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Transition regime analytical solution to gas mass flow rate in a rectangular micro channel

Dadzie, Kokou and Dongari, Nishanth (2012) Transition regime analytical solution to gas mass flow rate in a rectangular micro channel. In: 28th International Symposium on Rarefied Gas Dynamics, 2012-07-09 - 2012-07-13, Zaragosa.

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    Abstract

    We present an analytical model predicting the experimentally observed gas mass flow rate in rectangular micro channels over slip and transition regimes without the use of any fitting parameter. Previously, Sone [1] reported a class of pure continuum regime flows that requires terms of Burnett order in constitutive equations of shear stress to be predicted appropriately. The corrective terms to the conventional Navier-Stokes equation were named the ghost effect. We demonstrate in this paper similarity between Sone ghost effect model and newly so-called ‘volume diffusion hydrodynamic model’. A generic analytical solution to gas mass flow rate in a rectangular micro channel is then obtained. It is shown that the volume diffusion hydrodynamics allows to accurately predict the gas mass flow rate up to Knudsen number of 5. This can be achieved without necessitating the use of any adjustable parameters in boundary conditions or parametric scaling laws for constitutive relations. The present model predicts the non-linear variation of pressure profile along the axial direction and also captures the change in curvature with increase in rarefaction.

    Item type: Conference or Workshop Item (Paper)
    ID code: 40484
    Keywords: mass diffusion , volume diffusion hydrodynamics , microchannel gas flow , Knudsen paradox , pressure distribution , slip flows , Mechanical engineering and machinery, Mechanical Engineering, Mechanics of Materials, Computational Mechanics, Modelling and Simulation
    Subjects: Technology > Mechanical engineering and machinery
    Department: Faculty of Engineering > Mechanical and Aerospace Engineering
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    Depositing user: Pure Administrator
    Date Deposited: 19 Jul 2012 09:46
    Last modified: 02 May 2014 19:14
    URI: http://strathprints.strath.ac.uk/id/eprint/40484

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