On the influence of gravity on the thermal conductivity

TL;DR

This paper investigates how gravity affects the thermal conductivity of a gas under a thermal gradient, revealing anisotropic pressure and altered heat flux through a kinetic model analysis.

Contribution

It provides an exact perturbation solution of the BGK kinetic model to quantify gravity's influence on gas thermal conductivity without convection.

Findings

Pressure tensor becomes anisotropic under gravity.

Heat flux increases when heating from above, decreases from below.

Gravity induces measurable corrections to classical Fourier flow.

Abstract

In this paper we evaluate the corrections to the Navier-Stokes constitutive equations induced by the action of a gravitational field in a gas subjected to a thermal gradient parallel to the field with no convection. The analysis is performed from an exact perturbation solution of the BGK kinetic model for Maxwell molecules through sixth order in the field. The reference state (zeroth order approximation) corresponds to the exact solution in the pure planar Fourier flow, which holds for arbitrary values of the thermal gradient. The results show that the pressure tensor becomes anisotropic, so that the momentum flux along the field direction is enhanced. In addition, the heat flux increases (decreases) with respect to its Navier-Stokes value when the gas is heated from above (below).