Projects per year
Abstract
This paper presents a new technique that combines Grad's 13moment equations (G13) with a phenomenological approach. The combination of these approaches and the proposed solution technique manages to capture important nonequilibrium phenomena that start to appear in the early transitionflow regime. In contrast to the fullycoupled 13moment equations, a significant advantage of the present solution technique is that it does not require extra boundary conditions. The solution method is similar in form to the Maxwellian iteration used in the kinetic theory of gases. In our approach, Grad's equations for viscous stress and heat flux are used as constitutive relations for the conservation equations instead of being solved as equations of transport. This novel technique manages to capture nonequilibrium effects and its relative computational cost is low in comparison to other methods such as fullycoupled solutions involving many moments or discrete methods. In this study, the proposed numerical procedure is applied to a planar Couette flow and the results are compared to predictions obtained from the direct simulation Monte Carlo method. In the transition regime, this test case highlights the presence of normal viscous stresses and tangential heat fluxes that arise from nonequilibrium phenomena. These effects cannot be captured by the NavierStokesFourier constitutive equations or phenomenological modifications thereof. Moreover, simply using the G13 equations, along with the decoupled solution method, does not capture the nonlinearities occurring in the proximity of a solid wall. However, combining phenomenological scaling functions and slip boundary conditions with the G13 equations provides a better representation of these important nonequilibrium phenomena but at a relatively low computational cost.
Original language  English 

Title of host publication  Proceedings of the 4th International Conference on Nanochannels, Microchannels and Minichannels (ICNMM2006) 
Publication status  Published  2006 
Keywords
 G13
 microfluidics
 moment method
 nonequilibrium
 rarefication
Projects
 1 Finished

Fluid Flow and Heat Transfer in Gas Microsystems
Reese, J.
EPSRC (Engineering and Physical Sciences Research Council)
1/01/04 → 30/09/07
Project: Research