  We consider a dilute gas of inelastic hard spheres enclosed in a slab under
the action of gravity along the longitudinal direction. In addition, the gas is
subject to a white-noise stochastic force that mimics the effect of external
vibrations customarily used in experiments to compensate for the collisional
cooling. The system is described by means of a kinetic model of the inelastic
Boltzmann equation and its steady-state solution is derived through second
order in gravity. This solution differs from the Navier-Stokes description in
that the hydrostatic pressure is not uniform, normal stress differences are
present, a component of the heat flux normal to the thermal gradient exists,
and the temperature profile includes a positive quadratic term. As in the
elastic case, this new term is responsible for a bimodal shape of the
temperature profile. The results show that, except for high inelasticities, the
effect of inelasticity on the profiles is to slightly decrease the quantitative
deviations from the Navier-Stokes results.
