  Based on the exact solution of Boltzmann kinetic equation in the
relaxation-time approximation, the precision of the two most recent
formulations of relativistic second-order non-conformal viscous hydrodynamics
(14-moment approximation and causal Chapman-Enskog method), standard
Israel-Stewart theory, and anisotropic hydrodynamics framework, in the simple
case of one-dimensional Bjorken expansion, is tested. It is demonstrated that
the failure of Israel-Stewart theory in reproducing exact solutions of the
Boltzmann kinetic equation occurs due to neglecting and/or choosing wrong forms
of some of the second-order transport coefficients. In particular, the
importance of shear--bulk couplings in the evolution equations for dissipative
quantities is shown. One finds that, in the case of the bulk viscous pressure
correction, such coupling terms are as important as the corresponding
first-order Navier-Stokes term and must be included in order to obtain, at
least qualitative, overall agreement with the kinetic theory.
