There has been much interest in semiconductor superlattices because of their low thermal conductivities. This makes them especially suitable for applications in a variety of devices for the thermoelectric generation of energy, heat control at the nanometric length scale, etc. Recent experiments have confirmed that the effective thermal conductivity of superlattices at room temperature have a minimum for very short periods (in the order of nanometers) as some kinetic calculations had anticipated previously. This work will show advances on a thermodynamic theory of heat transport in nanometric 1D multilayer systems by considering the separation of ballistic and diffusive heat fluxes, which are both described by Guyer-Krumhansl constitutive equations. The dispersion relations, as derived from the ballistic and diffusive heat transport equations, are used to derive an effective heat conductivity of the superlattice and to explain the minimum of the effective thermal conductivity.

In this paper we undertake the theoretical analysis of a two-stage semiconductor thermoelectric module (TEM) which contains an arbitrary and different number of thermocouples, n₁ and n₂, in each stage (pyramid-styled TEM). The analysis is based on a dimensionless entropy balance set of equations. We study the effects of n₁ and n₂, the flowing electric currents through each stage, the applied temperatures and the thermoelectric properties of the semiconductor materials on the exergetic efficiency. Our main result implies that the electric currents flowing in each stage must necessarily be different with a ratio about 4.3 if the best thermal performance and the highest temperature difference possible between the cold and hot side of the device are pursued. This fact had not been pointed out before for pyramid-styled two stage TEM. The ratio n₁/n₂ should be about 8.

In this paper, we undertake the thermodynamical analysis of the diffusive transport to wave propagation transition in heat conducting thin films. Several constitutive equations have been conceived to describe heat transport but most fail at the nanometric length scales, where size effects must be taken into account or at time scales in the order of magnitude of heat carriers relaxation time, as for example when a laser pulse is applied to the system. The analysis is based on Jeffrey's model since it allows a jointed description of Fourier and Cattaneo heat conduction mechanisms. Jeffrey's model is complemented with a size dependent heat conductivity derived from Boltzmann transport equation. We study the diffusive transport to wave propagation transition in terms of the group and phase velocity of propagating modes, the system's effective thermodynamic susceptibility, the statistical properties of heat flux fluctuations, and the entropy produced in a thin heat conducting film. Jeffrey's model predicts a kind of discontinuity in the entropy production for thickness film of the order of magnitude of heat carrier mean free path which is corroborated by simulations results from the literature.

A non-Fourier thermal transport regime characterizes the heat conduction in solids with internal structure. Several thermodynamic theories attempt to explain the separation from the Fourier regime in such kind of systems. Here we develop a two-temperature model to describe the non-Fourier regime from the principles of non-equilibrium thermodynamics. The basic assumption is the existence of two well-separated length scales in the system, namely, one related with the matrix dimension (bulk) and the other with the characteristic length of the internal structure. Two Fourier type coupled transport equations are obtained for the temperatures which describe the heat conduction in each of the length scales. Recent experimental results from several groups on the thermal response of different structured materials are satisfactorily reproduced by using the coupling parameter as a fitting parameter. The similarities and differences of the present formalism with other theories are discussed.

In this paper, we address the problem of heat and electric charge transport in a thermoelectric nanoscaled layer when an electric current is applied. The analysis is based on constitutive equations of the Maxwell-Cattaneo type describing the time evolution of dissipative flows with transport and thermoelectric coefficients depending on the width of the layer. This introduces memory and nonlocal effects and consequently a wave-like behaviour of system's temperature. We study the effects of the application of an electric current in two cases, namely, a constant current and a pulsed current. The time evolution of the system and the stationary state are determined. Besides the well known supercooling effect obtained when the electric pulse is applied, our results show the existence of a similar effect during the transient due to the wave-like behaviour of the temperature. The thermal figure of merit (TFM) is calculated at the minimum temperature reached during the supercooling, both in the transient and the pulsed regime. The maximum value of TFM in the transient reaches 114 improving the value of long length scale devices by a factor of 100. When the electric pulse is applied, TFM is improved by a factor of 20 over long length scale devices. We use the spectral methods of solution which assure a well representation of wave behaviour of heat and electric charge in short time scales given their spectral convergence.

A restricted variational formulation for extended irreversible thermodynamics is proposed. Then, it is applied to a heat- and electricity-conducting viscous fluid, and the resulting equations are reduced to order two to be compared with those well known of kinetic theory. A better understanding of the phenomenological coefficients than in previous reported works is obtained.