Two Dimensional Nonlinear Nonequilibrium Kinetic Theory under Steady Heat Conduction

TL;DR

This paper explicitly solves the two-dimensional steady-state Boltzmann equation for hard-disk molecules under a temperature gradient, comparing results with BGK and information theory to reveal persistent qualitative differences.

Contribution

It provides an explicit second-order solution to the 2D Boltzmann equation under steady heat conduction, extending previous 3D findings to 2D systems.

Findings

Qualitative differences among theories persist in 2D case

Derived equation of state and physical quantities for 2D system

Comparison with BGK and information theory results

Abstract

The two-dimensional steady-state Boltzmann equation for hard-disk molecules in the presence of a temperature gradient has been solved explicitly to second order in density and the temperature gradient. The two-dimensional equation of state and some physical quantities are calculated from it and compared with those for the two-dimensional steady-state Bhatnagar-Gross-Krook(BGK) equation and information theory. We have found that the same kind of qualitative differences as the three-dimensional case among these theories still appear in the two-dimensional case.