  The Navier--Stokes transport coefficients for a model of a confined
quasi-two-dimensional granular binary mixture of inelastic hard spheres are
determined from the Boltzmann kinetic equation. A normal or hydrodynamic
solution to the Boltzmann equation is obtained via the Chapman--Enskog method
for states near the local version of the homogeneous time-dependent state. The
mass, momentum, and heat fluxes are determined to first order in the spatial
gradients of the hydrodynamic fields, and the associated transport coefficients
are identified. As expected, they are given in terms of the solutions of a set
of coupled linear integral equations. In addition, in contrast to previous
results obtained for low-density granular mixtures, there are also nonzero
contributions to the first-order approximations to the partial temperatures
$T_i^{(1)}$ and the cooling rate $\zeta^{(1)}$. Explicit forms for the
diffusion transport coefficients, the shear viscosity coefficient, and the
quantities $T_i^{(1)}$ and $\zeta^{(1)}$ are obtained by assuming the
steady-state conditions and by considering the leading terms in a Sonine
polynomial expansion. The above transport coefficients are given in terms of
the coefficients of restitution, concentration, and the masses and diameters of
the components of the mixture. The results apply in principle for arbitrary
degree of inelasticity and are not limited to specific values of concentration,
mass and/or size ratios. As a simple application of these results, the
violation of the Onsager reciprocal relations for a confined granular mixture
is quantified in terms of the parameter space of the problem.
