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Microchannel has become an important structure for many modern devices for improving heat and/or mass transfer performance as well as scaling down the component size. A microchannel reformer and a backing layer in a PEM fuel cell are good examples for applications. Therefore, the study of the flow and heat transfer in a microchannel is an important research problem for design purposes. In this paper, a numerical study by using the lattice Boltzmann method LBM, is performed to investigate a flow between parallel plates with a micro gap. Incompressible and compressible flows are calculated with a nine-velocity LBM model. The results for small Knudsen number (Kn) flow agree well with the exact solutions for traditional Navier-Stokes equation with no-slip boundary conditions. When the Kn is increased, the no-slip condition may not be valid on the wall and the flow may become slip flow. The slip velocity on the wall, the velocity profile, the pressure distribution and temperature distribution are presented in this work for various Kn. Results of the flow characteristics are in good agreement with the experimental results given in the literature.