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Analytical solution of gaseous slip flow in long microchannels

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Title Analytical solution of gaseous slip flow in long microchannels
 
Creator DONGARI, NISHANTH
AGRAWAL, ABHISHEK
AGRAWAL, AMIT
 
Subject boundary conditions
reynolds number
computer simulation
channel flow
 
Description In this paper we provide solution of the Navier–Stokes equations for gaseous slip flow in long microchannels with a second-order accurate slip boundary condition at the walls. The obtained solution is general enough to allow evaluation of various slip models proposed in the literature. We compare our solution against the first-order accurate slip boundary condition and show that the solution has a weak dependence on Reynolds number, which was neglected in the earlier theory. It is emphasized that first-order slip models do not predict the “Knudsen paradox” (appearance of a minima in normalized volume flux at Knudsen number approximately unity), or a change in curvature of centerline pressure at Knudsen numbers of 0.16. A comparison with Boltzmann’s solution suggests that the derived solution agrees reasonably well up to Knudsen number approximately 5, which shows that the validity of Navier–Stokes to rarefied gases can possibly be increased by using a high order slip boundary condition and proper choice of the slip coefficients. This result is significant from the perspective of numerical simulations of rarefied gases.
 
Publisher Elsevier
 
Date 2009-04-21T07:36:06Z
2011-11-25T20:56:34Z
2011-12-26T13:08:34Z
2011-12-27T05:56:30Z
2009-04-21T07:36:06Z
2011-11-25T20:56:34Z
2011-12-26T13:08:34Z
2011-12-27T05:56:30Z
2007
 
Type Article
 
Identifier International Journal of Heat and Mass Transfer 50(17-18), 3411-3421
0017-9310
http://dx.doi.org/10.1016/j.ijheatmasstransfer.2007.01.048
http://hdl.handle.net/10054/1167
http://dspace.library.iitb.ac.in/xmlui/handle/10054/1167
 
Language en