Journal
CONTINUUM MECHANICS AND THERMODYNAMICS
Volume 34, Issue 6, Pages 1455-1474Publisher
SPRINGER
DOI: 10.1007/s00161-022-01134-3
Keywords
Hyperbolic heat transfer; Pulse propagation; Second sound; Wave front; Memory effects; Non-local effects; Non-linear effects; Laplace transform
Categories
Funding
- GNFM (Italian National Group of Mathematical Physics, INdAM)
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A non-local and non-linear thermodynamical model of heat transfer at nanoscale beyond the well-known Maxwell-Cattaneo theory is derived and proven to be compatible with the second law of thermodynamics. The model is applied to investigate the linear propagation of a heat pulse in one-dimensional nanosystems, and the predicted results are compared with those from the Maxwell-Cattaneo theory, highlighting the possible influence of non-local effects and relaxation effects of higher-order fluxes. Some issues related to initial data and boundary conditions are also discussed.
A non-local and non-linear thermodynamical model of heat transfer at nanoscale beyond the well-known Maxwell-Cattaneo theory is derived. The compatibility of the proposed model with second law of thermodynamics is proved. The model is subsequently used to investigate the propagation of a heat pulse in one-dimensional nanosystems in the linear case. The predicted results are compared with those arising from the Maxwell-Cattaneo theory in order to point out the possible influence both of the non-local effects, and of the relaxation effects of the higher-order fluxes. Some problems related to initial data and boundary conditions are also discussed.
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