Slip boundary conditions
Background: For a given Knudsen number range, the NS 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. 
Re: Slip boundary conditions
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... 
Re: Slip boundary conditions
No, T_s is not equal to T_wall. If you'll waight till 3rd of July I'll provide you a reference :)

Re: Slip boundary conditions
thanks!

Re: Slip boundary conditions
Sorry, I'm a bit late :)
The formulas are Velocity U_s = ((2s)/s)*lambda_u*(dU/dn)_w Temperature T_s = T_w + ((2alfa)/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 DSMCCFD Simulations of Hypersonic Flow Over Sharp and Blunted Bodies, AIAA Paper 20033644, June. 
Re: Slip boundary conditions

slip_velocity
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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