Understanding of flux-limited behaviors of heat transport in nonlinear regime

• Exploring flux-limited behaviors based on a categorization of existing nonlinear heat transport models.
• Proposing phonon hydrodynamic model as a standard to evaluate heat flux limiters.
• Providing accurate modeling of nonlocal and nonlinear heat transport beyond the diffusive limit.

The classical Fourier's law of heat transport breaks down in highly nonequilibrium situations as in nanoscale heat transport, where nonlinear effects become important. The present work is aimed at exploring the flux-limited behaviors based on a categorization of existing nonlinear heat transport models in terms of their theoretical foundations. Different saturation heat fluxes are obtained, whereas the same qualitative variation trend of heat flux versus exerted temperature gradient is got in diverse nonlinear models. The phonon hydrodynamic model is proposed to act as a standard to evaluate other heat flux limiters because of its more rigorous physical foundation. A deeper knowledge is thus achieved about the phenomenological generalized heat transport models. The present work provides deeper understanding and accurate modeling of nonlocal and nonlinear heat transport beyond the diffusive limit.