8. Perspectives

36% in the performance, measured as mentioned above, of the coupled thermoelectric modules with respect to a single thermoelectric module is theoretically predicted. The analysis made in

We have analysed different aspects of the performance of thermoelectric films when an electric current flows through them, maintaining one of their sides at a constant temperature. First, we considered the effects of the size of the film on the Seebeck coefficient and the thermal and electrical conductivities as well as thermal inertia. This forms the basis for all the analysis of the problem of reducing the dimensions to the nanoscale. The introduction of such effects was done through the use of Eqs. (15)–(17) in the constitutive equations of the irreversible thermodynamics of electric charge and heat transport, Eqs. (12). When the latter are combined with the conservation equations of charge and energy, Eqs. (1)–(3), we arrive at the heat transport equation that was used systematically throughout the development of the analysis, Eq. (18). The different effects studied, namely, the wave behaviour of the propagation of heat, the response of the material to a pulse of electric current, the coupling of thermoelectric couples, the transition from the diffusive regime of heat transport to wave propagation, and so on were explained in terms of Eq. (18). The conclusions were diverse: (1)

Figure 11. Effect of Eqs. (15)–(17), which describe the variation of the transport and thermoelectric coefficients with the

<sup>E</sup>T=K.

size of the material <sup>l</sup>, on the thermoelectric figure of merit defined as usual: ZT <sup>¼</sup> <sup>σ</sup>S<sup>2</sup>

this section can be useful for the design of thermoelectric coolers.

7. Discussion and conclusions

56 Bringing Thermoelectricity into Reality

Undoubtedly, a work perspective in thermoelectric power generation and refrigeration systems is to bring to the nanoscale the dimensions of the elements that make up structured systems. There is a lot of work done in systems composed or structured from elements in the millimetric escale of lengths or in larger scales [38], but a very promising perspective is the construction of those energy converting systems from nano-components such as for instance, the case of 1D phononic crystals. Several problems on thermoelectric phenomena that require attention when going from the macro to the nanoscale are: effects of size on the thermoelectric properties of the components of the nanostructured systems, the wave character of the propagation of heat and the phenomena of thermal interference and resonance, the effect of wave propagation of heat in pulsed systems, the effects of size on irreversible processes, the simultaneous consideration of the effects of size and the temperature dependence of the properties of materials, the effect of thermal inertia on the wave propagation of heat. It is also necessary to study the relationship between entropy generation and thermoelectric conversion efficiency and between structure and efficiency. In relation to this, a working hypothesis is that it is possible to find a structure that minimizes the production of entropy and to exploit interference and resonance phenomena to improve the thermoelectric energy conversion efficiency.
