Steady-state heat conduction in quiescent fluids: Incompleteness of the Navier-Stokes-Fourier equations

► Linear irreversible thermodynamics is used to prove incompleteness of the Navier-Stokes-Fourier equations. ► The proof proceeds by counterexample involving steady-state heat conduction through fluids at rest. ► The proof is independent of the relation between the fluid's momentum and mass velocities.