scholarly journals On the second-order temperature jump coefficient of a dilute gas

2012 ◽  
Vol 707 ◽  
pp. 331-341 ◽  
Author(s):  
Gregg A. Radtke ◽  
N. G. Hadjiconstantinou ◽  
S. Takata ◽  
K. Aoki
Keyword(s):  
Hard Sphere ◽  
Temperature Jump ◽  
Second Order ◽  
Bgk Model ◽  
Volumetric Heating ◽  
Dilute Gas ◽  
The Poisson Equation ◽  
Jump Relation ◽  
Temperature Jump Coefficient ◽  
Time Dependent Problems

AbstractWe use LVDSMC (low-variance deviational Monte Carlo) simulations to calculate, under linearized conditions, the second-order temperature jump coefficient for a dilute gas whose temperature is governed by the Poisson equation with a constant forcing term, as in the case of homogeneous volumetric heating. Both the hard-sphere gas and the BGK model of the Boltzmann equation, for which slip/jump coefficients are not functions of temperature, are considered. The temperature jump relation and jump coefficient determined here are closely linked to the general jump relations for time-dependent problems that have yet to be systematically treated in the literature; as a result, they are different from those corresponding to the well-known linear and steady case where the temperature is governed by the homogeneous heat conduction (Laplace) equation.

scholarly journals Validation of a Second-Order Slip Model for Transition-Regime, Gaseous Flows

2004 ◽  
Author(s):  
Nicolas G. Hadjiconstantinou
Keyword(s):  
Second Order ◽  
Stress Fields ◽  
Gas Flows ◽  
Transition Regime ◽  
Slip Model ◽  
Dilute Gas ◽  
Transient Problems ◽  
Model Predictions ◽  
Gaseous Flows ◽  
Related Stress

We discuss and validate a recently proposed second-order slip model for dilute gas flows. Our discussion focuses on the importance of quantitatively accounting for the effect of Knudsen layers close to the walls. This is important, not only for obtaining an accurate slip model but also for interpreting the results of the latter since in transition-regime flows the Knudsen layers penetrate large parts of the flow. Our extensive validation illustrates the above points by comparing direct Monte Carlo solutions to the slip model predictions for an unsteady flow. Excellent agreement is found between simulation and the slip model predictions up to Kn = 0.4, for both the velocity profile and stress at the wall. This demonstrates that the proposed second-order slip model reliably describes arbitrary flowfields (and related stress fields) in a predictive manner at least up to Kn = 0.4 for both steady and transient problems.

Applying second-order adjoint perturbation theory to time-dependent problems

2013 ◽  
Vol 53 ◽  
pp. 9-18 ◽  
Author(s):  
L. Gilli ◽  
D. Lathouwers ◽  
J.L. Kloosterman ◽  
T.H.J.J. van der Hagen
Keyword(s):  
Perturbation Theory ◽  
Second Order ◽  
Time Dependent ◽  
Time Dependent Problems

Second-order Percus-Yevick theory for a confined hard-sphere fluid

1997 ◽  
Vol 89 (1-2) ◽  
pp. 233-247 ◽  
Author(s):  
Douglas Henderson ◽  
Stefan Sokolowski ◽  
Darsh Wasan
Keyword(s):  
Hard Sphere ◽  
Second Order ◽  
Hard Sphere Fluid

The Slip Problems for a Simple Gas

1971 ◽  
Vol 26 (6) ◽  
pp. 964-972 ◽  
Author(s):  
S.K. Loyalka
Keyword(s):  
Boltzmann Equation ◽  
Temperature Jump ◽  
Velocity Slip ◽  
Polyatomic Gas ◽  
Extra Effort ◽  
Linearized Boltzmann Equation ◽  
Multicomponent Gas ◽  
Interaction Law ◽  
Temperature Jump Coefficient ◽  
Polyatomic Gas Mixtures

Abstract Simple and accurate expressions for the velocity slip coefficient, the slip in the thermal creep, and the temperature jump coefficient are obtained by applying a variational technique to the linearized Boltzmann equation for a simple gas. Completely general forms of the boundary conditions are used, and the final results are presented in a form such that the results for any particular intermolecular force law or the gas-surface interaction law can easily be calculated. Further, it is shown that, with little extra effort, the present results can be easily extended to include the case of a polyatomic gas. It is felt that the present work, together with a recent paper in which the author has considered the solutions of the linearized Boltzmann equation for a monatomic multicomponent gas mixture, provide the desired basis for the consideration of the various slip problems associated with the polyatomic gas mixtures.

Properties of a Dense Hard-Sphere Gas Near the Walls of a Microchannel

2004 ◽  
Author(s):  
S. V. Nedea ◽  
A. J. H. Frijns ◽  
A. A. van Steenhoven ◽  
A. P. J. Jansen
Keyword(s):  
Particle Size ◽  
Hard Sphere ◽  
Md Simulation ◽  
Analytical Techniques ◽  
Dense Gas ◽  
Density Profiles ◽  
Dilute Gas ◽  
System L ◽  
Density Oscillation ◽  
Reduced Density

A mathematical model has been developed to characterize the effect of packing of molecules of a hard-sphere dense gas near the hard walls of a microchannel. Analytical techniques, Monte Carlo (MC) methods and Molecular Dynamics (MD) simulation methods have been used to characterize the influence of the characteristic parameters such as number density, reduced density, length of the system and molecular diameter on the equilibrium properties of the gas near the hard walls of the microchannel. The height and the position of the density oscillation peaks near the wall are characterized. Comparisons between MD and MC results for particles having different diameter are presented. For the same size of the particles and moderately dense gas, MC and MD results are similar, differences in the density profiles being limited only to the oscillatory region. For different particle sizes, MD and MC results are limited to a short distance near the wall for long size systems and moderately dense fluids. The effect of the boundary (particle size) on the simulation results is increasing with η (reduced density) and it is very small in case of a dilute gas. For small η and small particle size (R) relative to length of the system L, the height of the oscillations peaks is slowly increasing with R/L, and for high densities is always decreasing with R/L. The position of these peaks depends only on the size of the particles and when R is much smaller than L, it shows a small dependence on L.

The temperature-jump problem in rarefied-gas dynamics

2000 ◽  
Vol 11 (4) ◽  
pp. 353-364 ◽  
Author(s):  
L. B. BARICHELLO ◽  
C. E. SIEWERT
Keyword(s):  
Gas Dynamics ◽  
Computational Algorithm ◽  
Temperature Jump ◽  
Rarefied Gas ◽  
Rarefied Gas Dynamics ◽  
Discrete Ordinates ◽  
Jump Problem ◽  
Bgk Model ◽  
Discrete Ordinates Method ◽  
Density Distributions

An analytical version of the discrete-ordinates method is used here to solve the classical temperature-jump problem based on the BGK model in rarefied-gas dynamics. In addition to a complete development of the discrete-ordinates method for the application considered, the computational algorithm is implemented to yield very accurate results for the temperature jump and the complete temperature and density distributions in the gas. The algorithm is easy to use, and the developed code runs typically in less than a second on a 400 MHz Pentium-based PC.

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