Journal
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
Volume 468, Issue 2141, Pages 1217-1229Publisher
ROYAL SOC
DOI: 10.1098/rspa.2011.0584
Keywords
silicon thin layers; graphene sheets; non-local effects; heat propagation; temperature hump
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Funding
- Departament de Fisica of Universitat Aut noma de Barcelona
- Direccion General de Investigacion of the Spanish Ministry of Science and Innovation [2009-13370-C02-01]
- Consolider Project NanoTherm [CSD-2010-00044]
- Direccio General de Recerca of the Generalitat of Catalonia [2009-SGR-00164]
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We explore non-local effects in radially symmetric heat transport in silicon thin layers and in graphene sheets. In contrast to one-dimensional perturbations, which may be well described by means of the Fourier law with a suitable effective thermal conductivity, two-dimensional radial situations may exhibit a more complicated behaviour, not reducible to an effective Fourier law. In particular, a hump in the temperature profile is predicted for radial distances shorter than the mean-free path of heat carriers. This hump is forbidden by the local-equilibrium theory, but it is allowed in more general thermodynamic theories, and therefore it may have a special interest regarding the formulation of the second law in ballistic heat transport.
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