Abstract
The Guyer–Krumhansl equation is an extension to the classical Fourier law that is particularly appealing from a theoretical point of view because it provides a link between kinetic and continuum models and is based on well-defined physical parameters. Here we show how, subjected to a specific boundary condition analogous to the slip conditions for fluids, the Guyer–Krumhansl equation yields promising results in predicting the effective thermal conductivity of nanowires with circular and rectangular cross-sections.
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Acknowledgements
M. C. acknowledges that the research leading to these results has received funding from “La Caixa” Foundation. M. H. has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 707658. T. M. acknowledges the support of a Ministerio de Ciencia e Innovacion grant MTM2017-82317-P. P. T. and F. X. A. acknowledge the financial support of the Spanish Ministry of Economy and Competitiveness under Grant Consolider nanoTHERM CSD2010-00044, TEC2015-67462-C2-2-R (MINECO/FEDER), TEC2015-67462-C2-1-R (MINECO/FEDER). The authors have been partially funded by the CERCA Programme of the Generalitat de Catalunya.
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Calvo-Schwarzwälder, M., Hennessy, M.G., Torres, P., Myers, T., Alvarez, F.X. (2019). Thermal Transport Equations and Boundary Conditions at the Nanoscale. In: Faragó, I., Izsák, F., Simon, P. (eds) Progress in Industrial Mathematics at ECMI 2018. Mathematics in Industry(), vol 30. Springer, Cham. https://doi.org/10.1007/978-3-030-27550-1_5
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