Three-dimensional lattice Boltzmann BGK model and its application to flows with heat transfer in a rectangular microchannel

In this paper, we present a 3D lattice Boltzmann BGK model for simulation of micro ows with heat transfer. This model is an extension of the two-dimensional model that is based on the kinetic theory and the thermal lattice Boltzmann method. The kinetic relations of the relaxation times in this model were linked with the Knudsen number, and a di use scattering boundary condition for the velocity and thermal elds was presented for the 3D lattice Boltzmann method. The present 3D lattice Boltzmann model was successfully applied to simulate the ow and heat transfer in rectangular channels using the 3D TLLBM developed by the authors. Numerical results obtained by the present method show that the LBM can give a good prediction of the micro uidic behaviours with thermal e ects. Copyright ? 2005 John Wiley & Sons, Ltd.