301. Accessing temperature waves: A dispersion relation perspective.
- Author
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Gandolfi, Marco, Benetti, Giulio, Glorieux, Christ, Giannetti, Claudio, and Banfi, Francesco
- Subjects
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DISPERSION relations , *BANDPASS filters , *NANOELECTROMECHANICAL systems , *SCALAR field theory , *HEAT flux , *OSCILLATIONS , *GRAPHITE , *QUALITY factor - Abstract
• Optimal conditions for temperature wave in the frame of the Dual-Phase-Lag model. • Complex-valued dispersion relations and quality factor for the temperature field • Materials as frequency and wave vector bandpass filters for temperature waves. • Temperature wave-like oscillations in real materials are revisited. • Temperature waves in quantum materials at the nano and ultra-fast time scale. • Experimental temperature waves in graphite on ultra-fast time scale are revisited. In order to account for non-Fourier heat transport, occurring on short time and length scales, the often-praised Dual-Phase-Lag (DPL) model was conceived, introducing a causality relation between the onset of heat flux and the temperature gradient. The most prominent aspect of the first-order DPL model is the prediction of wave-like temperature propagation, the detection of which still remains elusive. Among the challenges to make further progress is the capability to disentangle the intertwining of the parameters affecting wave-like behaviour. This work contributes to the quest, providing a straightforward, easy-to-adopt, analytical mean to inspect the optimal conditions to observe temperature wave oscillations. The complex-valued dispersion relation for the temperature scalar field is investigated for the case of a localised temperature pulse in space, and for the case of a forced temperature oscillation in time. A modal quality factor is introduced showing that, for the case of the temperature gradient preceding the heat flux, the material acts as a bandpass filter for the temperature wave. The bandpass filter characteristics are accessed in terms of the relevant delay times entering the DPL model. The optimal region in parameters space is discussed in a variety of systems, covering nine and twelve decades in space and time-scale respectively. The here presented approach is of interest for the design of nanoscale thermal devices operating on ultra-fast and ultra-short time scales, a scenario here addressed for the case of quantum materials and graphite. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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