Thermal wave: from nonlocal continuum to molecular dynamics

AH Akbarzadeh and Y Cui and ZT Chen, RSC ADVANCES, 7, 13623-13636 (2017).

DOI: 10.1039/c6ra28831f

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.

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