Heat dissipation from nanoscale heat sources by phonon hydrodynamic model

It remains a challenging task to model heat dissipation from nanoscale heat source due to its multiscale nature. In this work, we tackle this problem by a macroscopic phonon hydrodynamic model via a finite volume scheme with non-uniform grids. A temperature equation is obtained as the classical Fourier heat diffusion equation with the usual source term and an additional one proportional to the Laplacian of the heat source. Thus the present model provides a good prediction of temperature and heat flux fields in heat dissipation from various nanoscale heat sources, as long as their characteristic sizes are larger than few times the average phonon mean free path. For a non-monotonic Gaussian heat source, we show hotspots around its center and anomalous heat conduction from cold to hot regions. In the limit of large system size, we also derive formulas for both temperature and heat flux that enable fast evaluation of non-Fourier solution from the Fourier solution. Therefore, this study provides an efficient approach for non-Fourier heat conduction with nanoscale heat sources, and also a way to manipulate the hotspot by tuning the heat source distribution.