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

Kokou Dadzie, Nishanth Dongari

Research output: Contribution to conferencePaper

2 Citations (Scopus)

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.
LanguageEnglish
Pages720-726
Number of pages7
Publication statusPublished - 9 Jul 2012
Event28th International Symposium on Rarefied Gas Dynamics - Zaragosa, Spain
Duration: 9 Jul 201213 Jul 2012

Conference

Conference28th International Symposium on Rarefied Gas Dynamics
CountrySpain
CityZaragosa
Period9/07/1213/07/12

Fingerprint

Microchannel
Flow Rate
Analytical Solution
Flow rate
Hydrodynamics
Gases
Predict
Knudsen number
Hydrodynamic Model
Scaling laws
Constitutive Relations
Diffusion Model
Scaling Laws
Term
Constitutive Equation
Constitutive equations
Shear Stress
Slip
Analytical Model
Navier Stokes equations

Keywords

  • mass diffusion
  • volume diffusion hydrodynamics
  • microchannel gas flow
  • Knudsen paradox
  • pressure distribution
  • slip flows

Cite this

Dadzie, K., & Dongari, N. (2012). Transition regime analytical solution to gas mass flow rate in a rectangular micro channel. 720-726. Paper presented at 28th International Symposium on Rarefied Gas Dynamics, Zaragosa, Spain.
Dadzie, Kokou ; Dongari, Nishanth. / Transition regime analytical solution to gas mass flow rate in a rectangular micro channel. Paper presented at 28th International Symposium on Rarefied Gas Dynamics, Zaragosa, Spain.7 p.
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Dadzie, K & Dongari, N 2012, 'Transition regime analytical solution to gas mass flow rate in a rectangular micro channel' Paper presented at 28th International Symposium on Rarefied Gas Dynamics, Zaragosa, Spain, 9/07/12 - 13/07/12, pp. 720-726.

Transition regime analytical solution to gas mass flow rate in a rectangular micro channel. / Dadzie, Kokou; Dongari, Nishanth.

2012. 720-726 Paper presented at 28th International Symposium on Rarefied Gas Dynamics, Zaragosa, Spain.

Research output: Contribution to conferencePaper

TY - CONF

T1 - Transition regime analytical solution to gas mass flow rate in a rectangular micro channel

AU - Dadzie, Kokou

AU - Dongari, Nishanth

PY - 2012/7/9

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N2 - 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 ofpure 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.

AB - 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 ofpure 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.

KW - mass diffusion

KW - volume diffusion hydrodynamics

KW - microchannel gas flow

KW - Knudsen paradox

KW - pressure distribution

KW - slip flows

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M3 - Paper

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Dadzie K, Dongari N. Transition regime analytical solution to gas mass flow rate in a rectangular micro channel. 2012. Paper presented at 28th International Symposium on Rarefied Gas Dynamics, Zaragosa, Spain.