  In the present work, we study heat transport through a one dimensional
time-dependent nanomechanical system. The microscopic model consists of coupled
chains of atoms, considering local and non-local interactions between
particles. We show that the system presents different stationary transport
regimes depending on the driving frequency, temperature gradients and the
degree of locality of the interactions. In one of these regimes, the system
operates as a phonon refrigerator, and its cooling performance is analyzed.
Based on a low frequency approach, we show that non-locality and its interplay
with dissipation cause a decrease in cooling capacity. The results are obtained
numerically by means of the Keldysh non-equilibrium Green's function formalism.
