The Heat Conduction in Nanosized Structures
Source abstract
Abstract
Thermal transport cannot be well described by classical Fourier’s law in nanosized structures. A novel gradient theory is developed in such structures adopting the size effect of heat conduction. This is achieved by considering the second derivatives of temperature in the constitutive equation for the high-order heat flux in an advanced continuum model. The variational principle is applied to derive the governing equations. The general two-dimensional boundary-value problem for heat conduction is analyzed by the finite element method (FEM). A mixed FEM with two independent C0 continuous interpolations for temperature and temperature gradients is developed. The constraints between temperature and its gradients are performed by the collocation approach. Parametric studies are given to evaluate the influence of the internal size on the temperature distribution.
Source: openalex_inverted_index · Quality: baseline
Research context
OpenAlex topics: Thermal properties of materials · Nonlocal and gradient elasticity in micro/nano structures · Thermoelastic and Magnetoelastic Phenomena
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (19)
Show source-provided references
1. Li, Z., He, Y., Lei, J., Guo, S., Liu, D., and Wang, L., A Standard Experimental Method for Determining the Material Length Scale Based on Modified Couple Stress Theory, Int. J. Mech. Sci., 2018, vol. 141, pp. 198–205. https://doi.org/10.1016/j.ijmecsci.2018.03.03510.1016/j.ijmecsci.2018.03.035 ↗
2. Li, Z., He, Y., Zhang, B., Lei, J., Guo, S., and Liu, D., Experimental Investigation and Theoretical Modelling on Nonlinear Dynamics of Cantilevered Microbeams, Eur. J. Mech. A. Solids, 2019, vol. 78, p. 103834. https://doi.org/10.1016/j.euromechsol.2019.10383410.1016/j.euromechsol.2019.103834 ↗
3. Majumdar, A., Microscale Heat Conduction in Dielectric Thin Films, J. Heat Transfer., 1993, vol. 115, pp. 7–16. https://doi.org/10.1115/1.291067310.1115/1.2910673 ↗
4. Allen, P.B., Size Effects in Thermal Conduction by Phonons, Phys. Rev. B, 2014, vol. 90, p. 054301. https://doi.org/10.1103/PhysRevB.90.05430110.1103/PhysRevB.90.054301 ↗
5. Challamel, N., Grazide, C., Picandet, V., Perrot, A., and Zhang, Y., A Nonlocal Fourier’s Law and Its Application to the Heat Conduction of One-Dimensional and Two-Dimensional Thermal Lattices, C. R. Mec., 2016, vol. 344, pp. 388–401. https://doi.org/10.1016/j.crme.2016.01.00110.1016/j.crme.2016.01.001 ↗
6. Yu, Y.J., Tian, X.G., and Liu, R., Size-Dependent Generalized Thermoelasticity Using Eringen’s Nonlocal Model, Eur. J. Mech. A. Solids, 2015, vol. 51, pp. 96–106. https://doi.org/10.1016/j.euromechsol.2014.12.00510.1016/j.euromechsol.2014.12.005 ↗
7. Sarkar, N., Thermoelastic Responses of a Finite Rod due to Nonlocal Heat Conduction, Acta Mech., 2020, vol. 231, pp. 947–955. https://doi.org/10.1007/s00707-019-02583-910.1007/s00707-019-02583-9 ↗
8. Filopoulos, S.P., Papathanasiou, T.K., Markolefas, S.I., and Tsamasphyros, G.J., Generalized Thermoelastic Models for Linear Elastic Materials with Microstructure. Part I: Enhanced Green–Lindsay Model, J. Therm. Stresses, 2014, vol. 37, pp. 624–641. https://doi.org/10.1080/01495739.2014.88532510.1080/01495739.2014.885325 ↗
