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The Navier--Stokes transport coefficients for a model of a confinedquasi-two-dimensional granular binary mixture of inelastic hard spheres aredetermined from the Boltzmann kinetic equation. A normal or hydrodynamicsolution to the Boltzmann equation is obtained via the Chapman--Enskog methodfor states near the local version of the homogeneous time-dependent state. Themass, momentum, and heat fluxes are determined to first order in the spatialgradients of the hydrodynamic fields, and the associated transport coefficientsare identified. As expected, they are given in terms of the solutions of a setof coupled linear integral equations. In addition, in contrast to previousresults obtained for low-density granular mixtures, there are also nonzerocontributions to the first-order approximations to the partial temperatures$T_i^{(1)}$ and the cooling rate $\zeta^{(1)}$. Explicit forms for thediffusion transport coefficients, the shear viscosity coefficient, and thequantities $T_i^{(1)}$ and $\zeta^{(1)}$ are obtained by assuming thesteady-state conditions and by considering the leading terms in a Soninepolynomial expansion. The above transport coefficients are given in terms ofthe coefficients of restitution, concentration, and the masses and diameters ofthe components of the mixture. The results apply in principle for arbitrarydegree of inelasticity and are not limited to specific values of concentration,mass and/or size ratios. As a simple application of these results, theviolation of the Onsager reciprocal relations for a confined granular mixtureis quantified in terms of the parameter space of the problem.

Navier--Stokes transport coefficients for a model of a confined quasi-two-dimensional granular binary mixture