  We performed event-driven simulations of a two-dimensional granular gas
between two vibrating walls and directly measured the local heat flux and
energy dissipation rate in the stationary state. Describing the local heat flux
as a function of the coordinate x in the direction perpendicular to the driving
walls, we use a generalization of Fourier's law, q_x(x) = kappa d_x T(x) + mu
d_x rho(x), to relate the local heat flux to the local gradients of the
temperature and density. This ansatz accounts for the fact that density
gradients also generate heat flux, not only temperature gradients. The
transport coefficients kappa and mu are assumed to be independent of x, and we
check the validity of this assumption in the simulations. Both kappa and mu are
determined for different system parameters, in particular, for a wide range of
coefficients of restitution. We also compare our numerical results to existing
hydrodynamic theories. Agreement is found for kappa for very small
inelasticities only. Beyond this region, kappa and mu exhibit a striking
non-monotonic behavior.
