  We consider an interacting particle system in the interval $[1,N]$ with
reservoirs at the boundaries. While the dynamics in the channel is the simple
symmetric exclusion process, the reservoirs are also particle systems which
interact with the given system by exchanging particles. In this paper we study
the case where the size of each reservoir is the same as the size of the
channel . We will prove that the hydrodynamic limit equation is the heat
equation with boundary conditions which relate first and second spatial
derivatives at the boundaries for which we will prove the existence and
uniqueness of weak solutions. The propagation of chaos property can also be
derived.
