  In this work we investigate heat conduction along a ladder-model conformed by
two coupled one dimensional lattices with different anharmonicity. We study how
the interchain coupling modifies the thermal properties of the isolated
systems. For a large enough coupling strength, we demonstrate that a harmonic
lattice interacting with an anharmonic one is able to support a linear thermal
gradient when it is connected to two heat reservoirs at different temperatures.
We estimate this critical coupling by applying the self-consistent phonon
theory (SCPT) to the anharmonic counterpart. By exchanging the heat baths
connections between the harmonic and the anharmonic chains, our results show
that the coupled system reveals as a thermal rectifier.
