On the motion induced in a gas confined in a small-scale gap due to instantaneous boundary heating

2007 ◽  
Vol 593 ◽  
pp. 453-462 ◽  
Author(s):  
A. MANELA ◽  
N. G. HADJICONSTANTINOU
Keyword(s):  
Early Time ◽  
Mean Free Path ◽  
Small Scale ◽  
Characteristic Time Scale ◽  
Relative Temperature ◽  
The Mean ◽  
Gas Molecules ◽  
Hydrodynamic Fields ◽  
Gap Width ◽  
Good Agreement

We analyse the time response of a gas confined in a small-scale gap (of the order of or smaller than the mean free path) to an instantaneous jump in the temperature of its boundaries. The problem is formulated for a collisionless gas in the case where the relative temperature jump at each wall is small and independent of the other. An analytic solution for the probability density function is obtained and the respective hydrodynamic fields are calculated. It is found that the characteristic time scale for arriving at the new equilibrium state is of the order of several acoustic time scales (the ratio of the gap width to the most probable molecular speed of gas molecules). The results are compared with direct Monte Carlo simulations of the Boltzmann equation and good agreement is found for non-dimensional times (scaled by the acoustic time) not exceeding the system Knudsen number. Thus, the present analysis describes the early-time behaviour of systems of arbitrary size and may be useful for prescribing the initial system behaviour in counterpart continuum-limit analyses.

Design and Optimization of Conductive Heat Trees at Micro and Nanoscales for Cooling Electronics

2012 ◽  
Author(s):  
Masoud Daneshi ◽  
Ebrahim Shirani
Keyword(s):  
Electronic Devices ◽  
Mean Free Path ◽  
Small Scale ◽  
Conductive Heat ◽  
Structural Dimension ◽  
Cooling Systems ◽  
Nano Technology ◽  
Conductive Material ◽  
Design And Optimization ◽  
The Mean

In this research, we consider the generation of conductive heat trees at micro and nano scales for cooling electronics which are considered as heat-generating disc-shaped solids. Due to the development of nano technology and its role in the production of small scale electronics in recent decades, the necessity of designing cooling systems for them will be revealed more than any other time. Therefore, tree-shape conduction paths of highly conductive material including radial patterns, structures with one level of branching, tree-with-loop architectures, and combination of structures with branching and structures with loop are generated for cooling such electronic devices. Furthermore, Constructal method which is used to analytically generate heat trees for cooling a disk-shaped body is modified in the present work, that we call it modified analytical method. Moreover, every feature of the tree-shaped architectures is optimized numerically to make a comparison between numerical and analytical results and to generate novel architectures. When the smallest features of the internal structure are so small, the conventional description of conduction breaks down. Hence, the effective thermal conductivity exhibits the “size effect”, and is governed by the smallest structural dimension which is comparable with the mean free path of the energy carriers. Therefore, we consider a model which was proposed for small-scale bodies in order to evaluate conductivity of heat trees.

scholarly journals Maximum Possible Colling Rate in Ultrafast Chip Nanocalorimetry: Fundamental Limitations Due to Thermal Resistance at the Membrane/Gas Interface

2021 ◽  
Author(s):  
Alexander A. Minakov ◽  
Christoph Schick
Keyword(s):  
Thermal Resistance ◽  
Cooling Rate ◽  
Materials Science ◽  
Mean Free Path ◽  
Heat Conducting ◽  
Controlled Cooling ◽  
Fundamental Limitations ◽  
The Mean ◽  
Gas Molecules ◽  
Hot Zone

Ultrafast chip nanocalorimetry opens up remarkable possibilities in materials science by allowing samples to be cooled and heated at extremely high rates. Due to heat transfer limitations, controlled ultrafast cooling and heating can only be achieved for tiny samples in calorimeters with a micron-thick membrane. Even if ultrafast heating can be controlled under quasi-adiabatic conditions, ultrafast controlled cooling can be performed if the calorimetric cell is located in a heat-conducting gas. It was found that the maximum possible cooling rate increases as 1/r0 with decreasing radius r0 of the hot zone of the membrane. The possibility of increasing the maximum cooling rate with decreasing r0 was successfully implemented in many experiments. In this regard, it is interesting to answer the question: what is the maximum possible cooling rate in such experiments if r0 tends to zero? Indeed, on submicron scales, the mean free path of gas molecules lmfp becomes comparable to r0, and the temperature jump that exists at the membrane/gas interface becomes significant. Considering the limitation associated with thermal resistance at the membrane/gas interface and considering the transfer of heat through the membrane, we show that the controlled cooling rate can reach billions of K/s, up to 1010 K/s.

scholarly journals Hydrodynamic Response of the Intergalactic Medium to Reionization. II. Physical Characteristics and Dynamics of Ionizing Photon Sinks

2021 ◽  
Vol 923 (2) ◽  
pp. 161
Author(s):  
Fahad Nasir ◽  
Christopher Cain ◽  
Anson D’Aloisio ◽  
Nakul Gangolli ◽  
Matthew McQuinn
Keyword(s):  
Intergalactic Medium ◽  
Mean Free Path ◽  
Small Scale ◽  
Hydrodynamic Simulations ◽  
Density Distributions ◽  
Ionization Fronts ◽  
Density Peaks ◽  
Hydrodynamic Response ◽  
The Mean ◽  
The Universe

