  In this work, we study the thermal transport properties of platelike
composite two-layer samples made of polyester resin and magnetite inclusions.
By means of photoacoustic spectroscopy and thermal relaxation, their effective
thermal diffusivity and conductivity were experimentally measured. The
composite layers were prepared under the action of a static magnetic field,
resulting in anisotropic inclusion structures with the formation of chains of
magnetite particles parallel to the faces of the layers. In one kind of
bilayers, a composite layer was formed on top of a resin layer while their
relative thickness was varied. These samples can be described by known models.
In contrast, bilayers with the same concentration of inclusions and the same
thickness on both sides, where only the angle between their inclusion
structures was systematically varied, show a nontrivial behaviour of their
thermal conductivity as a function of this angle. Through a lacunarity
analysis, we explain the observed thermal response in terms of the complexity
of the interface between the layers.
