Jose Ordonez-Miranda

On the thermal conductivity of particulate nanocomposites

The modified effective medium approximation model proposed by Minnich and Chen [Appl. Phys. Lett. 91, 073105 (2007)] for the thermal conductivity of nanocomposites is extended for spheroidal inclusions. It is shown that the dependence of the thermal conductivity of nanocomposites on the shape and size of particle inclusions can be described by: (1) the collision cross-section per unit volume of the particles and (2) the mean distance that the energy carriers (electrons or phonons) can travel inside the particles. The predictions of this analytical approach are in good agreement with available data obtained through numerical calculations of the Boltzmann equation.

Quantum thermal transistor

We demonstrate that a thermal transistor can be made up with a quantum system of three interacting subsystems, coupled to a thermal reservoir each. This thermal transistor is analogous to an electronic bipolar one with the ability to control the thermal currents at the collector and at the emitter with the imposed thermal current at the base. This is achieved by determining the heat fluxes by means of the strong-coupling formalism. For the case of three interacting spins, in which one of them is coupled to the other two, that are not directly coupled, it is shown that high amplification can be obtained in a wide range of energy parameters and temperatures. The proposed quantum transistor could, in principle, be used to develop devices such as a thermal modulator and a thermal amplifier in nanosystems.

The effect of the electron-phonon coupling on the effective thermal conductivity of metal-nonmetal multilayers

The metal-nonmetal interface plays a critical role in modern electronic and energy conversion devices. For example, metal-nonmetal multilayered structures have recently been proposed as promising materials for solid-state thermionic devices, which could potentially achieve an efficiency that might not be feasible for metals or semiconductors alone. In this work, the effective thermal conductivity of a metal-nonmetal multilayered system (superlattices) is studied using the two-temperature model of heat conduction. By defining the total interfacial thermal resistance, which strongly depends on the electron-phonon coupling factor, it is shown that the thermal conductivity of the system has a simple interpretation as the sum of thermal resistances in series. The role of the electron-phonon coupling and the phonon-phonon interfacial thermal resistance on the total interfacial thermal resistance is discussed. The derived analytical expressions show that the effective thermal conductivity of the multilayered str...

A crowding factor model for the thermal conductivity of particulate composites at non-dilute limit

The effective thermal conductivity models for particulate composites are usually restricted to the dilute limit, with volumetric concentrations of particles typically less than 15%. By considering the particle interactions through a crowding factor, in this work, a new formula is developed to describe the thermal conductivity of composites with a dielectric matrix, for volume fractions of particles up to their maximum packing fraction. The crowding factor model is then applied to analyze two particulate composites with dielectric or metallic particles, where the effects of both interfacial thermal resistance and the electron-phonon coupling are taken into account. It is shown that the predictions of the proposed crowding factor model are larger than the ones predicted by the dilute-limit models, for composites with high volume fractions of particles, due to the particle interactions. The proposed crowding factor model extends the applicability of various thermal conductivity models for composites reported...

A model for the effective thermal conductivity of metal-nonmetal particulate composites

The effective thermal conductivity of particulate composites with oriented spheroidal metallic particles embedded in a dielectric matrix is analyzed under the framework of the two-temperature model of heat conduction. The obtained analytical results show that the effective thermal conductivity depends strongly on (1) the relative size of the particle inclusions with respect to the electron-phonon coupling length and (2) the ratio between the electron and phonon thermal conductivities. The effect of the electron-phonon coupling inside metallic particles is expressed by the reduction of the composite thermal conductivity with respect to its corresponding values obtained for an infinite electron-phonon coupling factor, where the analysis could be established based on the Fourier law of heat conduction. It is shown that the composite thermal conductivity has upper and lower bounds, which are determined by the particle size in comparison with the electron-phonon coupling length. The generalized model for spher...

A constitutive equation for nano-to-macro-scale heat conduction based on the Boltzmann transport equation

A constitutive equation for heat conduction is derived from the exact solution of the Boltzmann transport equation under the relaxation time approximation. This is achieved by a series expansion on multiple space derivatives of the temperature and introducing the concept of thermal multipoles, where the thermal conductivity defined under the framework of the Fourier law of heat conduction is just the first thermal pole. It is shown that this equation generalizes the Fourier law and Cattaneo equation of heat conduction, and it depends strongly on the relative values of the length and time scales compared with the mean-free path and mean-free time of the energy carriers, respectively. In the limiting case of steady-state heat conduction, it is shown that the heat flux vector depends on a spatial scale ratio whose effects are remarkable in the micro-scale spatial domains. By applying a first-order approximation of the obtained thermal multipole expansion to the problem of transient heat conduction across a t...

