Federico Vázquez

The causal relationships between the physical fields that intervene in the description of heat transport in rigid heat-conducting solids are analyzed in the light of the transfer of information. The analysis runs through three heat transport models, namely, the Fourier (F), the Maxwell-Cattaneo-Vernotte (MCV), and the Jeffreys-Guyer-Krumhansl (J-GK) models. It is argued that the MCV model can be obtained (to first order) by introducing a delay time into the F model, and, similarly, the GK model can be obtained from the MCV model. This implicit causality allows to identify two sets of causal physical fields. The causal relationship of each of the pairs is then characterized by the transfer of information measured with the so-called transfer entropy. Validation experiments are used to interpret the results, which leads to our main conclusion: information flows from spatial inhomogeneities to heat flow and temporal temperature variation, thus clarifying causal relationships in the system. Such causality vanishes for long timescales.

In this work we propose a transfer entropy approach to discern time-delay couplings within non-linear and stochastic coupled systems. We introduce the concept of ‘time-wise transfer entropy’, which quantifies the reduction in future uncertainty for a process Y by considering the values of processes X and Y at a specific past moment. The key advantage of our approach is a reduction in the number of parameters required for estimation when compared to other transfer entropy methodologies. Our proposed time-wise transfer entropy not only lends itself to effective estimation from actual data but also enhances our understanding of the origins of seemingly ‘spurious’ couplings observed in some transfer entropy approaches. To validate our method, we apply it to determine coupling delays in minimal stochastic models where the time-wise transfer entropy can be precisely derived in terms of the Shannon entropy. We further assess the technique performance in coupled non-linear systems with delays, demonstrating its capacity to accurately reproduce the corresponding coupling delays. The developed technique may be useful in the analysis of multifactor non-linear physical systems where complex causal relationships may exist.

Due to their potential applications in energy production based on waste heat, direct solar radiation or other energy sources, semiconductor materials have for years attracted the attention of theoretical and experimental researchers. The focus has been on improving the performance of thermoelectric devices through several strategies and special interest has been placed on materials with spatially inhomogeneous transport properties. Inhomogeneity can be achieved in various ways, all of them leading, to a greater or lesser extent, to an improvement of the thermoelectric performance. In this paper, general linear heat and electric charge transport processes in inhomogeneous materials are addressed. The guiding idea followed here is that there exists a relationship between inhomogeneity (structuring), minimum entropy production and performance which may be fruitfully exploited for designing more efficient thermoelectric semiconductor devices. We first show that the stationary states of such materials are minimum global entropy production states. This constitutes an extension of the validity of Prigogine’s minimum entropy principle. The heat and charge transport equations obtained within the framework of classical irreversible thermodynamics are solved to find the stationary profiles of temperature and self-consistent electric potential in a one-dimensional model of a silicon–germanium alloy subjected to an external temperature difference. This allows us to assess the effect of the spatial inhomogeneity on the thermoelectric performance. We find that, regardless of the value of the applied temperature difference, the system may efficiently operate in a regime of minimum entropy production and high efficiency.

In this work, we consider a rigid heat conductor graded material subjected to an oscillating thermal signal applied on its boundary. We use a recently proposed novel concept, the so-called spectral diffusivity, to characterize the response of the material to an externally applied variable temperature difference. The spectral diffusivity has the physical meaning of an effective transport coefficient. We found a frequency window between 10−2 and 102 Hz wherein the spectral diffusivity increases, showing a maximum. The transport equation was numerically solved to calculate the average heat flowing through the material. We found that it also increased having a maximum in the mentioned range of frequencies. We then investigated the thermal rectification of the material finding a maximum in the same frequency range. The thermal rectification, as well as the spectral diffusivity, improved as the inhomogeneity of the heat conductivity of the material was higher. The spectral diffusivity enables a more in-depth analysis of heat wave transfer, and it contributes to a better understanding of the material response in front of periodic thermal disturbances.

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.

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.

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.

There has been much interest in semiconductor superlattices because of showing very low thermal conductivities. This makes them especially suitable for applications in a variety of devices for 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.

This paper presents a numerical analysis of the transient heat transfer problem arising when a functionally graded material is subjected to a fixed temperature difference. Varying the gradation of the system, the thermal performance of the material is assessed both in time-dependent and steady-state conditions by means of temperature profiles and entropy production. One of the main contributions of this paper is the analysis of the system in the transient, from which it is found that the entropy production has a non-monotonic behaviour since maximum and minimum values of this physical quantity could be identified by varying the grading profile of the material. The latter allows to propose an optimization criterion for functionally graded materials which consists of the identification of spatial regions where temperature gradients are large and find thermal conductivity profiles that attenuate those gradients, thus reducing the thermal stresses present inside the material.