Coupled nonlinear constitutive models for rarefied and microscale gas flows: subtle interplay of kinematics and dissipation effects

Abstract

The constitutive relations of gases in a thermal nonequilibrium (rarefied and microscale) can be derived by applying the moment method to the Boltzmann equation. In this work, a model constitutive relation determined on the basis of the moment method is developed and applied to some challenging problems in which classical hydrodynamic theories including the Navier-Stokes-Fourier theory are shown to predict qualitatively wrong results. Analysis of coupled nonlinear constitutive models enables the fundamentals of gas flows in thermal nonequilibrium to be identified: namely, nonlinear, asymmetric, and coupled relations between stresses and the shear rate; and effect of the bulk viscosity. In addition, the new theory explains the central minimum of the temperature profile in a force-driven Poiseuille gas flow, which is a well-known problem that renders the classical hydrodynamic theory a global failure.