Advances in manufacturing techniques over the last decade have made it possible to make
electrical devices with dimensions as small as 90 nanometers [I]. Using similar techniques,
devices that perform moving mechanical tasks less than 100 pm are being manufactured in
quantity [2] [3], e.g., pumps, turbines, valves and nozzles. These devices are incorporated
into microelectromechanical systems (MEMS) that can be potentially used in devices such
as medical and chemical sensors, and fuel cells. The gas and fluid flows in devices of this
size exhibit behavior that can not be described by the classical Navier-Stokes and Fourier
equations of continuum mechanics. This happens when flows become rarefied such that
the mean free path (distance between two subsequent particle collisions) is not negligible
compared to the characteristic length scale. The rarefaction of a fluid flow is also seen in
the upper atmosphere for larger length scales, e.g., for re-entry for space craft and some
supersonic jet aircraft.
Currently, when one looks to model fluid flow and heat transfer in a rarefied flow there are
two predominantly accepted choices. Either one uses jump and slip boundary conditions
with the Navier-Stokes and Fourier (NSF) equations, or a statistical particle model such as
direct simulation Monte-Carlo (DSMC) [4] and the Boltzmann equation. DSMC is computationally
intensive for complex flows and the NSF solutions are only valid for low degrees
of rarefaction.
As an alternative to these methods we have used Grad's 13 moment expansion of the
Boltzmann equation [5]. For its implementation, a set of boundary conditions and three
numerical methods for the solution have been devised. The model is applied to the solution
of 2-D micro Couette flow with heat transfer. Results are compared to those obtained from
the Navier-Stokes-Fourier equations, reduced Burnett equations, Regularized 13 moment
equations and DSMC simulations.
| Identifer | oai:union.ndltd.org:uvic.ca/oai:dspace.library.uvic.ca:1828/749 |
| Date | 10 April 2008 |
| Creators | Thatcher, Toby |
| Contributors | Struchtrup, Henning |
| Source Sets | University of Victoria |
| Detected Language | English |
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