  The transport coefficients of a granular fluid driven by a stochastic bath
with friction are obtained by solving the inelastic Enskog kinetic equation
from the Chapman-Enskog method. The heat and momentum fluxes as well as the
cooling rate are determined to first order in the deviations of the
hydrodynamic field gradients from their values in the homogeneous steady state.
Since the collisional cooling cannot be compensated locally for the heat
produced by the external driving force, the reference distribution $f^{(0)}$
(zeroth-order approximation) depends on time through its dependence on
temperature. This fact gives rise to conceptual and practical difficulties not
present in the undriven case. On the other hand, to simplify the analysis and
given that we are interested in computing transport in the first order of
deviations from the reference state, the steady-state conditions are considered
to get explicit forms for the transport coefficients and the cooling rate. A
comparison with recent molecular dynamics simulations for driven granular
fluids shows an excellent agreement for the kinematic viscosity although some
discrepancies are observed for the longitudinal viscosity and the thermal
diffusivity at large densities. Finally, a linear stability analysis of the
hydrodynamic equations with respect to the homogeneous steady state is
performed. As expected, no instabilities are found thanks to the presence of
the external bath.
