Second-order Description of Force-driven Compressible Plane Poiseuille Flow

There are cases in which large variations in velocity and/or thermal fields occur where it has been shown that the Navier-Stokes-Fourier (NSF) equations do not provide accurate results. Using continuum mechanics principles, a fully second order continuum theory of fluids was developed (Paolucci, Continnum Mech. Therm., Vol. 34, 185-215 (2022)). Computer experiments using the direct simulation Monte Carlo (DSMC) method have shown that at small Knudsen number the pressure and temperature profiles in force-driven compressible plane Poiseuille flow exhibits different qualitative behavior from the profiles obtained by NSF equations. We compare the DSMC measurements with numerical solutions of equations resulting from the second order theory. We find that the second order equations predict the bimodal temperature profile and recover many of the other anomalous features (e.g., non-constant pressure and non-zero parallel heat flux). Comparisons of the predictions coming from the second order theory are provided in order to critically assess its validity and usefulness.