2009•Advances in Applied Mathematics and MechanicsRequires access

Numerical Validation of Brenner's Hydrodynamic Model by Force Driven Poiseuille Flow

Zhaoli Guo, Kun Xu

Abstract

Recently Brenner (Physica A 349, 60 (2005)) proposed a modified Navier- Stokes set of equations. Based on some theoretical arguments and some limited ex- periments, the model is expected to be able to describe flows with a finite Knudsen number. In this work, we apply this model to the plane Poiseuille flow driven by a force, and compare the results with the Direct Simulation Monte Carlo (DSMC) measurements. It is found that Brenner's model is inadequate for flows with a finite Knudsen number. AMS subject classifications: 76A02, 76P05, 82C21

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Key concepts: Hagen–Poiseuille equation, Knudsen number, Direct simulation Monte Carlo, Mechanics, Flow (mathematics), Statistical physics, Work (physics), Plane (geometry)