Asymptotic Solutions of Pressure and Heat Flux of Highly Rarefied Gas Flows in Vacuum Packaged Micro-Electro-Mechanical System Devices

Abstract

This study analyzed a highly rarefied gas flow fields inside an enclosure. The enclosure is formed by four plates with two different temperatures. The plate surfaces are assumed completely diffuse; at the final steady flow stage for any point inside the enclosure or at the surface, the velocity distribution function was determined and all the macroscopic properties was determined by integrating the velocity distribution function. First, the collisionless flow solution was considered as the base solution, and then based on the Bhatnagar-Gross-Krook model, the characteristic relaxation time scale τ was used as a small parameter, and obtained general asymptotic analytical solutions for the flow fields and heat transfer expressions. To validate these asymptotic solutions, a series of numerical simulations with the direct simulation Monte Carlo method were performed and compared with the analytical results. In general, as Knudsen number decreases, the solutions for the pressure, temperature, and density fields deteriorate; the temperature fields had relatively better agreement than the density and pressure fields.