Theoretical Two-Dimensional Modeling of Gas Conduction Between Finite Parallel Plates in High Vacuum

Abstract

A theoretical approach based on gaskinetic theory is described and applied for the modeling of steady-state free-molecule gaseous heat conduction within a diffusive enclosure. With a representative model of microelectromechanical system (MEMS) devices with integrated heaters, the heat transfer between the heated component and its gaseous ambient enclosed in a high vacuum is studied in detail. A molecular simulation based on the direct simulation Monte Carlo (DSMC) method is also employed to validate the theoretical solutions and to study the effects of incomplete thermal accommodation. The impacts of the finite size of the heated beam as well as the gap between the beam and a substrate on the heat transfer are investigated to examine the appropriateness of the common assumptions employed in the modeling of Pirani sensors. Interesting phenomena that are unique in the free-molecule regime are observed and discussed. These studies are valuable to the design of MEMS devices with microheaters.