Nanoscale Thermal Transport in Plasmonic Nanofocusing Structure With Strong Nonlocality

2014 ◽  
Author(s):  
Chen Chen ◽  
Zhidong Du ◽  
Liang Pan
Keyword(s):  
Heat Generation ◽  
Rapid Development ◽  
Local Thermal Equilibrium ◽  
Energy Concentration ◽  
Boltzmann Transport ◽  
Energy Carriers ◽  
Optical Energy ◽  
Diffusive Model ◽  
Plasmonic Nanofocusing ◽  
Non Equilibrium

Nanoscale optical energy concentration and focusing is crucial for many high-throughput nanomanufacturing applications, such as material processing, imaging and lithography. The use of surface plasmons has resulted in the rapid development of nanofocusing devices and techniques at spatial confinements as good as a few nanometers associated with strong nonlocal plasmonic response. However, operations of these plasmonic nanofocusing structures usually require extremely high optical energy density at nanoscale, which leads to intense structure heating and causes unreliable device functions and short device lifetimes. In many plasmonic applications, optical heating has become a very important issue, which has not been investigated intensively yet. In these structures, the ballistic transport and interface scattering of the energy carriers both become significant because the characteristic lengths of the devices are comparable to or smaller than the mean free paths of the carriers. A comprehensive model is desired to understand the heat generation and transport inside the plasmonic nanofocusing structures. This work studied the electromagnetic and optothermal responses of plasmonic nanofocusing nanostructures. At the nanometer length scale, the local optical response and diffusive thermal model are no longer sufficient to describe the device optothermal response because of the strong interactions between energy carriers and the ballistic nature of carriers. Here, we used the hydrodynamic Drude model to consider the nonlocality of plasmonic response and calculate the heat generation inside the metallic nanostructures. Starting from Boltzmann transport equation, we derived the energy transport equations for both electron and phonon systems under the relaxation-time approximations. The obtained multi-carrier ballistic-diffusive model was used to study the non-equilibrium heat transports inside the structures. We assume that the ballistic electrons originate from boundaries and the electron-photon couplings inside the structure, experiencing out-scattering only in the material. The optically-generated “hot” electrons are considered as ballistic and are treated separately from the “ordinary” electrons which are in local thermal equilibrium and have significantly lower energies. Meanwhile, the electron-phonon couplings are considered under the non-equilibrium conditions between the electron and phonon systems. Using our model, we further investigated the transient optothermal responses of a one-dimensional (1D) plasmonic nanofocusing structure. In comparison to the diffusive transport description, our multi-carrier ballistic-diffusive model can more accurately describe the optothermal responses of the plasmonic nanofocusing structures which are crucial for predicting the performance and the lifetime of the plasmonic nanofocusing devices.

A Study of Spatially-Resolved Non-Equilibrium in Laser-Irradiated Graphene Using Boltzmann Transport Equation

2013 ◽  
Author(s):  
Ajit K. Vallabhaneni ◽  
James Loy ◽  
Dhruv Singh ◽  
Xiulin Ruan ◽  
Jayathi Murthy
Keyword(s):  
Thermal Conductivity ◽  
Steady State ◽  
Laser Irradiation ◽  
Density Functional ◽  
Boltzmann Transport ◽  
Energy Carriers ◽  
Spatially Resolved ◽  
Scattering Rate ◽  
Phonon Generation ◽  
Non Equilibrium

Raman spectroscopy is typically used to characterize graphene in experiments and also to measure properties like thermal conductivity and optical phonon lifetime. The laser-irradiation processes underlying this measurement technique include coupling between photons, electrons and phonons. Recent experimental studies have shown that e-ph scattering limits the performance of graphene-based electronic devices due to the difference in their timescales of relaxation resulting in various bottleneck effects. Furthermore, recently published thermal conductivity measurements on graphene are sensitive to the laser spot size which strengthens the possibility of non-equilibrium between various phonon groups. These studies point to the need to study the spatially-resolved non-equilibrium between various energy carriers in graphene. In this work, we demonstrate non-equilibrium in the e-ph interactions in graphene by solving the linearized electron and phonon Boltzmann transport equations (BTE) iteratively under steady state conditions. We start by assuming that all the electrons equilibrate rapidly to an elevated temperature under laser-irradiation and they gradually relax by phonon emission and reach a steady state. The electron and phonon BTEs are coupled because the e-ph scattering rate depends on the phonon population while the rate of phonon generation depends on the e-ph scattering rate. We used density-functional theory/density-functional perturbation theory (DFT/DFPT) to calculate the electronic eigen states, phonon frequencies and the e-ph coupling matrix elements. We calculated the rate of energy loss from the hot electrons in terms of the phonon generation rate (PGR) which serve as an input for solving the BTE. Likewise, ph-ph relaxation times are calculated from the anharmonic lattice dynamics (LD)/FGR. Through our work, we obtained the spatially resolved temperature profiles of all the relevant energy carriers throughout the entire domain; these are impossible to obtain through experiments.

