Boundary effect and heat vortices of hydrodynamic heat conduction in graphene

Abstract

A SIMPLE like algorithm is proposed for numerically solving the Guyer-Krumhansl equations. Results show that thermal conductivity of suspended graphene depends on the heat flux boundary conditions. If the strength of the point source is fixed, only when the strength of the point sink exceeds a critical value can the heat vortices occur in the heat flux vector field. We also find that heat vortices only appear when the side length perpendicular to the dominant heat flow direction exceeds a critical value. Furthermore, the no-slip boundary condition is beneficial for the generation of heat vortices, while the specular phonon-boundary interactions can disrupt the heat vortices. These findings will contribute to experiments on heat vortex in the heat flux field of suspended graphene. Finally, it is found that the heat can flow from some cold regions to hot regions for the hydrodynamic heat conduction in suspended single-layer graphene.