The purpose of this study is to model micro and nano scale flows with Lattice Boltzmann Method (LBM). The continuity assumption for fluid flows and consequently the validity of Navier-stokes equation (NSE) break down as the channel dimensions are reduced significantly. Therefore, some particle based methods such as Molecular Dynamics (MD), Direct Simulation Monte Carlo (DSMC) and LBM are used for the flow simulation in small scales. Among these methods, the LBM require less computational resources and with appreciate adjustment can be used for wide range of the Knudsen number. Moreover the Lattice Boltzmann Equation (LBE) is a more fundamental equation compared to the NSE, which is in theory valid for all reneges of Knudsen number. Therefore, the LBM can be used to simulate fluid flows in all regimes upon appreciate adjustments. Flows through micro and nano channels have been numerically simulated using a modified lattice Boltzmann method (LBM). These pressure driven flows have been performed inside channels with different dimensions which span a wide range of flow regimes covering the slip, transition and to some extend the free molecular regimes. To cover a wide range of the flow regimes, a new relaxation time formulation by considering the rarefaction effect and the effective dynamic viscosity has been obtained. Different boundary conditions, such as the specular reflection boundary condition (SRBC) and diffuse scattering boundary condition (DSBC) have been used. The present results agree very well with exiting empirical and numerical data. The velocity profile and pressure distribution are predicted as well as the volumetric flow rate. The well known Knudsen minimum has also been captured. Keywords lattice Boltzmann method, micro and nano flows, slip regime, transition regime, Knudsen minimum effect.
