Extended Navier-Stokes Equations and Treatments of Micro-Channel Gas Flows

Abstract

See, stats, and : http : / / www . researchgate . net / publication / 215493351 Extended - Stokes treatments - channel ARTICLE CITATIONS 2 READS 33 Available : Nishanth Retrieved : 15 Abstract Gas flows in micro - channels are , in general , theoretically treated with the Maxwell slip velocity as a boundary condition for the convection velocity at the wall . It is pointed out that wall slip is conventionally introduced in theoretical / numerical treatments of gas flows through micro - channels to obtain agreement with experimental results . In the present paper , we provide an alternative by solving the extended Navier - Stokes equations for compressible gas flows in micro - channels using the conventional no - slip velocity boundary condition for the convection velocity . Results obtained with this approach are presented and compared with experiments . It is also shown that the theoretical treatment of micro - channel gas flows using the " extended Navier - Stokes equations " also permits the phenomena such as the Knudsen paradox , to be treated in an analytical manner . Comparison with experimental data suggests that the derived analytical solution has excellent agreement up to Knudsen number of approximately 1 , which shows the validity of extended Navier - Stokes equations with the conventional no - slip velocity boundary condition up to the early transition regime of micro - channel gas flows .