Numerical Simulation of Gaseous Flow and Heat Transfer in Laminar Slip Flow Regime

No slip wall boundary condition is known to be valid only for Knudsen number below 0.001. Most of the practical gaseous flow in microchannel, on the other hand, are characterised by higher values of Knudsen, and some slip model has to be enforced. Furthermore, in gaseous flow Kn, Ma and Re are closely related, and an increase in Kn yields an increase in Ma, for a fixed value of Re. Thus, compressibility effects may have a significant impact on microchannel performances. In the present paper, first and second order slip flow boundary conditions are enforced in an hybrid finite difference/ finite volume, compressible flow solver. A plane microchannels geometry is considered, allowing for easy validation, although the code is formulated for arbitrary geometries. Both slip velocity and temperature jump are taken into account, and some detail is given on the stability issue of second order slip at the wall, following Karniadakis and Beskok approach. The slip models are first validated against analytical solutions in the limiting case of fully developed, low Mach number flow. In order to match the literature solutions, fixed temperature is imposed at the boundaries. Then, computation at different Mach number levels are presented and discussed, highlighting the effect of compressibility along the channel length. Results are given in term of Nusselt number and Poiseuille number, and comparison between first order, second order and no-slip results are shown as a function of Knudsen value.