Denis Lemonnier

Monte Carlo transient phonon transport in silicon and germanium at nanoscales

Heat transport at nanoscales in semiconductors is investigated with a statistical method. The Boltzmann transport equation (BTE), which characterizes phonon motion and interaction within the crystal lattice, has been simulated with a Monte Carlo technique. Our model takes into account media frequency properties through the dispersion curves for longitudinal and transverse acoustic branches. The BTE collisional term involving phonon scattering processes is simulated with the relaxation times approximation theory. A new distribution function accounting for the collisional processes has been developed in order to respect energy conservation during phonons scattering events. This nondeterministic approach provides satisfactory results in what concerns phonon transport in both ballistic and diffusion regimes. The simulation code has been tested with silicon and germanium thin films; temperature propagation within samples is presented and compared to analytical solutions (in the diffusion regime). The two-material bulk thermal conductivity is retrieved for temperature ranging between 100 K and 500 K. Heat transfer within a plane wall with a large thermal gradient (250 K to 500 K) is proposed in order to expose the model ability to simulate conductivity thermal dependence on heat exchange at nanoscales. Finally, size effects and validity of heat conduction law are investigated for several slab thicknesses.

Monte Carlo simulation of phonon confinement in silicon nanostructures: Application to the determination of the thermal conductivity of silicon nanowires

The authors study the thermal conductivity of silicon nanowires by simulation of phonon motion and interactions through a dedicated Monte Carlo model. This model solves the Boltzmann transport equation, taking into account silicon acoustic mode dispersion curves and three phonon interactions (the normal and umklapp processes). The confinement, which limits the thermal conductivity in such structures, is described by diffuse reflection at lateral boundaries of the nanowire without any adjustment by a boundary collision time, which depends on a specularity factor. They compare simulation results to experimental measurements on similar nanostructures. A good agreement is achieved for almost all the considered diameters.

Coupled Radiation and Double Diffusive Convection in Nongray Air-CO2 and Air-H2O Mixtures in Cooperating Situations

This study highlights the interaction between gas radiation and double diffusive convection in cooperating cases. We consider a square differentially-heated cavity filled with nongray air-CO2 or air-H2O mixtures. The governing equations are solved by a finite-difference method. The radiative sources are evaluated by the discrete ordinates method associated to the SLW spectral model. Results obtained for two average concentrations of CO2 and H2O (10% and 25%) show that radiation influences the temperature and concentration fields by creating oblique stratifications. The Nusselt numbers are decreased, whereas the Sherwood numbers are only slightly reduced. These effects are accentuated in air-H2O mixtures.

Modeling semiconductor nanostructures thermal properties: The dispersion role

We study heat transport in semiconductor nanostructures by solving the Boltzmann Transport Equation (BTE) by means of the Discrete Ordinate Method (DOM). Relaxation time and phase and group velocitiy spectral dependencies are taken into account. The Holland model of phonon relaxation time is revisited and recalculated from dispersion relations (taken in litterature) in order to match bulk silicon and germanium values. This improved model is then used to predict silicon nanowire and nanofilm thermal properties in both ballistic and mesoscopic regimes.

Interaction of radiation with double-diffusive natural convection in a three-dimensional cubic cavity filled with a non-gray gas mixture in cooperating cases

ABSTRACT A three-dimensional (3D) numerical study has been performed to investigate the effects of non-gray gas radiation on double-diffusive natural convection in a cubic enclosure filled with either air–H2O or air–CO2 mixtures in cooperating situations. Gas radiation was taken into account by the discrete ordinates method (DOM) associated with the spectral line weighted-sum-of-gray-gases (SLW) spectral model. Results obtained for two average concentrations of H2O and CO2 (10% and 20%) show that radiation modifies the temperature and concentration structures by creating oblique stratifications. The heat transfer rate is decreased, whereas mass transfer is not much modified. In addition, a comparison between 2D and 3D results is presented.

Experimental investigations in an air-filled differentially-heated cavity at large Rayleigh Numbers

A large-scale experimental differentially heated cavity was built and instrumented. Rayleigh numbers up to 1.2×1011 can be obtained with a temperature difference, ΔT = 20°C, between the hot and cold walls leaning in the range of validity of the Boussinesq approximation. Previous data obtained locally for mean velocity by 2D LDV in the range give rise to questions regarding the general air flow circulation in the cavity. Particularly, a downstream flow along the vertical boundary layer was observed. This reverse flow caused by the temperature stratification outside this layer is not present in the upstream parts and was not previously observed in smaller cavities. The question of the global circulation in this cavity is thus posed. Evolution laws providing Nusselt numbers are also given and when possible compared to the literature for a large range of Rayleigh numbers.

