An extended thermodynamic model for size-dependent thermoelectric properties at nanometric scales: Application to nanofilms, nanocomposites and thin nanocomposite films

Abstract

A new mathematical model is developed, describing size-dependent subcontinuum thermoelectric properties from an extended thermodynamic point of view. This model takes into account the non-local effects of heat transfer through phonons and electrons that are important at nanometric scales. These phenomena are extended to apply also for electric transfer as well as the Seebeck coefficient. This model includes at nanoscale size-dependent electron and phonon thermal conductivities, electric conductivity, Seebeck coefficient and carrier concentrations. We compared nanofilms to nanocomposites and assessed their thermoelectric performances in the form of a figure of merit using as an example Bismuth and BismuthTelluride materials. It appeared that the figure of merit increases considerably for nanofilms and nanocomposites with respect to bulk materials. This is caused by the scattering of phonons and electrons. Our model shows that this scattering effect is not only present at the boundary or particle-matrix interface of the nanosized material, but also within it. The effect of particle size and surface specularity has been investigated, showing that a decreasing value of the particle size and specularity increases the scattering effect and improves the thermoelectric properties. An extension towards thin films of nanocomposite has been presented.

Enhancement of a photovoltaic cell performance by a coupled cooled nanocomposite thermoelectric hybrid system, using extended thermodynamics

“…These equations give us now the evolution of , and , with the corresponding fluxes , and . The basic principles of EIT allow postulating additional evolution equations for these fluxes (who are now considered as independent variables) as [6] …”

“…In this approach, the heat flux is elevated to the status of independent variable at the same footing as the temperature. The total heat flux is assumed to be the sum of a phonon contribution and an electric one [6], which are due to the phonon and electron motion through the material:…”

“…One way to increase the efficiency of PV cells is using thermal management by means of heat sinks [2]. Otherwise, the waste heat can be used in order to be converted to more electricity via thermoelectric devices (TE) [3][4][5][6]. As a common PV cell converts a large amount of solar irradiant energy into heat, a hybrid PV cell and TE device (PVTE) may be a prospective way to improve the overall efficiency of solar energy [7].…”

“…The temperature difference stems from the operating system, while the figure of merit depends on material properties. For this purpose, we propose to use a nanocomposite TE device, so that the figure of merit can be considerably increased, even doubled [5,6]. The thermoelectric transport properties are derived by means of a new extended irreversible thermodynamic (EIT) model [5,13,14].…”

“…As for the TE device, the model takes into account, the nanoparticle size, both phonon and electron scattering in both the nanoparticles and the bulk matrix, the nanoparticle volume fraction. In order to maximize the thermoelectric efficiency, not only should the figure of merit be increased by the introduction of nanoparticles [6], but the temperature difference across it should also be optimized by means of a cooling (CL) device right under the TE device. By means of overall thermal modelling, it is the purpose to find optimal conditions for the PVTECL hybrid system.…”