  The local balance equations for the density, momentum, and energy of a dilute
gas of elastic or inelastic hard spheres, strongly confined between two
parallel hard plates are obtained. The starting point is a Boltzmann-like
kinetic equation, recently derived for this system. As a consequence of the
confinement, the pressure tensor and the heat flux contain, in addition to the
terms associated to the motion of the particles, collisional transfer
contributions, similar to those that appear beyond the dilute limit. The
complexity of these terms, and of the kinetic equation itself, compromise the
potential of the equation to describe the rich phenomenology observed in this
kind of systems. For this reason, a simpler model equation based on the
Boltzmann equation is proposed. The model is formulated to keep the main
properties of the underlying equation, and it is expected to provide relevant
information in more general states than the original equation. As an
illustration, the solution describing a macroscopic state with uniform
temperature, but a density gradient perpendicular to the plates is considered.
This is the equilibrium state for an elastic system, and the inhomogeneous
cooling state for the case of inelastic hard spheres. The results are in good
agreement with previous results obtained directly from the Boltzmann equation.
