High pressure gradient driven micro-channel flow modelling with very the high ratios of absolute pressure and temperature (see Agrawal et al. 2005 [1]) define the difference between physical and computational results using continuum approaches (see Maurer et al. 2003, Durst et al. 2006, Dongari et al. 2008 [3, 4, 8]). In the present paper this deviation of the computational results is explained by the statistical correlation of the molecular number density and the single molecule velocity inside a compressible gas flow. Classical solutions of Navier-Stokes equations do not satisfy the physical conditions of compressible, dilute molecular flows (see Brenner 2005, Greenshields and Reese 2007, Mizzi et al. 2008 [2, 6, 9]). Furthermore the consistent entropy production and the comparison between macroscopic physical values and the molecular diffusion closure are shown. Finally the computational results using this statistical model are compared with algebraic solutions verifying the thermodynamic consistence of the present statistical moment closure model.

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