  We study the constraints imposed by conformal symmetry on the equations of
fluid dynamics at second order in gradients of the hydrodynamic variables. At
zeroth order conformal symmetry implies a constraint on the equation of state,
E=2/3 P, where E is the energy density and P is the pressure. At first order,
conformal symmetry implies that the bulk viscosity must vanish. We show that at
second order conformal invariance requires that two-derivative terms in the
stress tensor must be traceless, and that it determines the relaxation of
dissipative stresses to the Navier-Stokes form. We verify these results by
solving the Boltzmann equation at second order in the gradient expansion. We
find that only a subset of the terms allowed by conformal symmetry appear.