Coupled temperature and velocity measurements in turbulent natural convection flows

The goal of this paper is to develop simultaneous measurements of the temperature and velocity in order to contribute to the development of models adapted to natural convection flows and better apprehend their turbulent characteristics. The experimental setup consists in a vertical open channel whose sidewalls are kept at ambient temperature. A heated square bar is placed into the lower part of this channel close from one of its wall. It drives air in the whole channel. The temperature of the bar is chosen to obtain a turbulent air flow. This study focuses on the measurement technique developed to realize synchronized temperature and velocity measurements in a turbulent natural convection flow. This technique permit to measure turbulent heat fluxes ( or ). Measurement strategies will be presented and discussed in the paper. Some experimental care is needed to avoid disturbing the airflow. The challenge is to choose two complementary measurement techniques which have to be synchronized but which cannot be carried out at the same location when a laser is used. In this study, the velocity and the temperature measurements are respectively carried out using PIV technique and a specific K type micro-thermocouple (12.7 ?m in diameter). The location of the thermocouple with respect to the laser sheet has been investigated as well as the influence of the laser on the temperature measurements. The criterion used for finding the best location is the correlation coefficient between the temperature and the velocity data. Some preliminary results of coupled velocity-temperature measurements are provided showing the feasibility of this kind of measurements.

Numerical investigation of coupled natural convection and radiation in a differentially heated cubic cavity filled with humid air. Effects of the cavity size

ABSTRACT A numerical study of natural convection with surface and air/H2O mixture radiation in a differentially heated cubic square cavity is presented. The coupled flow and heat transfers in the cavity are predicted by coupling a finite volume method with a spectral line weighted sum of gray gase model to describe gas radiative properties. The radiative transfer equation is solved by means of the discrete ordinate method. Simulations are performed at Ra = 106, considering different combinations of passive wall and/or gas radiation properties and different cavity length. It was found that in presence of a participative medium representative of building, cavity length has a strong influence on temperature and velocity fields which affect the global circulation and heat transfers in the cavity. For each steady-state solution, the convective and radiative contributions to the global heat transfer are discussed. More specifically, boundary layer thickness, thermal stratification parameter, and three-dimensional effects are compared to pure convective case results. The results suggest that radiative effects, often considered as negligible in view of the relatively low optical thickness, may not be neglected when trying to predict regime transitions.

Non-gray gas radiation effect on mixed convection in lid driven square cavity

A numerical study is performed to investigate the effect of non-gray radiation on mixed convection in a vertical two sided lid driven square cavity filled with air-H2O-CO2 gas mixture. The vertical moving walls of the enclosure are maintained at two different but uniform temperatures. The horizontal walls are thermally insulated and considered as adiabatic walls. The governing differential equations are solved by a finite-volume method and the SIMPLE algorithm was adopted to solve the pressure–velocity coupling. The radiative transfer equation (RTE) is solved by the discrete ordinates method (DOM). The spectral line weighted sum of gray gases model (SLW) is used to account for non-gray radiation properties. Simulations are performed in configurations where thermal and shear forces induce cooperating buoyancy forces. Streamlines, isotherms, and Nusselt number are analyzed for three different values of Richardson’s number (from 0.1 to 10) and by considering three different medium (transparent medium, gray m...

Buoyancy ratio effects on coupled radiation and double-diffusive convection in non-gray air-H 2 O mixtures

In this paper we study the effect of the (mass-to-thermal) buoyancy ratio N on the interaction between gas radiation and double diffusive convection in a square cavity filled with a non-gray air-H2O mixtures at constant average concentration of H2O (13%). Uniform temperatures and concentrations are imposed along the vertical walls, while the horizontal walls are assumed to be adiabatic and impermeable to mass transfer. The governing equations are solved by a finite-difference method and the spectral dependency of gas radiative properties is handled by the SLW model of Denison and Webb. The results obtained, in opposing flow case, are graphically displayed for three value of N (-0.15, -0.95 and -1.91) to illustrate the influence of this parameter on concentration, temperature and velocity profiles as well as heat and mass flux. Non-gray results are also compared to gray solutions.