Cross-stream pressure and non-equilibrium transport in pressure-driven microscale and rarefied Poiseuille flows based on analytical modelling and direct simulation Monte Carlo

This study investigates the non-equilibrium transport characteristics of pressure-driven microscale and rarefied Poiseuille flows based on analytical modelling and the direct simulation Monte Carlo (DSMC) method. A closed-form analytical solution for the cross-stream pressure and viscous stress distributions is derived from the second-order nonlinear coupled constitutive relation model. This solution reveals a compact tangent-function form, demonstrating that the convex pressure profiles observed in rarefied flows – unaccounted for by classical Navier–Stokes–Fourier theory – are driven by the coupling of kinematic stress constraints and geometric confinement. Complementing this theory, an extensive set of DSMC simulations is performed across a wide range of Knudsen numbers (up to 13.23), Mach numbers (up to 0.868) and channel aspect ratios. These simulations analyse the effects of rarefaction and pressure ratio, with a special emphasis on entropy and entropy generation. A kinetic decomposition of the heat flux and an energy-budget analysis demonstrate a pronounced non-Fourier regime in highly rarefied channels, in which the streamwise heat flux reverses sign and transports energy upstream and from colder core regions towards the hotter inlet, extending linear Onsager-based predictions to nonlinear, pressure-driven microchannel flows at moderate Mach number. This anomaly arises not from anomalous diffusion but from stress–work coupling between anisotropic normal stresses and velocity gradients that force the heat-flux divergence to balance expansion work when convective cooling collapses. Our findings highlight the importance of non-equilibrium constitutive models to accurately predict irreversible processes in microscale and rarefied gas flows inside channels, establishing the analytical and computational results as reference data.