  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).
