Modelling thermal flow in the transition regime using a lattice Boltzmann approach

Centre for Microfluidics and Microsystems Modelling, Computational Science and Engineering Department, CCLRC Daresbury Laboratory - Warrington, WA4 4AD, UK

Corresponding author: Y.Zhang@dl.ac.uk

Received: 18 September 2006
Accepted: 1 December 2006

Abstract

Lattice Boltzmann models are already able to capture important rarefied flow phenomena, such as velocity-slip and temperature jump, provided the effects of the Knudsen layer are minimal. However, both conventional hydrodynamics, as exemplified by the Navier-Stokes-Fourier equations, and the lattice Boltzmann method fail to predict the nonlinear velocity and temperature variations in the Knudsen layer that have been observed in kinetic theory. In the present paper, we propose an extension to the lattice Boltzmann method that will enable the simulation of thermal flows in the transition regime where Knudsen layer effects are significant. A correction function is introduced that accounts for the reduction in the mean free path near a wall. This new approach is compared with direct simulation Monte Carlo data for Fourier flow and good qualitative agreement is obtained for Knudsen numbers up to 1.58.