the temperatures at two points, A and B, equidistant from the center,
we find that T A ≠ T B . The electrical current has disturbed the temperature profile in the wire. This effect gave rise
to the Kelvin coefficient, τ, defined as
_Q
τ = lim K
ΔT!0 IðΔTÞ = _q K ′
J E ðdT/dXÞ
(19.17)
where _q K ′ is the Kelvin heating or cooling rate per unit volume, and J E = I/A is the electrical current density (or
electron flux). It can be shown that the Kelvin coefficient is related to the absolute Seebeck coefficient by
τ = −Tðdα/dTÞ, where T is the absolute temperature of the junction. For a thermocouple with conductors A and
B, the difference in the Kelvin coefficients for the two conductors is
τ A − τ B = τ AB = −T d
dT ðα A − α B Þ = −T dα AB
dT
19.4.4 The Fourier Effect 6
A temperature difference in a homogeneous conductor produces a heat flow in the direction of decreasing temperature
(see Figure 19.5).
Heat
Uniform conductor
Cool
T C T A T H T B
T C < T H
FIGURE 19.4
A schematic of the Kelvin effect.
Current I
T H T C < T H
Heat out
Heat in
x
Area, A
FIGURE 19.5
A schematic of the Fourier effect.
5 Discovered in 1854 by the Irish mathematician, physicist, and engineer William Thomson (Lord Kelvin) (1824–1907).
6 Discovered in 1822 by the French mathematician Jean Baptiste Joseph Fourier (1768–1830).