Radiative Transport Within an Ablating Body

1961 ◽  
Vol 83 (2) ◽  
pp. 215-224 ◽  
Author(s):  
Leo P. Kadanoff
Keyword(s):  
Optical Properties ◽  
Steady State ◽  
Temperature Distribution ◽  
Free Path ◽  
Liquid Layer ◽  
Effective Conductivity ◽  
Mean Free Path ◽  
Radiative Transport ◽  
Scattering Media ◽  
Infinite Body

The emission and reabsorption of thermal radiation within a semitransparent material provides a mechanism which supplements ordinary thermal conduction in transporting energy from hotter to colder regions. A method has been developed for the calculation of net radiative flux and temperature distribution within a semi-infinite body which emits, absorbs, and scatters this radiation and which allows some radiation to escape from its surface. This method has been applied to the problem of calculating temperature distributions within bodies in steady-state ablation. The bodies are characterized by their refractive index, surface reflectivity, absorption and scattering coefficient, ablation velocity, and surface temperature as well as by their heat capacity and thermal conductivity. Numerical results are presented for the temperature distribution with various values of these parameters. As a result of this analysis, simple formulas are presented for the temperature distribution very near the surface of an ablating body which are particularly useful in predicting the temperature distribution in the “liquid layer” of a glassy ablating body. These simple formulas are presented for two limiting cases: Case I, in which the liquid layer is so thin that it is almost completely transparent to radiation, and Case II, in which the radiation mean free path is so short that radiative transport can be completely neglected in determining the temperature distribution in the liquid layer. Also resulting from this numerical analysis is a simple relation between the ablation rate and the emissive power of a body in steady-state ablation. The concept of effective conductivity is extended to scattering media. It is noted that this concept fails whenever the temperature or optical properties of the medium change appreciably within one radiation mean free path. In particular, the optical properties change discontinuously at any boundary. Thus, in general, the effective conductivity concept fails near a boundary and results in completely wrong answers for the temperature distribution in the liquid layer.

Theoretical Considerations of Molecular Mean Free Path Influenced Slip in Self-Acting Gas-Lubricated Plain Journal Bearings

1984 ◽  
Vol 198 (1) ◽  
pp. 25-31 ◽  
Author(s):  
M Malik
Keyword(s):  
Steady State ◽  
Beneficial Effect ◽  
Free Path ◽  
Dynamic Performance ◽  
Mean Free Path ◽  
Journal Bearings ◽  
Performance Characteristics ◽  
Wide Range ◽  
Theoretical Investigations ◽  
Theoretical Considerations

The purpose of this paper is to study the effect of slip under the influence of molecular mean free path on the steady state and dynamic performance characteristics of plain gas journal bearings. The theoretical investigations have been made over a wide range of compressibility number. It is found that slip usually impairs the bearing performance, particularly at low compressibility numbers, A; the effect of slip, however, diminishes with increasing values of A. In fact at high compressibility numbers, theory suggests that slip has a beneficial effect of improving the dynamic performance of the bearing.

Modelling of CW Laser Annealing of Multilayer Structures

1981 ◽  
Vol 4 ◽  
Author(s):  
I.D. Calder ◽  
R. Sue ◽  
Emad-Eldin A.A. Aly
Keyword(s):  
Phase Transition ◽  
Thermal Conductivity ◽  
Optical Properties ◽  
Steady State ◽  
Temperature Distribution ◽  
Thermal Model ◽  
Laser Annealing ◽  
Multilayer Structures ◽  
Cw Laser ◽  
Arbitrary Thickness

ABSTRACTA thermal model is developed for cw laser annealing of multilayer structures. Each layer has arbitrary thickness, thermal conductivity and optical properties. Steady state conditions with no phase transition are assumed. A procedure is presented for obtaining the temperature distribution in any system and explicit integral expressions are developed for the two and three layer cases. Results are calculated for the Si/glass and Si/SiO2 /Si systems.

Lattice Boltzmann Modeling of Phonon Heat Conduction in Superlattice Structures

2010 ◽  
Author(s):  
Cristian J. San Marti´n ◽  
Amador M. Guzma´n ◽  
Rodrigo A. Escobar
Keyword(s):  
Thermal Conductivity ◽  
Free Path ◽  
Lattice Boltzmann ◽  
Phonon Dispersion ◽  
Effective Conductivity ◽  
Mean Free Path ◽  
One Dimension ◽  
The Mean ◽  
Superlattice Structures ◽  
Boltzmann Method

The results of temperature prediction and determination of effective thermal conductivity in periodic Si-Ge superlattice in one dimension, at length scale comparable to the mean free path are presented. Classical heat transfer models such as Fourier’s law do not represent what actually happens within electronic devices at these length scales. Phonon-border and phonon-interface scattering effects provide discontinuous jumps in temperature distribution when the mean free path is comparable with the device’s characteristic length, a relation given by the Knudsen number (Kn). For predicting the temperature within the periodic Si-Ge superlattice use is made of the lattice Boltzmann method in one dimension, using Debye’s model in the phonon dispersion relation. The predictions show that as Kn increases, so do the jumps at the borders, the same as at the interfaces. The prediction also shows that the effective conductivity of the Si-Ge superlattice decreases as Kn and the number of layers of material increase, and that keff decreases as the magnitude of p increases, a factor that allows heat flow between one layer and another. Use of gray LBM leads to good approximations of the actual temperature field and thermal conductivity values for the superlattice materials model when the physics of phonons established by Debye’s model is used.

