Hatim Machrafi

An extended thermodynamic model of transient heat conduction at sub-continuum scales

A thermodynamic description of transient heat conduction at small length and timescales is proposed. It is based on extended irreversible thermodynamics and the main feature of this formalism is to elevate the heat flux vector to the status of independent variable at the same level as the classical variable, the temperature. The present model assumes the coexistence of two kinds of heat carriers: diffusive and ballistic phonons. The behaviour of the diffusive phonons is governed by a Cattaneo-type equation to take into account the high-frequency phenomena generally present at nanoscales. To include non-local effects that are dominant in nanostructures, it is assumed that the ballistic carriers are obeying a Guyer–Krumhansl relation. The model is applied to the problem of transient heat conduction through a thin nanofilm. The numerical results are compared with those provided by Fourier, Cattaneo and other recent models.

An extended irreversible thermodynamic modelling of size-dependent thermal conductivity of spherical nanoparticles dispersed in homogeneous media

The effective thermal conductivity of nanocomposites constituted by nanoparticles and homogeneous host media is discussed from the point of view of extended irreversible thermodynamics. This formalism is particularly well adapted to the description of small length scales. As illustrations, dispersion of Si nanoparticles in Ge (respectively, SiO2 in epoxy resin) homogeneous matrices is investigated, the nanoparticles are assumed to be spherical with a wide dispersion. Four specific problems are studied: the dependence of the effective thermal conductivity on the volume fraction of particles, the type of phonon scattering at the interface particle–matrix, the radius of the nanoparticles and the temperature.

Effective thermal conductivity of spherical particulate nanocomposites: comparison with theoretical models, Monte Carlo simulations and experiments

The purpose of this work is to study heat conduction in systems that are composed out of spherical micro-and nanoparticles dispersed in a bulk matrix. Special emphasis will be put on the dependence of the effective heat conductivity on various selected parameters as dimension and density of particles, interface interaction with the matrix. This is achieved by combining the effective medium approximation and extended irreversible thermodynamics, whose main feature is to elevate the heat flux vector to the status of independent variable. The model is illustrated by three examples: Silicium-Germanium, Silica-epoxy-resin and Copper-Silicium systems. Predictions of our model are in good agreement with other theoretical models, Monte-Carlo simulations and experimental data.

Time-dependent Marangoni-Bénard instability of an evaporating binary-liquid layer including gas transients

We are here concerned with Benard instabilities in a horizontal layer of a binary liquid, considering as a working example the case of an aqueous solution of ethanol with a mass fraction of 0.1. Both the solvent and the solute evaporate into air (the latter being insoluble in the liquid). The system is externally constrained by imposing fixed “ambient” pressure, humidity, and temperature values at a certain effective transfer distance above the liquid-gas interface, while the ambient temperature is also imposed at the impermeable rigid bottom of the liquid layer. Fully transient and horizontally homogeneous solutions for the reference state, resulting from an instantaneous exposure of the liquid layer to ambient air, are first calculated. Then, the linear stability of these solutions is studied using the frozen-time approach, leading to critical (monotonic marginal stability) curves in the parameter plane spanned by the liquid layer thickness and the elapsed time after initial contact. This is achieved fo...

General constitutive equations of heat transport at small length scales and high frequencies with extension to mass and electrical charge transport

Abstract A generalized heat transport equation applicable at small length and short time scales is proposed. It is based on extended irreversible thermodynamics with an infinite number of high-order heat fluxes selected as state variables. Extensions of Fick’s and Ohm’s laws are also formulated. As a numerical illustration, heat conduction in a rigid body subject to fixed and oscillatory temperature boundary conditions is discussed.

Heat transfer at nanometric scales described by extended irreversible thermodynamics

Abstract The purpose of this work is to present a study on heat conduction in systems that are composed out of spherical and cylindrical micro- and nanoparticles dispersed in a bulk matrix. Special emphasis is put on the dependence of the effective heat conductivity on various selected parameters as particle size and also its shape, surface specularity and density, including particle-matrix interaction. The heat transfer at nanometric scales is modelled using extended irreversible thermodynamics, whose main feature is to elevate the heat flux vector to the status of independent variable. The model is illustrated by a Copper-Silicium (Cu-Si) system. It is shown that all the investigated parameters have a considerable influence, the particle size being especially useful to either increase or decrease the effective thermal conductivity.

Effect of including a gas layer on the gel formation process during the drying of a polymer solution

Abstract.In this paper, we study the influence of the upper gas layer on the drying and gelation of a polymer solution. The gel is formed due to the evaporation of the binary solution into (inert) air. A one-dimensional model is proposed, where the evaporation flux is more realistically described than in previous studies. The approach is based on general thermodynamic principles. A composition-dependent diffusion coefficient is used in the liquid phase and the local equilibrium hypothesis is introduced at the interface to describe the evaporation process. The results show that the high thickness of the gas layer reduces evaporation, thus leading to longer drying times. Our model is also compared with more phenomenological descriptions of evaporation, for which the mass flux through the interface is described by the introduction of a Peclet number. A global agreement is found for appropriate values of the Peclet numbers and our model can thus be considered as a tool allowing to link the value of the empirical Peclet number to the physics of the gas phase. Finally, in contrast with other models, our approach emphasizes the possibility of very fast gelation at the interface, which could prevent all Marangoni convection during the drying process.Graphical abstract