Thermal conductivity for a general bidimensional dilute gas within the Chapman-Enskog approximation

TL;DR

This paper analytically calculates the thermal conductivity of a bidimensional dilute gas using Chapman-Enskog's method, providing results for different molecular interaction models and confirming known temperature dependencies.

Contribution

It derives an explicit expression for thermal conductivity in a bidimensional dilute gas for general interactions, including hard disks and Maxwellian molecules, within the Chapman-Enskog framework.

Findings

Hard disks yield a $T^{1/2}$ temperature dependence.

Maxwellian molecules show a linear temperature dependence.

Results are consistent with previous studies for specific interactions.

Abstract

In this work we explicitly calculate the thermal conductivity for a general bidimensional dilute gas of neutral molecules by solving Boltzmann's equation. Chapman-Enskog's method is used in order to analytically obtain this transport coefficient to first approximation in terms of a collision integral for an unspecified molecular interaction model. In the particular case of hard disks interactions, the result is shown to be consistent with previous work by J. V. Sengers \cite{Sengers}, yielding the expected $T^{1/2}$ dependence with the temperature. This dependence is widely used for dense gases as the low density limit in the Enskog expansion. The case of Maxwellian molecules is also explored where a linear dependence with the temperature is obtained.