Numerical studies on dispersion of thermal waves

Heat may transport as waves under ultrafast heat pulse conditions. In this paper, our numerical analyses considering typical thermal wave modes, i.e. Cattaneo–Vernotte (CV), dual-phase-lagging (DPL), and thermomass (TM), disclose that dispersion may occur during the heat propagation processes like water, sound, and light waves. The unified implicit finite difference method for the Fourier, CV, DPL, and TM models was adopted to analyze the heat propagation process in solids. The validity of this numerical method for the Fourier, CV, DPL and TM models was confirmed. The dispersion of thermal waves was observed in their propagation processes for the first time. As the thermal waves moving forward, many peaks appear in the rear of the thermal waves relative to the propagation direction. The underlying mechanism for the dispersion of the thermal waves is that they can travel faster in the points with higher temperature considering the temperature dependence of the relaxation time. For the CV-waves and DPL-waves, the origins of the dispersion are both due to the inertia term of heat flux to time τq∂q∂t. For the TM-waves, the origins are due to the inertia term of heat flux to time, inertia term of temperature to time, and inertia term of heat flux to space in the TM model, and effects of the inertia term of temperature to space on the dispersion can be neglected, where the inertia term to space comes from the nonlocal effects. The dispersion of the TM-waves is mainly dominated by the inertia term of heat flux to time. In the TM model, the characteristic time τTM decreases with the increase of temperature, and therefore the dispersion will appear in the propagation process of the TM-wave. For actual materials, if considering that τq decreases with the temperature increasing, the dispersion of the CV-wave and DPL-wave will also appear under the appropriate amplitude of heat flux pulse, relaxation times τq and τT. The increase of the amplitude of heat flux pulse and the decrease of the initial temperature both can enhance the dispersion of the TM-wave. The increase of the amplitude of heat flux pulse and the relaxation time τq can both enhance the dispersion of the CV-wave and DPL-wave, while the increase of the relaxation time τT will weaken the dispersion of the DPL-wave.