A computational method for solving thermodynamically consistent Eu's generalized hydrodynamic equations is presented. The computational method is based on the finite volume formulation and exactly the same as the Navier-Stokes codes, except for an additional routine of calculating shear stress and heat flux from the given conserved variables and thermodynamic forces. A new slip boundary condition based on Langmuir's theory of adsorption phenomena is also presented that yields a trend of increasing pressure curve nonlinearity with increasing rarefaction in a long microchannel coinciding with the experimental observation.

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