A High Order Theory for an Isothermal Rarefied Gas Flow in Micro Channels

Gas flows take place in a number of micro-electro-mechanical systems (MEMS). Since the dimensions of the MEMS are within μm range, it is necessary to take into account the gas rarefaction effects in investigations of these flows. This paper presents the solution and analysis of isothermal compressible gas flow through micro channels with slow varying cross section under low Mach number conditions. The problem is solved by the introduction of the small parameter ε that presents the square of the Mach and Reynolds numbers ratio. Small parameter ε is used in a regular perturbation analysis of the problem. The exact dependence among Mach, Reynolds and Knudsen number is utilized, which leads to accurate prediction of the influence of the inertia forces and the slip boundary conditions.