Gad-el-Hak, M.The Fluid mechanics of microdevices-the Freeman Scholar lecture. ASME J. Fluids Eng., 121: 5–33,1999.
Beskok, A.Validation of a new velocity-slip model for separated gas microflows, Num. Heat Transfer, Part B, 40: 451–471,2001.
Cercignani, C.The Boltzmann Equation and Its Applications. Springer-Verlag, New York, 1988.
Bird, G.Molecular Gas Dynamics and the Direct Simulation of Gas Flows. Clarendon Press, Oxford, 1994.
Tang, G. H., Tao, W. Q. and He, Y. L.Lattice Boltzmann method for gaseous microflows using kinetic theory boundary conditions. Phys. Fluids, 17: 058101, 2005.
Tang, G. H., Zhang, Y. H., Gu, X. J. and Emerson, D. R.Lattice Boltzmann modelling Knudsen layer effect in non-equilibrium flows. Europhys. Lett., 83: 40008, 2008.
Mieussens, L.Discrete-velocity models and numerical schemes for the Boltzmann-BGK equation in plane and axisymmetric geometries. J. Comput. Phys., 162: 429–466, 2000.
Sharipov, F.Non-isothermal gas flow through rectangular microchannels. J. Micromech. Microeng., 9: 394–401, 1999.
Titarev, V. A.Implicit unstructured-mesh method for calculating Poiseuille flows of rarefied gas. Commun.Comput. Phys., 8: 427–444,2010.
Xu, K. and Huang, J. C.A unified gas-kinetic scheme for continuum and rarefied flows. J. Comput. Phys., 229: 7747–7764, 2010.
Gu, X. J. and Emerson, D. R.A high-order moment approach for capturing non-equilibrium phenomena in the transition regime. J. Fluid Mech., 636: 177–216,2009.
Taheri, P., Torrilhon, M. and Struchtrup, H.Couette and Poiseuille microflows: Analytical solutions for regularised 13-moment equations. Phys. Fluids, 21: 017102, 2009.
Gu, X. J., Emerson, D. R. and Tang, G. H.Kramers’ problem and the Knudsen minimum: A theoretical analysis using a linearised 26-moment approach. Contin. Mech. Thermodyn., 21: 345–360, 2009.
Taheri, P. and Struchtrup, H.An extended macroscopic transport model for rarefied gas flows in long capillaries with circular cross section. Phys. Fluids, 22: 112004, 2010.
Gu, X. J. and Emerson, D. R.Modeling oscillatory flows in the transition regime with a high-order moment method. Microfluid. Nanofluid., 10: 389–401,2011.
Grad, H.On the kinetic theory of rarefied gases. Comm. Pure Appl. Math., 2: 331–407,1949.
Struchtrup, H. and Torrilhon, M.Regularization of Grad’s 13 moment equations: Derivation and linear analysis. Phys. Fluids, 15: 2668–2680,2003.
Struchtrup, H.Macroscopic Transport Equations for Rarefied Gas Flows. Springer, Berlin Heidelberg, 2005.
Lockerby, D. A., Reese, J. M. and Gallis, M. A.The usefulness of higher-order constitutive relations for describing the Knudsen layer. Phys. Fluids, 17: 100609, 2005.
Lockerby, D. A. and Reese, J. M.On the modelling of isothermal gas flows at the microscale. J. Fluid Mech., 604: 235–261,2008.
Young, J. B.Calculation of Knudsen layers and jump conditions using the linearized G13 and R13 moment methods. Int. J. Heat Mass Transfer, 54: 2902–2912,2011.
Struchtrup, H. and Torrilhon, M.Higher order effects in rarefied channel flows. Phys. Rev. E, 78: 046301, 2008
Maxwell, J. C.On stresses in rarefied gases a rising from inequalities of temperature. Phil. Trans. Roy. Soc., 17: 231–256,1879.
Struchtrup, H. and Weiss, W.Temperature jump and velocity slip in the moment method. Contin. Mech. Thermodyn., 12: 1–18, 2000.
Hadjiconstantinou, N. G.Oscillatory shear-driven gas flows in the transition and free molecular flow regimes. Phys. Fluids, 17: 100611, 2005.
Patankar, S. V.Numerical Heat Transfer and Fluid Flow. Hemisphere Publishing Corporation, 1980.
Rhie, C. M. and Chow, W. L.Numerical study of turbulent flow past an airfoil with trailing edge separation. AIAA J., 21: 1525–1532, 1983.
Gallis, M. A., Rader, D. J. and Torczynski, J. R.Calculations of the near-wall thermophoretic force in rarefied gas flow. Phys. Fluids, 14: 4290–4301, 2002.
Li, Q., He, Y. L., Tang, G. H. and Tao, W. Q.Lattice Boltzmann modeling of microchannel flows in the transition flow regime. Microfluid. Nanofluid., 10: 607–618,2011.
Shen, C., Tian, D. B., Xie, C. and Fan, J.Examination of the LBM in simulation of microchannel flow in transitional regime. Microscale Thermal Eng., 8: 423–432, 2010.
Arkilic, E. B., Schmidt, M. A. and Breuer, K. S.Slip flow in microchannel. J. Microelectromech. Syst., 6: 167–174, 1997.
Tang, G. H., He, Y. L. and Tao, W. Q.Comparison of gas slip models with solutions of lin-earized Boltzmann equation and direct simulation of Monte Carlo method. Int. J. Mod. Phys. C, 18: 203–216, 2007.
Hadjiconstantinou, N. G. and O, SimekConstant-wall-temperature Nusselt number in micro and nano-channels. ASME J. Heat Transfer 124(2): 356–364, 2002.
Ohwada, T., Sone, Y. and Aoki, K.Numerical analysis of the Poiseuille and thermal transpi-ration flows between two parallel plates on the basis of the Boltzmann equation for hardsphere molecules. Phys. Fluids A, 1: 2042–2049, 1989.
Loyalka, S. K. and Hamoodi, S. A.Poiseuille flow of a rarefied gas in a cylindrical tube: Solution of linearized Boltzmann equation. Phys. Fluids A, 2: 2061–2065, 1990.