In this chapter, the physical principles to be taken into account in thermoelectricity at the nanometre scale are discussed. We argue that the numerical methods must also be adapted to the emergence of new physical behaviours at that scale, namely, wave propagation of heat, diffusive-ballistic transition, nonlocal effects, among others. It is first shown that thermoelectric phenomena at the nanoscale can be described by introducing thermodynamic inertia and nonlocal effects. The transport equations are obtained from the thermodynamics of irreversible processes. After this, we introduce the Spectral Chebyshev Collocation method as a well-suited numerical method to deal with the new physical behaviours appearing at the nanoscale. We then show the use of these formalisms to analyse specific and interesting aspects of the optimization of pulsed thermoelectricity and coupled thermoelectric modules.
Part of the book: Bringing Thermoelectricity into Reality