Derivation of linearly stable Onsager symmetry principle-consistent equations and their validation for force-driven Poiseuille flow

In this work, we derive higher-order transport equations starting from the Boltzmann equation using a second-order accurate distribution function within the 13-moment framework. The equations are shown to be unconditionally linearly stable and consistent with Onsager’s symmetry principle. We also show that the equations comply with the second law of thermodynamics by establishing the non-negativity of the bulk entropy generation rate using the linearised form of the proposed equations. The force-driven Poiseuille flow problem, a standard benchmark problem, is selected to establish the validity of the equations. A complete analytical solution for this problem is proposed and compared against the Navier–Stokes, regularised 13, Grad 13 solutions and direct simulation Monte Carlo data. The proposed solution captures key rarefaction effects, including the Knudsen layer, non-uniform bimodal pressure profile, non-Fourier heat flux and the characteristic temperature dip at the centre. The analytical solution for the field variables indicates that the equations outperform the existing models in the slip- and transition-flow regimes for the problem considered. These satisfactory results point to the accuracy and applicability of the proposed equations, and the equations hold significant promise for rarefied gas dynamics at large Knudsen numbers.