Local Thermal Non-equilibrium Analysis of Boundary Layer Flow of Carreau Fluid Over a Wedge in a Porous Medium

2021 ◽  
Author(s):  
Ramesh Kudenatti ◽  
Sandhya L
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Porous Medium ◽  
Boundary Layer Flow ◽  
Fluid Phase ◽  
Equilibrium Analysis ◽  
Local Thermal Equilibrium ◽  
Carreau Fluid ◽  
Layer Flow ◽  
Non Equilibrium

Abstract This work examines the steady two-dimensional mixed convection boundary layer flow of non-Newtonian Carreau fluid embedded in a porous medium. The impermeable wedge is at rest over which the momentum and thermal boundary layers form due to motion of Carreau fluid with a large Reynolds number. We consider local thermal non-equilibrium for which the temperature of the solid porous medium is different from that of fluid phase, and hence, a single heat-transport equation is replaced by a two-temperature model. The governed equations for flow and heat transfer are converted into a system of ordinary differential equations using a similarity approach. It is observed that local thermal non-equilibrium effects are dominant for small interphase heat transfer rate and porosity scaled conductivity parameters. It is shown that the temperature at any location of the solid porous medium is always higher than that of fluid phase. When these parameters are increased gradually the local thermal equilibrium phase is recovered at which the temperatures of the fluid and solid are identical at each pore. Similar trend is noticed for both shear-thinning and shear-thickening fluids. The results further show that heat exchange between the fluid and solid porous medium is similar to both assisted and opposed flows and Carreau fluid. The velocity and temperature fields for the various increasing fluid index, Grashof number and permeability show that the thickness of the momentum and thermal boundary layer is thinner.

Assessment of Thermal Non-Equilibrium Condition on Heat Transfer through a Channel Lined with Porous Media – Constant Wall Temperature

2011 ◽  
Vol 312-315 ◽  
pp. 33-38
Author(s):  
M. Abkar ◽  
P. Forooghi ◽  
A. Abbassi
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Porous Layer ◽  
Biot Number ◽  
Equilibrium Condition ◽  
Solid Phase ◽  
Local Thermal Equilibrium ◽  
Thermal Conductivity Ratio ◽  
Constant Wall Temperature ◽  
Non Equilibrium

In this paper, forced convection in a channel lined with a porous layer is investigated. The main goal is to assess the effect of local thermal non-equilibrium condition on overall heat transfer in the channel. The effects of thermal conductivity of solid and thickness of porous layer are also studied. Flow assumed to be laminar and fully developed. The Brinkman-Forchheimer model for flow as well as the two equation energy model is used. The results showed that when the problem tends to local thermal equilibrium condition, heat transfer is enhanced due to heat conduction through solid phase. Another factor, which can facilitate the heat transfer, is the increase of the thermal conductivity of solid material. This trend is sensitive to the thickness of porous layer and modified Biot number, which is a measure (criterion) of local fluid to solid heat transfer. As thickness and modified Biot number increase, the Nusselt number becomes more sensitive to the thermal conductivity ratio.

Numerical Analysis of Electro-Thermal Phenomena in Metal by Boltzmann Transport Equation for Electron

2005 ◽  
Author(s):  
Kohei Ito ◽  
Ryohei Muramoto ◽  
Isamu Shiozawa ◽  
Yasushi Kakimoto ◽  
Takashi Masuoka
Keyword(s):  
Transport Equation ◽  
Equilibrium Distribution ◽  
Boltzmann Transport Equation ◽  
Quasi Equilibrium ◽  
Boltzmann Transport ◽  
Simulation Based ◽  
Far From Equilibrium ◽  
New Formulation ◽  
Thermal Phenomena ◽  
Non Equilibrium

By the development of micro-fabrication technology, much smaller-size electronic devices will be soon available. In such a smaller device, a non-equilibrium state might appear in metal and/or semiconductor. In this case, it is difficult to estimate the device performance by the macroscopic transport equations that assume quasi-equilibrium distribution. We are developing a numerical simulation based on Boltzmann transport equation (BTE), which can analyze thermal and electric phenomena even when the state is far from equilibrium. In this study, we show a new formulation of BTE for free electron in metal and its calculation result: the thermoelectric power obtained agreed with that of experimental value: the heat flux derived by the non-equilibrium distribution was two-orders small than that estimated by thermal conductivity.