Abstract Becker et al. measured the mean free path of Lyman-limit photons in the intergalactic medium (IGM) at z = 6. The short value suggests that absorptions may have played a prominent role in reionization. Here we study physical properties of ionizing photon sinks in the wake of ionization fronts (I-fronts) using radiative hydrodynamic simulations. We quantify the contributions of gaseous structures to the Lyman-limit opacity by tracking the column-density distributions in our simulations. Within Δt = 10 Myr of I-front passage, we find that self-shielding systems (N H I > 1017.2 cm−2) are comprised of two distinct populations: (1) overdensity Δ ∼ 50 structures in photoionization equilibrium with the ionizing background, and (2) Δ ≳ 100 density peaks with fully neutral cores. The self-shielding systems contribute more than half of the opacity at these times, but the IGM evolves considerably in Δt ∼ 100 Myr as structures are flattened by pressure smoothing and photoevaporation. By Δt = 300 Myr, they contribute ≲10% to the opacity in an average 1 Mpc3 patch of the universe. The percentage can be a factor of a few larger in overdense patches, where more self-shielding systems survive. We quantify the characteristic masses and sizes of self-shielding structures. Shortly after I-front passage, we find M = 104–108 M ⊙ and effective diameters d eff = 1–20 ckpc h −1. These scales increase as the gas relaxes. The picture herein presented may be different in dark matter models with suppressed small-scale power.

Applicability of the Wright Polynomial Correction for Time-Resolved Laser-Induced Incandescence in the Transition Regime

2012 ◽  
Author(s):  
K. J. Daun ◽  
S. C. Huberman
Keyword(s):  
Heat Conduction ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Mean Free Path ◽  
Knudsen Layer ◽  
Transition Regime ◽  
Time Resolved ◽  
Laser Induced Incandescence ◽  
The Mean ◽  
Gas Molecules

Sizing aerosolized nanoparticles through time-resolved laser-induced incandescence (TiRe-LII) requires an accurate model of the heat conduction from the laser-energized particle to the surrounding gas. Under transition regime conditions this is often done using Fuchs’ boundary-sphere method, which requires the analyst to specify the thickness of a collisionless layer surrounding the particle, representing the Knudsen layer. Traditionally the boundary layer thickness is set to the mean free path of the gas at the boundary temperature, but recently some TiRe-LII practitioners have adopted a more complex treatment that accounts for particle curvature and directional distribution of gas molecules. This paper presents a critical reassessment of this approach; while this modification is more representative of the true Knudsen layer thickness, it does not improve the accuracy of heat conduction rates estimated using Fuchs’ boundary sphere methods under conditions prevailing in most TiRe-LII experiments.

Influence of Harmonic Perturbation on Speed of Billiard Particle as Combination of Deterministic Acceleration and White Noise

2019 ◽  
Vol 18 (02) ◽  
pp. 1940012 ◽  
Author(s):  
Alexander Dubkov ◽  
Alexandra Krasnova ◽  
Olga Chichigina
Keyword(s):  
White Noise ◽  
Numerical Simulations ◽  
Free Path ◽  
Gaussian Noise ◽  
Mean Free Path ◽  
Acceleration Of Particles ◽  
Harmonic Force ◽  
Harmonic Perturbation ◽  
The Mean ◽  
Good Agreement

Chaotic system under influence of harmonic force is considered. Namely, the motion of Fermi-accelerated billiard particles interacting with scatterers with harmonically oscillating boundaries is investigated. The domain of main parameters in which the acceleration of particles does not depend on the period of scatterers oscillations is found. In this domain, the effect of such oscillations can be considered as an impact of white Gaussian noise whose intensity depends only on the amplitude of velocity of scatterer oscillations and the mean free path of particles. The results of numerical simulations are in good agreement with the results of analytical considerations.

DSMC Simulation of Supersonic Gas Flow in Microchannel

2011 ◽  
Author(s):  
Mohamad M. Joneidipour ◽  
Reza Kamali
Keyword(s):  
Gas Flow ◽  
Characteristic Length ◽  
Flow Characteristics ◽  
Mean Free Path ◽  
Incoming Flow ◽  
Characteristic Length Scale ◽  
Flow Pressure ◽  
Supersonic Gas Flow ◽  
The Mean ◽  
Gas Molecules

The present study is concerned with the flow characteristics of a microchannel supersonic gas flow. The direct simulation Monte Carlo (DSMC) method is employed for predicting the density, velocity and temperature distributions. For gas flows in micro systems, the continuum hypothesis, which underpins the Navier-Stokes equations, may be inappropriate. This is because the mean free path of the gas molecules may be comparable to the characteristic length scale of the device. The Knudsen number, Kn, which is the ratio of the mean free path of the gas molecules to the characteristic length scale of the device, is a convenient measure of the degree of rarefaction of the flow. In this paper, the effect of Knudsen number on supersonic microchannel flow characteristics is studied by varying the incoming flow pressure or the microchannel height. In addition, the microchannel height and the incoming flow pressure are varied simultaneously to investigate their effects on the flow characteristics. Meanwhile, the results show that until the diffuse reflection model is used throughout the microchannel, the temperature and the Mach number in the microchannel entrance may not be equal to free-stream values and therefore a discontinuity appear in the flow field.

