References
- 1. C. W. Chang, D. Okawa, A. Majumdar, and A. Zettl, Solid-state thermal rectifier,, vol. 314, no. 5802, pp. 1121–1124, 2006.
- 2. L. Wang and B. Li, Thermal memory: a storage of phononic information,, vol. 101, no. 26, p. 267203, 2008.
- 3. G. Wu and B. Li, Thermal rectifiers from deformed carbon nanohorns,, vol. 20, no. 17, p. 175211, 2008.
- 4. M. Criado-Sancho, L. del Castillo, J. Casas-Vazquez, and D. Jou, Theoretical analysis of thermal rectification in a bulk Si/nanoporous Si device,, vol. 376, no. 19, pp. 1641–1644, 2012.
- 5. N. Yang, G. Zhang, and B. Li, Carbon nanocone: a promising thermal rectifier,, vol. 93, no. 24, p. 243111, 2008.
- 6. W. Kobayashi, Y. Teraoka, and I. Terasaki, An oxide thermal rectifier,, vol. 95, no. 17, p. 171905, 2009.
- 7. N. Yang, G. Zhang, and B. Li, Thermal rectification in asymmetric graphene ribbons,, vol. 95, no. 3, p. 033107, 2009.
- 8. C. R. Otey, W. T. Lau, and S. Fan, Thermal rectification through vacuum,, vol. 104, no. 15, p. 154301, 2010.
- 9. M. Schmotz, J. Maier, E. Scheer, and P. Leiderer, A thermal diode using phonon rectification,, vol. 13, no. 11, p. 113027, 2011.
- 10. S. H. Ju and X. G. Liang, Thermal rectification and phonon scattering in asymmetric silicon nanoribbons,, vol. 112, no. 2, p. 024307, 2012.
- 11. S. H. Ju and X. G. Liang, Thermal rectification and phonon scattering in silicon nanofilm with cone cavity,, vol. 112, no. 5, p. 054312, 2012.
- 12. M. Maldovan, Narrow low-frequency spectrum and heat management by thermocrystals,, vol. 110, no. 2, p. 025902, 2013.
- 13. R. Chen, A. I. Hochbaum, P. Murphy, and A. Majumdar, Thermal conductance of thin silicon nanowires,, vol. 101, no. 10, p. 105501, 2008.
- 14. A. Majumdar, Microscale heat conduction in dielectric thin films,, vol. 115, no. 1, pp. 7–16, 1993.
- 15. G. Chen, Thermal conductivity and ballistic-phonon transport in the cross-plane direction of superlattices,, vol. 57, no. 23, p. 14958, 1998.
- 16. R. Yang and G. Chen, Thermal conductivity modeling of periodic two-dimensional nanocomposites,, vol. 69, no. 19, p. 195316, 2004.
- 17. A. J. H. McGaughey, E. S. Landry, D. P. Sellan, and et al., Size-dependent model for thin film and nanowire thermal conductivity,, vol. 99, no. 13, p. 131904, 2011.
- 18. R. A. Guyer and J. A. Krumhansl, Solution of the linearized phonon boltzmann equation,, vol. 148, no. 2, p. 766, 1966.
- 19. R. A. Guyer and J. A. Krumhansl, Thermal conductivity, second sound, and phonon hydrodynamic phenomena in nonmetallic crystals,, vol. 148, no. 2, p. 778, 1966.
- 20. M. Asheghi, M. Toulzebaev, K. Goodson, Y. Leung, and S. Wong, Temperature-dependent thermal conductivity of single-crystal silicon layers in soi substrates,, vol. 120, no. 1, pp. 30–36, 1998.
- 21. Y. Ju and K. Goodson, Phonon scattering in silicon films with thickness of order 100 nm,, vol. 74, no. 20, pp. 3005–3007, 1999.
- 22. W. Liu and M. Asheghi, Phonon boundary scattering in ultrathin single-crystal silicon layers,, vol. 84, no. 19, pp. 3819–3821, 2004.
- 23. Y. Ju, Phonon heat transport in silicon nanostructures,, vol. 87, no. 15, p. 153106, 2005.
- 24. D. Li, Y. Wu, P. Kim, L. Shi, P. Yang, and A. Majumdar, Thermal conductivity of individual silicon nanowires,, vol. 83, no. 14, pp. 2934–2936, 2003.
- 25. A. Sellitto, F. Alvarez, and D. Jou, Geometrical dependence of thermal conductivity in elliptical and rectangular nanowires,, vol. 55, no. 11, pp. 3114–3120, 2012.
- 26. A. Sellitto, F. Alvarez, and D. Jou, Phonon hydrodynamics and phonon-boundary scattering in nanosystems,, vol. 105, no. 1, p. 014317, 2009.
- 27. F. X. Alvarez, D. Jou, and A. Sellitto, Second law of thermodynamics and phonon-boundary conditions in nanowires,, vol. 107, no. 6, p. 064302, 2010.
- 28. Y. Dong, B. Y. Cao, and Z. Guo, Generalized heat conduction laws based on thermomass theory and phonon hydrodynamics,, vol. 110, no. 6, p. 063504, 2011.
- 29. M. Wang and Z. Y. Guo, Understanding of temperature and size dependences of effective thermal conductivity of nanotubes,, vol. 374, no. 42, pp. 4312–4315, 2010.
- 30. M. Wang, N. Yang, and Z. Y. Guo, Non-fourier heat conductions in nanomaterials,, vol. 110, no. 6, p. 064310, 2011.
- 31. Y. Dong, B. Y. Cao, and Z. Guo, Size dependent thermal conductivity of Si nanosystems based on phonon gas dynamics,, vol. 56, pp. 256–262, 2014.
- 32. J. M. Ziman,. Oxford: Oxford University Press, 2001.
- 33. Y. Ma, Size-dependent thermal conductivity in nanosystems based on non-fourier heat transfer,, vol. 101, no. 21, p. 211905, 2012.
- 34. C. de Tomas, A. Cantarero, A. F. Lopeandia, and F. X. Alvarez, From kinetic to collective behavior in thermal transport on semiconductors and semiconductor nanostructures,, vol. 115, no. 16, p. 164314, 2014.
DOI: https://doi.org/10.1515/caim-2016-0004 | Journal eISSN: 2038-0909
Language: English
Page range: 26 - 38
Submitted on: Nov 1, 2014
Accepted on: Mar 5, 2015
Published on: May 20, 2016
Published by: Italian Society for Applied and Industrial Mathemathics
In partnership with: Paradigm Publishing Services
Related subjects:
© 2016 Yuan Dong, published by Italian Society for Applied and Industrial Mathemathics
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.