Fractional derivative heat conduction modeling based on thermal elements combination

摘要

This paper proposes a general theoretical framework to establish the time-space fractional derivative models for non-Fourier heat conduction. Similar to viscoelastic modeling in mechanics, some new heat conduction elements are proposed instead of mechanical ones. With different combinations of the thermal elements, the time-space fractional generalizations, such as the Kelvin-Voigt model, the Maxwell model, and the Zener model, are presented. In addition, it is possible to obtain the fractional derivative heat conduction equations from the corresponding transport equations. While incorporating the existing non-Fourier heat conduction models into the proposed theoretical framework, some new time-space fractional derivative models are presented. Finally, the nonlocal models considering the long-range heat fluxes are investigated and confirmed to be consistent with the proposed framework.