scholarly journals Experimental and theoretical studies of the behaviour of slow electrons in air. I

1949 ◽  
Vol 196 (1046) ◽  
pp. 402-426 ◽  
Keyword(s):  
Drift Velocity ◽  
Mean Free Path ◽  
Free Electrons ◽  
Direct Measurements ◽  
Electronic Motion ◽  
The Mean ◽  
Gas Molecules ◽  
Slow Electrons ◽  
Experimental And Theoretical Studies ◽  
Unit Pressure

This paper is an account of an experimental investigation of the motions of free electrons in air by the method developed by Townsend. An improved form of apparatus is described with the appropriate theory. The following parameters of the electronic motion were determined as functions of the ratio Z/p of the electric field strength Z to the gas pressure p : Townsend’s energy factor k r the drift velocity W , the mean free path at unit pressure L and the mean proportion n of its energy lost in collisions with gas molecules. The experimental data are given in the form of tables and curves. The drift velocity W is found by a new procedure based on the Hall effect and by comparing the velocities W so obtained with the direct measurements of W by Nielsen & Bradbury it is seen that the velocities of agitation are distributed approximately according to Druyvesteyn’s law when Z/p exceeds 0.5. Bailey’s factor G , which is of importance in ionospheric studies, is obtained from the experimental dependence of η on k r . Theoretical formulae are derived for k r and W in terms of L, G and Z/p . The theory of the new method for measuring W is given in an appendix.

Development of New Design Fatigue Curves in Japan: Discussion of Best-Fit Curves Based on Fatigue Test Data With Small-Scale Test Specimen

2018 ◽  
Author(s):  
Yun Wang ◽  
Hisamitsu Hatoh ◽  
Masato Yamamoto ◽  
Motoki Nakane ◽  
Akihiko Hirano ◽  
...  
Keyword(s):  
Tensile Strength ◽  
Fatigue Tests ◽  
Small Scale ◽  
Stress Effect ◽  
Mean Stress ◽  
Mean Stress Effect ◽  
Scale Test ◽  
The Mean ◽  
Best Fit ◽  
Good Agreement

Based on the precedent design fatigue curves and recent fatigue data obtained from materials with different mechanical properties, new design fatigue curves with high general versatility in air have been developed by The Japan Welding Engineering Society (JWES). Structural materials with different tensile strength are utilized in fatigue tests to verify the validity of these design fatigue curves and discuss the mean stress effect. The materials employed in this study are austenitic stainless steel (SS) SUS316LTP, carbon steel (CS) STPT370, low-alloy steels (LASs) SQV2A and SCM435H, all of which are used in the structural components of nuclear power plants of Japan. The best-fit curves (BFCs) are formulated by using the parameter of tensile strength to describe the relationship between strain (stress) amplitude and fatigue life [1]. The results of fully reversed axial fatigue tests conducted with small-scale test specimens of those materials in air at ambient temperature show good agreement with the developed BFCs. The results of fatigue tests also indicate that the mean stress effect is remarkable in materials with higher tensile strength. The applicability of Modified Goodman and Smith-Watson-Topper (SWT) approaches to the design fatigue curves is compared and discussed when considering mean stress effect. The correction of mean stress effect with SWT approach shows a good agreement with the developed BFCs.

scholarly journals Determination of the coefficient of inter-diffusion of gases and the velocity of ions under an electric force, in terms of mean free paths

1912 ◽  
Vol 86 (586) ◽  
pp. 197-206 ◽  
Keyword(s):  
Free Path ◽  
Equations Of Motion ◽  
Mean Free Path ◽  
Electric Force ◽  
Mean Velocity ◽  
The Mean ◽  
Definition Of ◽  
Good Agreement ◽  
Diffusion Of Gases

1. The properties of gases which depend on the velocity of agitation of molecules and the lengths of their free paths may easily be expressed in terms of the mean velocity of agitation and the mean free path when certain assumptions are made in order to simplify the investigations. The expressions thus found on the principles of the kinetic theory are in good agreement with the experimental results in most cases, but the formulæ that have been obtained for the coefficient of inter-diffusion of gases and the velocity of particles acted on by an external force are not so satisfactory. The equations of motion of two inter-diffusing gases have been given by Maxwell, and it may be shown from these that the exact value of the ratio of the coefficient of diffusion of ions to the velocity under unit electric force is N e /II, where N is the number of molecules per cubic centimetre of a gas at pressure II, and e the charge on an ion. The method adopted by Maxwell is perfectly general, there are no assumptions made as to the distribution of the velocities of agitation, and no particular definition of a collision of a free path is involved, so that there can be little doubt as to the accuracy of the result.

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