2008
DOI: 10.1016/j.physa.2008.07.009
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A continuum model of gas flows with localized density variations

Abstract: This version is available at https://strathprints.strath.ac.uk/6991/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any prof… Show more

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Cited by 47 publications
(62 citation statements)
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“…First, we note that flux J c appearing in equation (3.2b) is a consequence of distinguishing between the pure mass continuity equation and an equation describing the true molecular spatial distribution involving an evolution of the gas volume containing these molecules (Dadzie et al 2008). As a consequence, this flux is only attributable to a molecular diffusive flux with respect to the mass-average velocity U .…”
Section: Constitutive Equations and Compatibility With Thermodynamicsmentioning
confidence: 99%
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“…First, we note that flux J c appearing in equation (3.2b) is a consequence of distinguishing between the pure mass continuity equation and an equation describing the true molecular spatial distribution involving an evolution of the gas volume containing these molecules (Dadzie et al 2008). As a consequence, this flux is only attributable to a molecular diffusive flux with respect to the mass-average velocity U .…”
Section: Constitutive Equations and Compatibility With Thermodynamicsmentioning
confidence: 99%
“…Following Liouville's theorem of conservation of probability density, a Boltzmann-like kinetic evolution equation may be written for f(t, X, ξ, c) as (Dadzie et al 2008)…”
Section: The Kinetic Model and Macroscopic Equationsmentioning
confidence: 99%
“…Another way of implementing this physical aspect in the modelling consists of introducing the local volume as an independent microscopic random variable. This rather more complete version of kinetic equation (1) was presented in [23] and a transport equation developed for the local volume. The associated set of macroscopic equations, after neglecting non-linear diffusive fluxes, may be written as follows [24]; denoting the material derivative by D/Dt = ∂/∂t + U m · ∇:…”
Section: Existence Of a Consistent Volume-mass Diffusion Model Atmentioning
confidence: 99%
“…In the above set of equations, the volume-mass diffusive flux is J v in equation (35c). It appears primarily through the expression of the shear stress, equation (35a), and is associated with another form of velocity, U v , termed the volume velocity [23]. Velocity U m , used in the material derivative, is the traditional mass current velocity, giving the mass flux and satisfying the continuity equation (34a).…”
Section: Existence Of a Consistent Volume-mass Diffusion Model Atmentioning
confidence: 99%
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