Derivations of extended Navier-Stokes equations from upscaled molecular transport considerations for compressible ideal gas flows: towards extended constitutive forms

Abstract

This paper deals with the derivations of the extended forms of the continuum conservation equations for ideal gas flows with heat and mass transfer, from upscaled molecular transport considerations. It is shown that for strong local temperature and/or density gradients, diffusive transport of momentum, heat, and mass over subcontinuum length scales gives rise to additional terms in the corresponding continuum level constitutive relationships. An exact analogy with kinematically hypothesized extended rheological forms is established by casting the expression for momentum flux in an equivalent linear form, with the postulation of a gradient-based hypothesis. Possible considerations of extending the theory to more general flow conditions are also discussed.