Steady state and modulated heat conduction in layered systems predicted by the analytical solution of the phonon Boltzmann transport equation

Based on the phonon Boltzmann transport equation under the relaxation time approximation, analytical expressions for the temperature profiles of both the steady state and modulated heat conduction inside a thin film deposited on a substrate are derived and analyzed. It is shown that these components of the temperature depend strongly on the ratio between the film thickness and the average phonon mean free path (MFP), and they exhibit the diffusive behavior as predicted by the Fouriers law of heat conduction when this ratio is much larger than unity. In contrast, in the ballistic regime when this ratio is comparable to or smaller than unity, the steady-state temperature tends to be independent of position, while the amplitude and the phase of the modulated temperature appear to be lower than those determined by the Fouriers law. Furthermore, we derive an invariant of heat conduction and a simple formula for the cross-plane thermal conductivity of dielectric thin films, which could be a useful guide for understanding and optimizing the thermal performance of the layered systems. This work represents the Boltzmann transport equation-based extension of the Rosencwaig and Gersho work [J. Appl. Phys. 47, 64 (1976)], which is based on the Fouriers law and has widely been used as the theoretical framework for the development of photoacoustic and photothermal techniques. This work might shed some light on developing a theoretical basis for the determination of the phonon MFP and relaxation time using ultrafast laser-based transient heating techniques.

Thermal conductivity of nano-layered systems due to surface phonon-polaritons

The effective thermal conductivity of a layered system due to the propagation of surface phonon-polaritons is studied. We analytically demonstrate that the thermal conductivity of a set of nanolayers can be described as one of a single layer with an effective permittivity, which does not ordinarily appear in nature and depends on the permittivities and thicknesses of the individual components. For a two-layer system of SiO2 and BaF2 surrounded by air, it is shown that: (i) the propagation length of surfaces phonon-polaritons can be as high as 3.3 cm for a 200 nm-thick system. (ii) The thermal conductivity of the system with total thickness of 50 nm is 3.4 W/m·K, which is twice that of a single layer of SiO2, at 500 K. Higher values are found for higher temperatures and thinner layers. The results show that an ensemble of layers provides more channels than a single layer for the propagation of surface phonon-polaritons and therefore for the enhancement of the thermal conductivity of common polar materials.

On the stability of the exact solutions of the dual-phase lagging model of heat conduction.

The dual-phase lagging (DPL) model has been considered as one of the most promising theoretical approaches to generalize the classical Fourier law for heat conduction involving short time and space scales. Its applicability, potential, equivalences, and possible drawbacks have been discussed in the current literature. In this study, the implications of solving the exact DPL model of heat conduction in a three-dimensional bounded domain solution are explored. Based on the principle of causality, it is shown that the temperature gradient must be always the cause and the heat flux must be the effect in the process of heat transfer under the dual-phase model. This fact establishes explicitly that the single- and DPL models with different physical origins are mathematically equivalent. In addition, taking into account the properties of the Lambert W function and by requiring that the temperature remains stable, in such a way that it does not go to infinity when the time increases, it is shown that the DPL model in its exact form cannot provide a general description of the heat conduction phenomena.

Optimized thermal amplification in a radiative transistor

The thermal performance of a far-field radiative transistor made up of a VO2 base in between a blackbody collector and a blackbody emitter is theoretically studied and optimized. This is done by using the grey approximation on the emissivity of VO2 and deriving analytical expressions for the involved heat fluxes and transistor amplification factor. It is shown that this amplification factor can be maximized by tuning the base temperature close to its critical one, which is determined by the temperature derivative of the VO2 emissivity and the equilibrium temperatures of the collector and emitter. This maximization is the result of the presence of two bi-stable temperatures appearing during the heating and cooling processes of the VO2 base and enables a thermal switching (temperature jump) characterized by a sizeable variation of the collector-to-base and base-to-emitter heat fluxes associated with a slight change of the applied power to the base. This switching effect leads to the optimization of the ampl...