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

Dadzie, Kokou S and Dongari, Nishanth (2012) Transition regime analytical solution to gas mass flow rate in a rectangular micro channel. In: UNSPECIFIED.

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Abstract

We present an analytical model predicting the experimentally observed gas mass flow rate in rectangular microchannels over slip and transition regimes without the use of any fitting parameter. Previously, Sone 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
Additional Information: Copyright 2012 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Dadzie, S.K. and Dongari, N. (2012) 'Transition regime analytical solution to gas mass flow rate in a rectangular micro channel'. [Paper presented to 28th International Symposium on Rarefied Gas Dynamics, Zaragoza, Spain, July 9-13 2012] website of the conference is located at http://rgd28.es/ later published in the American Institute of Physics Conference Proceedings and may be found this paper was later published in the American Institute of Physics Conference Proceedings and may be found at http://rgd28.es/Book_of_Abstracts.pdf
Keywords: mass diffusion, volume diffusion hydrodynamics, microchannel gas flow, Knudsen paradox, pressure distribution, slip flows, bi-velocity hydrodynamics
Divisions: ?? GlyndwrUniversity ??
Depositing User: ULCC Admin
Date Deposited: 10 Aug 2012 00:12
Last Modified: 11 Dec 2017 20:07
URI: http://glyndwr.repository.guildhe.ac.uk/id/eprint/4008

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