NDLI: Second-Order Gaseous Flow Models in Long Circular and Noncircular Microchannels and Nanochannels

Content Provider	The American Society of Mechanical Engineers (ASME) Digital Collection
Author	Duan, Zhipeng
Copyright Year	2011
Abstract	Gaseous flow in circular and noncircular microchannels has been examined and a simple analytical model with second-order slip boundary conditions for normalized Poiseuille number is proposed. The model is applicable to arbitrary length scale. It extends previous studies to the transition regime by employing the second-order slip boundary conditions. The effects of the second-order slip boundary conditions are analyzed. As in slip and transition regimes, no solutions or graphical and tabulated data exist for most geometries, the developed simple model can be used to predict friction factor, mass flow rate, tangential momentum accommodation coefficient, pressure distribution of gaseous flow in noncircular microchannels by the research community for the practical engineering design of microchannels such as rectangular, trapezoidal, double-trapezoidal, triangular, rhombic, hexagonal, octagonal, elliptical, semielliptical, parabolic, circular sector, circular segment, annular sector, rectangular duct with unilateral elliptical or circular end, annular, and even comparatively complex doubly-connected microducts. The developed second-order models are preferable since the difficulty and “investment” is negligible compared with the cost of alternative methods such as molecular simulations or solutions of Boltzmann equation. Navier-Stokes equations with second-order slip models can be used to predict quantities of engineering interest such as Poiseuille number, tangential momentum accommodation coefficient, mass flow rate, pressure distribution, and pressure drop beyond its typically acknowledged limit of application. The appropriate or effective second-order slip coefficients include the contribution of the Knudsen layers in order to capture the complete solution of the Boltzmann equation for the Poiseuille number, mass flow rate, and pressure distribution. It could be reasonable that various researchers proposed different second-order slip coefficients because the values are naturally different in different Knudsen number regimes. The transition regime is a varying mixture of different transport mechanisms and the mixed degree relies on the magnitude of the Knudsen number. It is analytically shown that the Knudsen’s minimum can be predicted with the second-order model and the Knudsen value of the occurrence of Knudsen’s minimum depends on inlet and outlet pressure ratio. The compressibility and rarefaction effects on mass flow rate and the curvature of the pressure distribution by employing first-order and second-order slip flow models are analyzed and compared. The condition of linear pressure distribution is given. This paper demonstrates that with some relatively simple ideas from knowledge, observation, and intuition, one can predict some fairly complex flows.
Sponsorship	Heat Transfer Division
Starting Page	305
Ending Page	317
Page Count	13
File Format	PDF
ISBN	9780791844632
DOI	10.1115/ICNMM2011-58040
Volume Number	ASME 2011 9th International Conference on Nanochannels, Microchannels, and Minichannels, Volume 1
Conference Proceedings	ASME 2011 9th International Conference on Nanochannels, Microchannels, and Minichannels
Language	English
Publisher Date	2011-06-19
Publisher Place	Edmonton, Alberta, Canada
Access Restriction	Subscribed
Subject Keyword	Slip flow Poiseuille number Compressibility Mass flow rate Pressure distribution Second-order model Rarefaction Knudsen’s minimum Transition regime Microchannels Noncircular Gas flow Poiseuille flow Flow (dynamics) Pressure
Content Type	Text
Resource Type	Article

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