Michel Lallemand

Analyse de la conduction de la chaleur aux temps ultra-courts dans un solide par la thermodynamique irréversible étendue et la dynamique moléculaire

Abstract Instantaneous heat propagation and thermodynamic local equilibrium cannot be assumed when solving space and time microscale problems. Therefore, we reconsider the thermodynamics basis of the Fourier law in order to obtain the new heat conduction models: the hyperbolic heat equation (EH) and the modified hyperbolic equation (EHM). We have performed molecular dynamics (DM) experiments which are independent of any thermodynamic model, to test the macroscopic approaches. We show that the solutions of the EH and the EHM do not agree with the numerical experiments and that the MD results are strongly dependent on the way from which the macroscopic conditions are simulated in the microscopic point of view.

Conductive–radiative coupling in an absorbing–emitting axisymmetric medium

Abstract A modeling of simultaneous radiation–conduction in axisymmetric semi-transparent motionless bodies (hereafter labeled stm) is proposed. The stm is an emitting–absorbing medium with gray spectral radiative properties. Its interfaces are smooth with specular reflection; they are assumed to be opaque or transparent. The two-dimensional modeling is based on a double-grid representation: (i) a physical one corresponding to curvilinear coordinates adapted to the stm body shape, in which the radiative source is calculated by means of a ray-tracing technique and the formal solution of the radiative transfer equation (RTE), and (ii) an abstract one with an orthogonal grid for which the enthalpy equation is solved by a finite differences scheme. The nonlinear discretized equations are solved iteratively by passing from one to the other representation. Results are presented for the cases of a finite length cylinder and a truncated paraboloid both fitted with prescribed temperatures at the ending black cross sections, the lateral surface being opaque or transparent, and subjected to an imposed uniform temperature. In the case of the cylinder, results are compared with those obtained by a discrete ordinates method in curvilinear orthogonal coordinates.

Transient heat transfer in a Lennard-Jones crystal by molecular dynamics

The phenomenological description of heat conduction problems in non-continuous media by the Fourier law, is called into question when thermal transfers are studied at both temporal and space microscales. Several Equilibrium and Non Equilibrium Molecular Dynamics (EMD and NEMD) experiments have been carried out in order to specify the nature of the heat transfer at short times in a Lennard-Jones solid. Presented are (i) the hydrodynamic, the heat flux and the phonon relaxation times (respectively ru, rv and rp) computations done thanks to EMD experiments. ~v is deduced from a heat flux fluctuations description, and re is worked out from the Peierls thermal conductivity definition in the frame of the Deybe model. (ii) The response of the lattice to a kinetic energy step which displays wave-like phenomena of coherent and incoherent nature for times of the order of some phonon relaxation times. An analysis in terms of mode velocities confirms the presence of acoustic and thermal (second sound) wave propagation.

SPECIFIC FREQUENCY INTEGRATION METHOD APPLIED TO THERMALLY NONHOMOGENEOUS HYDROGEN-HELIUM GAS MIXTURE

Abstract A frequency integration method applied to the calculation of total radiative quantities in thermally inhomogeneous hydrogen-helium gas mixture is presented. First, the absorption spectrum of an hydrogen-helium gas mixture at high temperature (in the range 3000–30 000 K) has to be determined. Consequently, a review of the theoretical determination of the hydrogen-helium gas mixture absorption properties is performed under the assumption of local chemical and thermodynamical equilibria for a given set of temperature, pressure and initial molar fractions of the mixture. Cross-sections calculations are presented for the following absorption optical processes: electronic transitions bound-free and free-free of the negative hydrogen ion, bound-free, free-free and bound-bound of the hydrogen atom and the determination of the exact lines shapes is carefully detailed in the framework of three models. The frequency integration method suitable for the hydrogen-helium absorption coefficient spectrum is based on a spectral data bank that makes it fast and accurate. Absorbing and emitting radiative properties resulting from the model are checked in the case of a parallel plane layer with prescribed temperature whose the exact solution is known. A study on the different spectral ranges contribution in the radiative source and the net radiative flux near the walls is performed. Then, the appropriated choice of the lines calculation model is discussed.