What is it about?
Discrete heat equations for the multi-layered periodic systems with allowance for the thermal resistance between the layers and corresponding dispersion relations in ω-k space have been derived and analyzed. The discrete equations imply a finite velocity of thermal disturbances and guarantee the positiveness of the solutions. Analytical expressions for the attenuation distance, phase and group velocities have been obtained as functions of frequency and thermal resistance between the discrete layers.
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Why is it important?
The discrete equation contains an infinite hierarchy of continuous partial differential equations, which starts with the Fourier law, proceeds with the hyperbolic equation, the Guyer-Krumhansl (or Jeffreys type) equation, and then with higher-order equations. The partial differential equations with a finite number of terms are only approximations of the discrete equation, which implies that on the ultrashort space and time scales the discrete approach is preferable.
Perspectives
This work provides a relatively simple, easy-to-adopt, conceptual tool, together with analytical expressions allowing to study ultrafast wave-like heat conduction regimes in periodic multi-layered metamaterials.
Sergey Sobolev
Institute of Problems of Chemical Physics
Read the Original
This page is a summary of: Discrete heat equation for a periodic layered system with allowance for the interfacial thermal resistance: General formulation and dispersion analysis, May 2024, American Physical Society (APS),
DOI: 10.1103/physreve.109.054102.
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