Analysis of three nonlinear effects in a continuum approach to heat transport in nanosystems

Nonlinear effects may be especially relevant in heat transport at the nanoscale, because small temperature differences divided by minute lengths may yield very high temperature gradients. Here we discuss such effects using a generalized heat-transport equation, whose nonlinear terms are explored in three situations of potential practical interest, namely: length dependence of the thermal conductivity of carbon nanotubes, heat rectification in troncoconical nanowires, and anomalies in the temperature profile in radial heat transport in thin layers or graphene sheets. Their thermodynamic aspects are also discussed.