ABSTRACT
During the nineteenth century, several phenomena linking thermal
energy transport and electrical currents in solid materials were
discovered within a time interval of 30 years, spanning from 1821
to 1851 (Fig. 1.1). These phenomena are collectively known as
thermoelectric effects, and we will devote this section to briefly introducing them.a
Let us start by considering an elementary thermal effect:
experience shows us that when a piece of matter is subjected to a
temperature difference between its ends heat spontaneously flows
from the region of higher temperature, TH , to the region of lower temperature, TC (Fig. 1.2a). This heat current is maintained over time until thermal equilibrium (TH = TC ≡ T ) is reached and the temperature gradient vanishes (Fig. 1.2b). It was Jean Baptiste
Joseph Fourier who first introduced the mathematical formulation
describing this well-known fact in 1822. According to the so-called
in Km−1) induces in the material a heat current density h (measured in Wm−2 units) which is given bya
h = −κ ∇T , (1.1) where κ is a characteristic property of the considered material, re-
ferred to as its thermal conductivity (measured in Wm−1K−1 units). In general, the thermal conductivity depends on the temperature of
the material, that is, κ(T ), and it always takes on positive values (κ > 0), so that the minus sign in Eq. (1.1) is introduced to
properly describe the thermal current propagation sense. Indeed, if
we reverse the temperature gradient (∇T → −∇T ) in Eq. (1.1) we get a heat flow reversal (h → −h), so that heat always diffuses the same way: from the hot side to the cold one.
