The Thermoelectric Effect Interface implements thermoelectric effect, which is the direct conversion of temperature differences to electric voltage or vice versa. Devices such as thermoelectric coolers for electronic cooling or portable refrigerators rely on this effect. While Joule heating (resistive heating) is an irreversible phenomenon, the thermoelectric effect is, in principle, reversible.
Historically, the thermoelectric effect is known by three different names, reflecting its discovery in experiments by Seebeck, Peltier, and Thomson. The Seebeck effect is the conversion of temperature differences into electricity, the
Peltier effect is the conversion of electricity to temperature differences, and the
Thomson effect is heat produced by the product of current density and temperature gradients. These effects are thermodynamically related by the Thomson relations:
where P is the Peltier coefficient (SI unit: V),
S is the Seebeck coefficient (SI unit: V/K),
T is the temperature (SI unit: K), and
μTh is the Thomson coefficient (SI unit: V/K). These relations show that all coefficients can be considered different descriptions of one and the same quantity. The COMSOL formulation primarily uses the Seebeck coefficient. The Peltier coefficient is also used as an intermediate variable, but the Thomson coefficient is not used.
where σ is the electrical conductivity and
k the thermal conductivity.
The general formulation of thermoelectric effect redefines the heat flux and the electric current according to Equation 4-127 and
Equation 4-128, respectively. This formulation does not necessarily correspond to the formulation used when only a particular aspect of thermoelectric effect is considered: Seebeck, Peltier, or Thomson. This paragraph describes how these separated effects can be recognized in the general formulation.
This contribution is obtained again by developing the divergence of the q term in the heat equation when
q is defined following
Equation 4-127. This time consider the term
−TJ ⋅ ∇S. Assuming that
S is function of
T, then: