Introducing a novel slip boundary condition for the compressible gas flow through a micro/nano channel

In this paper, using a solution of the Boltzmann equation along the walls, a new model of slip velocity boundary condition is presented. In the continuation of researches on the effect of gas compressibility on the flow through micro/nano channels, the present slip model shows analytically how the slip velocity boundary condition affected by compressibility of gas. In comparison with shen’s slip velocity model, this model includes an additional term due to compressibility factor gradient along the flow direction. We used the virial equation of state to calculate the compressibility factor gradient along the flow direction. In order to verify the present slip velocity boundary condition and investigate the advantages of it, poiseuille flow through a micro/nano channel in the slip regime and transition regime is studied. The non-dimensional velocity in three inverse Knudsen number calculated. Also, non-dimensional flow rate calculated from Knudsen number 0.005 until 5. The new model accurately predicts minimum flow rate around D=1. In addition, in whole range of Knudsen in comparison with other slip boundary conditions such as first order model, second order model and shen’s model, the present model shows better agreement with that calculated by the linearized Boltzmann equation which is specifically the result of taking the effects of compressibility into account.