Influence of size effect and boundary conditions on temperature overshooting in nanoscale thermal conduction

The temperature overshooting phenomenon in one-dimensional nanoscale heat conduction in thin films is studied for various boundary conditions. The results show that when ballistic heat transport strongly affects the heat transport process, temperature overshooting is more likely to occur. A sudden increase of temperature on only one surface of a thin film cannot trigger temperature overshooting, while symmetric boundary temperature perturbations lead to the largest temperature overshooting. Two-dimensional heat conduction is also studied in a nanoscale area. The analytic results show that Fourier's law may severely underestimate the temperatures in nanofilms as well as in nanoareas when temperature overshooting occurs.