The rarefied gas flow through a long microchannel with multi throats is studied in both slip and transition flow regimes by the lattice Boltzmann method with Two Relaxation Times (TRT). The power-law analytical function is applied to improve the slippage velocity on the microchannel surfaces. The slip velocity correction at the corner point of microchannel is used. Therefore, a slip coefficient basis on the kinetic theory is considered. The Zou-He and Bounce back-Specular Reflection boundary conditions are used at the inlet-outlet of the geometry and on the microchannel wall surfaces, respectively. The present model results coincide with the Direct Simulation Monte Carlo and the Information Preservation values. The present model predicts the slippage velocity with higher accuracy as compared with the single relaxation time one. Moreover, this model has low cost and running time in comparison with the mention models.

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