  We prove the hydrodynamic limit for a one-dimensional harmonic chain of
interacting atoms with a random flip of the momentum sign. The system is open:
at the left boundary it is attached to a heat bath at temperature $T_-$, while
at the right endpoint it is subject to an action of a force which reads as
$\bar F + \frac 1{\sqrt n} \widetilde{\mathcal F} (n^2 t)$, where $\bar F \ge0$
and $\widetilde{\mathcal F}(t)$ is a periodic function. Here $n$ is the size of
the microscopic system. Under a diffusive scaling of space-time, we prove that
the empirical profiles of the two locally conserved quantities - the volume
stretch and the energy - converge, as $n\to+\infty$, to the solution of a
non-linear diffusive system of conservative partial differential equations with
a Dirichlet type and Neumann boundary conditions on the left and the right
endpoints, respectively.
