2.1.2 Peltier Effect

To some extent, the Peltier effect describes the phenomenologically reverse effect of the Seebeck effect. However, the physical effect is different, since the Peltier effect is only present at the presence of an electric current, while the Seebeck effect also causes a voltage at open circuit conditions. An electrical current driven through two connected rods causes a temperature difference between the two soldered points. Accordingly, heat is absorbed and rejected, respectively and thus a heat flux throughout the rods is induced. The heat flux at the junctions can be understood by considering energy conservation within the junction and a change of the total energy of the carriers when passing the junction.

The heat flux throughout the rods depends on the charge current as well as the Peltier coefficient and is given by

$$\ensuremath{\ensuremath{\mathitbf{J}}^\mathrm{q}}_\ensuremath{\ma... ...{\pi}_\ensuremath{\mathrm{ab}} \mathrm{q}\ensuremath{\ensuremath{\mathitbf{J}}}$$ (2.6)

where the Peltier coefficient of a junction $\ensuremath{\pi}_\ensuremath{\mathrm{ab}}$ is defined by the difference of the coefficients of the constituent materials $\ensuremath{\pi}_\ensuremath{\mathrm{ab}}=\ensuremath{\pi}_\ensuremath{\mathrm{a}}-\ensuremath{\pi}_\ensuremath{\mathrm{b}}$ . The direction of heat flow at a junction is thus defined by the choice of materials as well as the direction of the passing current. Furthermore, the Peltier coefficients are temperature dependent, just as the Seebeck coefficients.

Peltier coefficient and Seebeck coefficient are not independent of each other. From both a systematic approach using the method of moments as carried out in Chapter 3 as well as phenomenological thermodynamics (first Kelvin relation) [9], it follows that

$$\ensuremath{\pi}_\ensuremath{\mathrm{ab}} = \ensuremath{\alpha}_\ensuremath{\mathrm{ab}} \ensuremath{T}\,.$$ (2.7)

M. Wagner: Simulation of Thermoelectric Devices