9. Filopoulos, S.P., Papathanasiou, T.K., Markolefas, S.I., and Tsamasphyros, G.J., Generalized Thermoelastic Models for Linear Elastic Materials with Microstructure. Part II: Enhanced Lord–Shulman Model, J. Therm. Stresses, 2014, vol. 37, pp. 642–659. https://doi.org/10.1080/01495739.2014.88532710.1080/01495739.2014.885327 ↗
10. Lindsay, L., Katre, A., Cepellotti, A., and Mingo, N., Perspective on Ab Initio Phonon Thermal Transport, J. Appl. Phys., 2019, vol. 126, p. 050902. https://doi.org/10.1063/1.510865110.1063/1.5108651 ↗
11. Beardo, A., Calvo-Schwarzwalder, M., Camacho, J., Myers, T.G., Torres, P., Sendra, F.X., and Bafaluy, J., Hydrodynamic Heat Transport and Holey Silicon Thin Films, Phys. Rev. Appl., 2019, vol. 11, p. 034003. https://doi.org/10.1103/PhysRevApplied.11.03400310.1103/PhysRevApplied.11.034003 ↗
12. Yu, Y.J., Tian, X.G., and Xiong, Q.L., Nonlocal Thermoelasticity Based on Nonlocal Heat Conduction and Nonlocal Elasticity, Eur. J. Mech. A. Solids, 2016, vol. 60, pp. 238–253. https://doi.org/10.1016/j.euromechsol.2016.08.00410.1016/j.euromechsol.2016.08.004 ↗
13. Yu, Y.J. and Deng, Z.C., New Insights on Microscale Transient Thermoelastic Responses for Metals with Electron-Lattice Coupling Mechanism, Eur. J. Mech. A. Solids, 2020, vol. 80, p. 103887. https://doi.org/10.1016/j.euromechsol.2019.10388710.1016/j.euromechsol.2019.103887 ↗
14. Sladek, J., Sladek, V., Repka, M., and Pan, E., A Novel Gradient Theory for Thermoelectric Material Structures, Int. J. Solids Struct., 2020, vol. 206, pp. 292–303. https://doi.org/10.1016/j.ijsolstr.2020.09.02310.1016/j.ijsolstr.2020.09.023 ↗
15. Lazar, M. and Polyzos, D., On Non-Singular Crack Fields in Helmholtz Type Enriched Elasticity Theories, Int. J. Solids Struct., 2015, vol. 62, pp. 1–7. https://doi.org/10.1016/j.ijsolstr.2014.01.00210.1016/j.ijsolstr.2014.01.002 ↗
16. Sladek, J., Sladek, V., Stanak, P., Zhang, Ch., and Tan, C.L., Fracture Mechanics Analysis of Size-Dependent Piezoelectric Solids, Int. J. Solids Struct., 2017, vol. 113, pp. 1–9. https://doi.org/10.1016/j.ijsolstr.2016.08.01110.1016/j.ijsolstr.2016.08.011 ↗
17. Sladek, J., Sladek, V., Repka, M., and Schmauder, S., Gradient Theory for Crack Problems in Quasicrystals, Eur. J. Mech. A. Solids, 2019, vol. 77, p. 103813. https://doi.org/10.1016/j.euromechsol.2019.10381310.1016/j.euromechsol.2019.103813 ↗
18. Bishay, P.L., Sladek, J., Sladek, V., and Atluri, S.N., Analysis of Functionally Graded Multiferric Composites Using Hybrid/Mixed Finite Elements and Node-Wise Material Properties, Comput. Mater. Continua, 2012, vol. 29, pp. 213–262. https://doi.org/10.3970/cmc.2012.029.21310.3970/cmc.2012.029.213 ↗
19. Dong, L. and Atluri, S.N., A Simple Procedure to Develop Efficient and Stable Hybrid/Mixed Elements, and Voronoi Cell Finite Elements for Macro- and Micromechanics, Comput. Mater. Continua, 2011, vol. 24, pp. 61–104. https://doi.org/10.3970/cmc.2011.024.06110.3970/cmc.2011.024.061 ↗