Thermal pulse propagation beyond the Maxwell-Cattaneo theory: Application to one-dimensional nanosystems

A non-local and non-linear thermodynamical model of heat transfer at nanoscale beyond the well-known Maxwell-Cattaneo theory is derived. The compatibility of the proposed model with second law of thermodynamics is proved. The model is subsequently used to investigate the propagation of a heat pulse in one-dimensional nanosystems in the linear case. The predicted results are compared with those arising from the Maxwell-Cattaneo theory in order to point out the possible influence both of the non-local effects, and of the relaxation effects of the higher-order fluxes. Some problems related to initial data and boundary conditions are also discussed.