Researchers from Germany's Max Planck Institute for Polymer Research and Singapore have shown that the thermal conductivity of graphene changes with the size of the graphene - which actually contradicts Fourier’s law in the micrometer scale. This was shown with computer simulations and later verified in experiments.
The researchers say that "the very concept of thermal conductivity as an intrinsic property does not hold for graphene, at least for patches as large as several micrometers". The researcher found out that the thermal conductivity logarithmically increases as a function of the size of the graphene samples. The longer the graphene patches, the more heat can be transferred per length unit.