  Explicit expressions for the heat and momentum fluxes are given for a
low-density multicomponent mixture in a steady state with temperature and
velocity gradients. The results are obtained from a formally exact solution of
the Gross-Krook model [Phys. Rev. {\bf 102}, 593 (1956)] of the Boltzmann
equation for a multicomponent mixture. The transport coefficients (shear
viscosity, viscometric functions, thermal conductivity and a cross coefficient
measuring the heat flux orthogonal to the thermal gradient) are nonlinear
functions of the velocity and temperature gradients and the parameters of the
mixture (particle masses, concentrations, and force constants). The description
applies for conditions arbitrarily far from equilibrium and is not restricted
to any range of mass ratios, molar fractions and/or size ratios. The results
show that, in general, the presence of the shear flow produces an inhibition in
the transport of momentum and energy with respect to that of the Navier-Stokes
regime. In the particular case of particles mechanically equivalent and in the
tracer limit, previous results are recovered.
