A model for flows in channels, pipes, and ducts at micro and nano scales

Rarefied gas flows in channels, pipes, and ducts with smooth surfaces are s tudied in a wide range of Knudsen number (Kn) at low Mal number (M) with th e objective of developing simple, physics-based models. Such flows are enco untered in microelectromechanical systems (MEMS) in nanotechnology applicat ions, and in low-pressure environments. A new general boundary condition th at accounts for the reduced momentum and heat exchange with wall surfaces i s proposed and its validity is investigated. It is shown that it is applica ble in the entire Knudsen range and is second-order accurate in Kn in the s lip flow regime. Based on this boundary condition, a universal scaling for the velocity profile is obtained, which is used to develop a unified model predicting mass flow rate and pressure distribution with reasonable accurac y for channel, pipe, and duct flows in the regime (0 less than or equal to Kn < infinity). A rarefaction coefficient is introduced into this two-param eter model to account for the increasingly reduced intermolecular collision s in the transition and free-molecular regimes. The new model is validated with comparisons against direct-simulation Monte Carlo results, linearized Boltzmann solutions, and experimental data.