Thermal wave: from nonlocal continuum to molecular dynamics

Abstract

It is well known that the continuum model of Fourier's law of heat conduction violates the relativity theory, admits an instantaneous thermal response, and assumes a quasi-equilibrium thermodynamic condition. Transient heat transport, however, is a non-equilibrium phenomenon with a finite thermal wave speed for applications involving very low temperatures, extremely high temperature gradients, and ballistic heat transfers. Hyperbolic and phase-lag heat conduction models have enabled detection of the finite thermal wave speed in heat transport. To accommodate effects of thermomass and size-dependency of thermophysical properties on nano/microscale heat transport and to remove the theoretical singularity of temperature gradients across the thermal wavefront, a nonlocal, fractional-order, three-phase-lag heat conduction is introduced. The model is capable of simulating heat conduction phenomena in multiple spatio-temporal scales. To confirm the existence of thermal waves in nano/microscale heat transport, a molecular dynamics simulation is implemented for the heat transfer within a nanoscale copper slab. Correlating thermal responses in continuum and atomistic scales sheds light on the effect of length scale, fractional order, and phase-lags in multiscale heat transport. The multiscale simulation is of practical importance for microelectromechanical system design, photothermal techniques, and ultrafast laser-assisted processing of advanced materials.