Modeling Electron-Phonon Nonequilibrium in Gold Films Using Boltzmann Transport Model

2009 ◽  
Vol 131 (8) ◽  
Author(s):  
Arvind Pattamatta ◽  
Cyrus K. Madnia
Keyword(s):  
Film Thickness ◽  
Pulse Duration ◽  
Laser Fluence ◽  
Laser Heating ◽  
Gold Film ◽  
Transport Model ◽  
Melting Time ◽  
Gold Films ◽  
Boltzmann Transport ◽  
Energy Carriers

Ultrashort-pulsed laser irradiation on metals creates a thermal nonequilibrium between electrons and the phonons. Previous computational studies used the two-temperature model and its variants to model this nonequilibrium. However, when the laser pulse duration is smaller than the relaxation time of the energy carriers or when the carriers’ mean free path is larger than the material dimension, these macroscopic models fail to capture the physics accurately. In this paper, the nonequilibrium between energy carriers is modeled via a numerical solution of the Boltzmann transport model (BTM) for electrons and phonons, which is applicable over a wide range of lengths and time scales. The BTM is solved using the discontinuous Galerkin finite element method for spatial discretization and the three-step Runge–Kutta temporal discretization. Temperature dependent electron-phonon coupling factor and electron heat capacity are used due to the strong electron-phonon nonequilibrium considered in this study. The results from the proposed model are compared with existing experimental studies on laser heating of macroscale materials. The model is then used to study laser heating of gold films, by varying parameters such as the film thickness, laser fluence, and pulse duration. It is found that the temporal evolution of electron and phonon temperatures in nanometer size gold films is very different from the macroscale films. For a given laser fluence and pulse duration, the peak electron temperature increases with a decrease in the thickness of the gold film. Both film thickness and laser fluence significantly affect the melting time. For a fluence of 1000 J/m2, and a pulse duration of 75 fs, gold films of thickness smaller than 100 nm melt before reaching electron-phonon equilibrium. However, for the film thickness of 2000 nm, even with the highest laser fluence examined, the electrons and phonons reach equilibrium and the gold film does not melt.

scholarly journals Thermal non-equilibrium of porous flow in a resting matrix applicable to melt migration: a parametric study

2021 ◽  
Author(s):  
Laure Chevalier ◽  
Harro Schmeling
Keyword(s):  
Heat Transfer ◽  
Parameter Space ◽  
Thermal Equilibrium ◽  
Scaling Laws ◽  
Numerical Solutions ◽  
Local Thermal Equilibrium ◽  
Physical Parameters ◽  
Minor Effect ◽  
Solid Temperature ◽  
Non Equilibrium

Abstract. Fluid flow through rock occurs in many geological settings on different scales, at different temperature conditions and with different flow velocities. Depending on these conditions the fluid will be in local thermal equilibrium with the host rock or not. To explore the physical parameters controlling thermal non-equilibrium the coupled heat equations for fluid and solid phases are formulated for a fluid migrating through a resting porous solid by Darcy flow. By non-dimensionalizing the equations three non-dimensional numbers can be identified controlling thermal non-equilibrium: the Peclet number Pe describing the fluid velocity, the heat transfer number A describing the local interfacial heat transfer from the fluid to the solid, and the porosity ϕ. The equations are solved numerically for the fluid and solid temperature evolution for a simple 1D model setup with constant flow velocity. Three stages are observed: a transient stage followed by a stage with maximum non-equilibrium fluid to solid temperature difference, ∆Tmax, and a stage approaching the steady state. A simplified time-independent ordinary differential equation for depth-dependent (Tf  – Ts) is derived and analytically solved. From these solutions simple scaling laws of the form (Tf  – Ts) = f (Pe, A, ϕ, H), where H is the non-dimensional model height, are derived. The solutions for ∆Tmax and the scaling laws are in good agreement with the numerical solutions. The parameter space Pe, A, ϕ, H is systematically explored. In the Pe – A – parameter space three regimes can be identified: 1) at high Pe (> 1) strong thermal non-equilibrium develops independently of Pe and A; 2) at low Pe (< 1) and low A (< 1) non-equilibrium decreases proportional to decreasing Pe; 3) at low Pe (<1) and large A (>1) non-equilbrium scales with Pe/A and thus becomes unimportant. The porosity ϕ has only a minor effect on thermal non-equilibrium. The time scales for reaching thermal non-equilibrium scale with the advective time-scale in the high Pe-regime and with the interfacial diffusion time in the other two low Pe – regimes. Applying the results to natural magmatic systems such as mid-ocean ridges can be done by estimating appropriate orders of Pe and A. Plotting such typical ranges in the Pe – A regime diagram reveals that a) interstitial melt flow is in thermal equilibrium, b) melt channelling as e.g. revealed by dunite channels may reach moderate thermal non-equilibrium, and c) the dyke regime is at full thermal non-equilibrium.

