Navier–Stokes–Fourier equations as a parabolic limit of a general hyperbolic system of rational extended thermodynamics

This paper aims to prove that a general system of 14 balance laws for a compressible, possibly dense, gas that satisfies the universal principles of Rational Extended Thermodynamics (RET) converges to the Navier–Stokes–Fourier equations in the first step of the Maxwellian iteration. Moreover, in a theory not far from equilibrium, we show that the production terms of the hyperbolic system are uniquely determined as soon as the heat conductivity, the shear viscosity, and the bulk viscosity are assigned. The obtained results are tested on the RET theories for rarefied monatomic and polyatomic gases.