**Microscopic molecular dynamics characterization of the second-order non-
Navier-Fourier constitutive laws in the Poiseuille gas flow**

A Rana and R Ravichandran and JH Park and RS Myong, PHYSICS OF FLUIDS, 28, 082003 (2016).

DOI: 10.1063/1.4959202

The second-order non-Navier-Fourier constitutive laws, expressed in a
compact algebraic mathematical form, were validated for the force-driven
Poiseuille gas flow by the deterministic atomic-level microscopic
molecular dynamics (MD). Emphasis is placed on how completely different
methods (a second-order continuum macroscopic theory based on the
kinetic Boltzmann equation, the probabilistic mesoscopic direct
simulation Monte Carlo, and, in particular, the deterministic
microscopic MD) describe the non-classical physics, and whether the
second-order non-Navier-Fourier constitutive laws derived from the
continuum theory can be validated using MD solutions for the viscous
stress and heat flux calculated directly from the molecular data using
the statistical method. Peculiar behaviors (non-uniform tangent pressure
profile and exotic instantaneous heat conduction from cold to hot **R. S.
Myong, "A full analytical solution for the force-driven compressible
Poiseuille gas flow based on a nonlinear coupled constitutive relation,"
Phys. Fluids 23(1), 012002 (2011)**) were re-examined using atomic-level
MD results. It was shown that all three results were in strong
qualitative agreement with each other, implying that the second-order
non-Navier-Fourier laws are indeed physically legitimate in the
transition regime. Furthermore, it was shown that the non-Navier-Fourier
constitutive laws are essential for describing non-zero normal stress
and tangential heat flux, while the classical and non-classical laws
remain similar for shear stress and normal heat flux. Published by AIP
Publishing.

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