The planar Couette flow with slip and jump boundary conditions in a microchannel

Abstract

Abstract The steady state of a dilute gas enclosed within a rectangular cavity, whose upper and lower sides are in relative motion, is considered in the slip and early transition regimes. The DSMC (Direct simulation Monte Carlo) method is used to solve the Boltzmann equation for analysing a Newtonian viscous heat conducting ideal gas with the slip and jump boundary conditions (SJBC) in the vicinity of horizontal walls. The numerical results are compared with the Navier–Stokes solutions, with and without SJBC, through the velocity, temperature, and normal heat flux profiles. The parallel heat flux and shear stress are also evaluated as a function of rarefaction degree; estimated by the Knudsen number K n ${K_{n}}$ . Thus, the breakdown of the classical Navier–Stokes theory is clarified in the non-equilibrium area, so-called Knudsen layer, near the top and bottom sides.