Boundary effect and heat vortices of hydrodynamic heat conduction in graphene

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.

Automated summary

This study proposes a simple algorithm for solving the Guyer-Krumhansl equations and examines the relationship between thermal conductivity of suspended graphene and heat flux boundary conditions. The results show that heat vortices can occur in the heat flux field when the strength of the point sink exceeds a critical value. Additionally, it is observed that the formation of heat vortices is also influenced by the side length perpendicular to the dominant heat flow direction. Furthermore, the study finds that the no-slip boundary condition facilitates the generation of heat vortices, while specular phonon-boundary interactions disrupt their formation. Interestingly, it is discovered that hydrodynamic heat conduction allows heat to flow from cold regions to hot regions in suspended single-layer graphene.