A high-order continuum model for micro-scale flows is investigated. The Burnett equations are applied to the steady-state micro Couette flow of a Maxwellian monatomic gas. Solutions to these equations are shown to be stable for all Knudsen numbers (Kn) up to the limit of the equations' validity (Kn→1). The reason why previous researchers have failed to obtain solutions to this problem for Kn much greater than 0.1 is explained. A procedure is proposed to overcome these difficulties, and its application successfully demonstrated. Results are obtained on high-resolution numerical grids and show good agreement with data obtained from direct simulation methods. A reduced-order procedure is also described for calculating the implicitly defined first-order slip boundary conditions prior to the solution of the full equations. This method can be used to generate accurate initial guesses for an iterative solution. The comparative utility of second-order boundary conditions is explored and alternatives discussed.
- burnett equations
- micro couette flow
- second-order continuum methods
- rarefied flows
- microelectromechanical systems
- mechanical engineering