Prediction of Non-Equilibrium Heat Conduction Using Parallel Computation of the Phonon Boltzmann Transport Equation

2014 ◽  
Author(s):  
Syed A. Ali ◽  
Gautham Kollu ◽  
Sandip Mazumder ◽  
P. Sadayappan
Keyword(s):  
Heat Conduction ◽  
Transport Equation ◽  
Parallel Computation ◽  
Large Scale ◽  
Phonon Scattering ◽  
Boltzmann Transport Equation ◽  
Computational Time ◽  
Spectral Space ◽  
Boltzmann Transport ◽  
Non Equilibrium

Non-equilibrium heat conduction, as occurring in modern-day sub-micron semiconductor devices, can be predicted effectively using the Boltzmann Transport Equation (BTE) for phonons. In this article, strategies and algorithms for large-scale parallel computation of the phonon BTE are presented. An unstructured finite volume method for spatial discretization is coupled with the control angle discrete ordinates method for angular discretization. The single-time relaxation approximation is used to treat phonon-phonon scattering. Both dispersion and polarization of the phonons are accounted for. Three different parallelization strategies are explored: (a) band-based, (b) direction-based, and (c) hybrid band/cell-based. Subsequent to validation studies in which silicon thin-film thermal conductivity was successfully predicted, transient simulations of non-equilibrium thermal transport were conducted in a three-dimensional device-like silicon structure, discretized using 604,054 tetrahedral cells. The angular space was discretized using 400 angles, and the spectral space was discretized into 40 spectral intervals (bands). This resulted in ∼9.7×109 unknowns, which are approximately 3 orders of magnitude larger than previously reported computations in this area. Studies showed that direction-based and hybrid band/cell-based parallelization strategies resulted in similar total computational time. However, the parallel efficiency of the hybrid band/cell-based strategy — about 88% — was found to be superior to that of the direction-based strategy, and is recommended as the preferred strategy for even larger scale computations.

Investigation of the Non-Equilibrium Flow Phenomena in the Boundary Layer of the Scramjet Engine

2013 ◽  
Vol 284-287 ◽  
pp. 795-799
Author(s):  
Fa Qing Fan ◽  
Pei Yong Wang
Keyword(s):  
Boundary Layer ◽  
Stokes Equations ◽  
Operating Conditions ◽  
Local Thermal Equilibrium ◽  
Navier Stokes ◽  
Equilibrium Flow ◽  
Navier Stokes Equations ◽  
Flow Phenomena ◽  
Scramjet Engine ◽  
Non Equilibrium

High-speed and high-temperature are the characteristics of the flow field in scramjet engine; the regular non-slip wall boundary condition requires zero speed at wall; in the same time, the material temperature limit does not allow high wall temperature; therefore the velocity gradient and temperature gradient in the engine boundary layer are huge. If these gradients are too large, the traditional assumption of the local thermal equilibrium in the fluid will fail, the Navier-Stokes equations are no longer valid in the boundary layer. For the first time, the non-equilibrium flow phenomena in Scramjet engine is studied here. Appropriate turbulence model and fine grid are used to analyze the turbulent boundary layer of the Hyshot scramjet engine with three different operating conditions. The result of the CFD simulation shows that the local Knudsen number in the engine boundary layer is greater than the critical value with the operating conditions 40Km/Ma8 and 30Km/Ma8; they are non-equilibrium flow and the Navier-Stokes equations fails. Special treatment of the boundary conditions are needed for these kinds of flow. With the operating condition of 20Km/Ma6, the local thermal equilibrium condition is observed and conventional CFD method is valid.

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