Joule Heating and Thermal Conductivity Determination of Nanoscale Metallic Thin Films and Interconnects

2005 ◽  
Author(s):  
Siva P. Gurrum ◽  
William P. King ◽  
Yogendra K. Joshi ◽  
Koneru Ramakrishna
Keyword(s):  
Thin Films ◽  
Thermal Conductivity ◽  
Free Path ◽  
Joule Heating ◽  
High Performance ◽  
Effective Conductivity ◽  
Mean Free Path ◽  
Current Crowding ◽  
Metal Line ◽  
Thin Metallic Film

Evolution of high performance microprocessors has resulted in a steady decrease in on-chip feature sizes. Increasing requirements on maximum current density are expected to increase interconnect temperature drastically due to Joule heating. As interconnect dimensions approach the electron mean free path range, effective conductivity reduces due to size effects. Thermal characterization of sub-micron interconnects and thin films is thus highly important. This work investigates current crowding and the associated Joule heating near a constriction in a thin metallic film and proposes a novel technique to determine thermal conductivity of thin metallic films and interconnects in the sub-100 nm range. Scanning Joule Expansion Microscopy (SJEM) measures the thermal expansion of the structure whose thickness is comparable to the mean free path of electrons. Numerical solution of heat conduction equation in the frequency space is used to obtain a fit for effective thermal conductivity. A thermal conductivity of ~ 80.0 W/mK provides a best fit to the data. This is about one-third the bulk thermal conductivity of gold, which is 318 W/mK at room temperature. Using Wiedemann-Franz Law a thermal conductivity of 92.0 W/mK is obtained after measuring the electrical resistivity of the metal line. This is close to that obtained through numerical fit.

THE TEMPERATURE DISTRIBUTION PRODUCED BY ACOUSTIC ABSORPTION: II. BOLTZMANN EQUATION APPROACH

1966 ◽  
Vol 44 (12) ◽  
pp. 3013-3023 ◽  
Author(s):  
S. Simons
Keyword(s):  
Boltzmann Equation ◽  
Temperature Distribution ◽  
Free Path ◽  
Low Temperatures ◽  
Mean Free Path ◽  
Collision Term ◽  
Acoustic Absorption ◽  
Time Approximation ◽  
Relaxation Time Approximation ◽  
The Mean

A calculation is given of the time-independent temperature distribution produced by the absorption of an acoustic wave under conditions in which the mean free path of the thermal particles is of the order of the specimen dimensions. Results are obtained for plane geometry by solving the relevant Boltzmann equation with a relaxation time approximation for the collision term. The results suggest an experimental method for obtaining the mean free path of electrons in metals at low temperatures, similar in some respects to the method of conduction in thin films.

Inelastic mean free path and phase-shift determinations in NiO, using EXELFS

1993 ◽  
Vol 3 (7) ◽  
pp. 1649-1659
Author(s):  
Mohammad A. Tafreshi ◽  
Stefan Csillag ◽  
Zou Wei Yuan ◽  
Christian Bohm ◽  
Elisabeth Lefèvre ◽  
...  
Keyword(s):  
Phase Shift ◽  
Free Path ◽  
Mean Free Path ◽  
Inelastic Mean Free Path

High-speed isotachophoresis. Analytical aspects of the steady-state longitudinal temperature profiles

1979 ◽  
Vol 44 (3) ◽  
pp. 841-853 ◽  
Author(s):  
Zbyněk Ryšlavý ◽  
Petr Boček ◽  
Miroslav Deml ◽  
Jaroslav Janák
Keyword(s):  
Steady State ◽  
Temperature Distribution ◽  
Electric Field ◽  
Field Intensity ◽  
Electric Field Intensity ◽  
Minor Component ◽  
Physical Models ◽  
Temperature Profiles ◽  
Longitudinal Temperature ◽  
Continuous Character

The problem of the longitudinal temperature distribution was solved and the bearing of the temperature profiles on the qualitative characteristics of the zones and on the interpretation of the record of the separation obtained from a universal detector was considered. Two approximative physical models were applied to the solution: in the first model, the temperature dependences of the mobilities are taken into account, the continuous character of the electric field intensity at the boundary being neglected; in the other model, the continuous character of the electric field intensity is allowed for. From a comparison of the two models it follows that in practice, the variations of the mobilities with the temperature are the principal factor affecting the shape of the temperature profiles, the assumption of a discontinuous jump of the electric field intensity at the boundary being a good approximation to the reality. It was deduced theoretically and verified experimentally that the longitudinal profiles can appreciably affect the longitudinal variation of the effective mobilities in the zone, with an infavourable influence upon the qualitative interpretation of the record. Pronounced effects can appear during the analyses of the minor components, where in the corresponding short zone a temperature distribution occurs due to the influence of the temperatures of the neighbouring zones such that the temperature in the zone of interest in fact does not attain a constant value in axial direction. The minor component does not possess the steady-state mobility throughout the zone, which makes the identification of the zone rather difficult.

The measurement of mean free path λs using a slowing down time lead spectrometer in the 1–10 eV energy region

1968 ◽  
Vol 22 (4) ◽  
pp. 261-262
Author(s):  
M.P. Navalkar ◽  
K. Chandramoleshwar ◽  
D.V.S. Ramkrishna
Keyword(s):  
Free Path ◽  
Energy Region ◽  
Mean Free Path ◽  
Slowing Down ◽  
Time Lead
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