New and Recent Results for Thermoelectric Energy Conversion in Graded Alloys at Nanoscale

In this article, we review the main features of nonlocal and nonlinear heat transport in nanosystems and analyze some celebrated differential equations which describe this phenomenon. Then, we present a new heat-transport equation arising within the so-called thermomass theory of heat conduction. We illustrate how such a theory can be applied to the analysis of the efficiency of a thermoelectric energy generator constituted by a Silicon-Germanium alloy, as the application and new results for a nanowire of length L=100 nm, are presented as well. The thermal conductivity of the nanowire as a function of composition and temperature is determined in light of the experimental data. Additionally, the best-fit curve is obtained. The dependency of the thermoelectric efficiency of the system on both the composition and the difference of temperature applied to its ends is investigated. For the temperatures T=300 K, T=400 K, and T=500 K, we calculate the values of the composition corresponding to the optimal efficiency, as well as the optimal values of the thermal conductivity. Finally, these new results are compared with recent ones obtained for a system of length L=3 mm, in order to point out the benefits due to the miniaturization in thermoelectric energy conversion.