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Analysis of the thermomechanical inconsistency of some extended hydrodynamic models at high Knudsen number

Dadzie, Kokou and Reese, Jason (2012) Analysis of the thermomechanical inconsistency of some extended hydrodynamic models at high Knudsen number. Physical Review E, 85 (4). ISSN 1539-3755

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    Abstract

    There are some hydrodynamic equations that, while their parent kinetic equation satisfies fundamental mechanical properties, appear themselves to violate mechanical or thermodynamic properties. This article aims to shed some light on the source of this problem. Starting with diffusive volume hydrodynamic models, the microscopic temporal and spatial scales are first separated at the kinetic level from the macroscopic scales at the hydrodynamic level. Then we consider Klimontovich’s spatial stochastic version of the Boltzmann kinetic equation, and show that, for small local Knudsen numbers, the stochastic term vanishes and the kinetic equation becomes the Boltzmann equation. The collision integral dominates in the small local Knudsen number regime, which is associated with the exact traditional continuum limit. We find a sub-domain of the continuum range which the conventional Knudsen number classification does not account for appropriately. In this sub-domain, it is possible to obtain a fully mechanically-consistent volume (or mass) diffusion model that satisfies the second law of thermodynamics on the grounds of extended non-local-equilibrium thermodynamics.

    Item type: Article
    ID code: 39217
    Keywords: Stochastic kinetic equatio n, Boltzmann equation , Rarefied Gas , Non-continuum flow , Volume and mass diffusion , Navier-Stokes equations , Mechanical engineering and machinery, Physics, Mechanical Engineering, Computational Mechanics, Modelling and Simulation
    Subjects: Technology > Mechanical engineering and machinery
    Science > Physics
    Department: Faculty of Engineering > Mechanical and Aerospace Engineering
    Technology and Innovation Centre > Advanced Engineering and Manufacturing
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    Depositing user: Pure Administrator
    Date Deposited: 18 Apr 2012 09:11
    Last modified: 27 Mar 2014 22:06
    URI: http://strathprints.strath.ac.uk/id/eprint/39217

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