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

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.