# Slip boundary conditions

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 June 28, 2005, 17:02 Slip boundary conditions #1 NS-fan Guest   Posts: n/a Background: For a given Knudsen number range, the N-S equation viability can be extended into rarefied flows with the use of slip/jump conditions for velocity and temperature. With such, there's a finite difference between the gas particle velocity and temperature (T_s and u_s) adjacent to the wall and the wall itself (T_s and u_s). How are normal gradients for temperature calculated from the first node next to the wall for these slip conditions? Is it T_grad = (Tnode - T_s)/x ? Or is it T_grad = (Tnode - T_wall)/x ? x is the normal outward coord. from the wall. Also how is T_s obtained if we have an adiabatic wall? Any sources would be appreciated.

 June 29, 2005, 12:44 Re: Slip boundary conditions #2 NS-fan Guest   Posts: n/a My question put alternatively: - Adiabatic wall - There's a thin Knudson layer along the wall with restricted communication of molecular energy between the wall and fluid above the Knudson layer - T_s taken at top of Knudson layer (is this so?) Does the above mean T_s = T_wall??? I'm trying to look beyond the obvious in this esoteric physical situation...

 July 1, 2005, 04:35 Re: Slip boundary conditions #3 Anton Lyaskin Guest   Posts: n/a No, T_s is not equal to T_wall. If you'll waight till 3rd of July I'll provide you a reference

 July 1, 2005, 13:46 Re: Slip boundary conditions #4 NS-fan Guest   Posts: n/a thanks!

 July 5, 2005, 06:42 Re: Slip boundary conditions #5 Anton Lyaskin Guest   Posts: n/a Sorry, I'm a bit late The formulas are Velocity U_s = ((2-s)/s)*lambda_u*(dU/dn)_w Temperature T_s = T_w + ((2-alfa)/alfa)*lambda_t*(dT/dn)_w lambda_u = 2*mu/(ro*c) - meen free path for momentum, lambda_t = 2*k/(ro*c*c_v) - meen free path for energy, c = sqrt(8*R*T/pi) - meen molecular speed, s - accomodation coefficient for momentum, alfa - accomodation coefficient for energy I'm citing this from the following paper M. Giangi, F. Paglia, F. Stella, A. Nanni, A CONTINUUM MODEL FOR THE STUDY OF A SLIP FLOW REGIME, 4st International Conference on Computational Heat and Mass Transfer (I can send you a copy if you need), and the reference is to Wang, W.L. and Boyd, I.D., 2003, Hybrid DSMC-CFD Simulations of Hypersonic Flow Over Sharp and Blunted Bodies, AIAA Paper 2003-3644, June.

 July 5, 2005, 12:15 Re: Slip boundary conditions #6 NS-fan Guest   Posts: n/a Anton, you are a hero. Please send to motec383@yahoo.com and cc to STAGED@email.sae.org cheers

 October 21, 2010, 09:00 slip_velocity #7 New Member   anwar assaf Join Date: Oct 2010 Posts: 2 Rep Power: 0 dear Anton would u pls send me the paper M. Giangi, F. Paglia, F. Stella, A. Nanni, A CONTINUUM MODEL FOR THE STUDY OF A SLIP FLOW REGIME, 4st International Conference on Computational Heat and Mass Transfer on muaddi13@yahoo.com thanx in advance

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