  In the classical framework, the Navier-Stokes-Fourier equations are obtained
through the linear uncoupled thermodynamic force-flux relations which guarantee
the non-negativity of the entropy production. However, the conventional
thermodynamic description is only valid when the Knudsen number is sufficiently
small. Here, it is shown that the range of validity of the
Navier-Stokes-Fourier equations can be extended by incorporating the nonlinear
coupling among the thermodynamic forces and fluxes. The resulting system of
conservation laws closed with the coupled constitutive relations is able to
describe many interesting rarefaction effects, such as Knudsen paradox,
transpiration flows, thermal stress, heat flux without temperature gradients,
etc., which can not be predicted by the classical Navier-Stokes-Fourier
equations. For this system of equations, a set of phenomenological boundary
conditions, which respect the second law of thermodynamics, is also derived.
Some of the benchmark problems in fluid mechanics are studied to show the
applicability of the derived equations and boundary conditions.
