Transient, Sub-Continuum, Heat Conduction in Irregular Geometries

Saad Bin Mansoor; Bekir S. Yilbas

doi:10.1515/jnet-2021-0065

Article

Transient, Sub-Continuum, Heat Conduction in Irregular Geometries

Saad Bin Mansoor and Bekir S. Yilbas

Published/Copyright: January 4, 2022

Published by

Become an author with De Gruyter Brill

Submit Manuscript Author Information

From the journal Journal of Non-Equilibrium Thermodynamics Volume 47 Issue 1

Abstract

Phonon transfer in irregular shapes is important for assessing the influence of shape effect on thermal transport characteristics of low-scale films. It becomes critical for evaluating the contribution of the scattering phonons to the phonon intensity distribution inside the film. Hence, the sub-continuum ballistic-diffusive model is incorporated to formulate the phonon transport in an irregular geometry of low-size film adopting the transient, frequency-independent, equation of phonon radiative transfer. The discrete ordinate method is used in the numerical discretization of the governing transport equation. It is demonstrated that the geometric feature of the film influences the phonon intensity distribution within the film material. The transport characteristics obtained from the Fourier and the ballistic-diffusive models are markedly different in their spatial and temporal behavior. This is true when the device sizes are of the same order of magnitude as the mean-free path of the heat carriers.

Keywords: phonon transfer; non-orthogonal; ballistic-diffusive; low-dimensional film

Funding statement: The authors acknowledge the support of the Deanship of Research (DSR) at King Fahd University of Petroleum & Minerals (KFUPM) for the funded project RG181003 and for the funded project DF191001; and acknowledgement is extended to King Abdullah City for Atomic and Renewable Energy (K. A. CARE) and Interdisciplinary Research Center for Renewable Energy and Power Systems.

References

[1] H. C. Kim, T. L. Alford and D. R. Allee, Thickness dependence on the thermal stability of silver thin films, Appl. Phys. Lett. 81 (2002), 4287.10.1063/1.1525070Search in Google Scholar

[2] G. Chen, Ballistic-diffusive equations for transient heat conduction from nano to macroscales, J. Heat Transf. 124 (2001), no. 2, 320–328.10.1115/IMECE2001/HTD-24403Search in Google Scholar

[3] A. J. Minnich, G. Chen, S. Mansoor and B. S. Yilbas, Quasi-ballistic heat transfer studied using the frequency-dependent Boltzmann transport equation, Phys. Rev. B 84 (2011), 23. Art. No. 235207.Search in Google Scholar

[4] A. Majumdar, Microscale heat conduction in dielectric thin films, ASME J. Heat Transf. 115 (1993), 7–16.10.1115/1.2910673Search in Google Scholar

[5] K. Miyazaki, T. Arashi, D. Makino and H. Tsukamoto, Heat conduction in microstructured materials, IEEE Trans. Compon. Packag. Technol. 29 (2006), no. 2, 247–253.10.1109/TCAPT.2006.875905Search in Google Scholar

[6] A. J. Minnich, G. Chen, S. Mansoor and B. S. Yilbas, Quasiballistic heat transfer studied using the frequency-dependent Boltzmann transport equation, Phys. Rev. B, Condens. Matter Mater. Phys. 84 (2011), 23. Art. no. 235207.10.1103/PhysRevB.84.235207Search in Google Scholar

[7] S. Bin Mansoor and B. S. Yilbas, Phonon transport in silicon/silicon and silicon/diamond thin films: consideration of thermal boundary resistance at interface, Physica B, Condens. Matter 406 (2011), no. 11, 2186–2195.10.1016/j.physb.2011.03.028Search in Google Scholar

[8] S. Bin Mansoor and B. S. Yilbas, Temperature distribution in silicon-aluminum thin films with presence of thermal boundary resistance, Transp. Theory Stat. Phys. 40 (2011), no. 3, 153–181.10.1080/00411450.2011.603403Search in Google Scholar

[9] L. Pilon and K. M. Katika, Modified method of characteristics for simulating microscale energy transport, ASME J. Heat Transf. 126 (2004), 735–743.10.1115/1.1795233Search in Google Scholar

[10] S. B. Mansoor and B. S. Yilbas, Laser short-pulse heating of silicon-aluminum thin films, Opt. Quantum Electron. 42 (2011), no. 9–10, 601–618.10.1007/s11082-011-9482-7Search in Google Scholar

[11] S. B. Mansoor and B. S. Yilbas, Phonon transport in aluminum and silicon film pair: laser short-pulse irradiation at aluminum film surface, Can. J. Phys. 92 (2014), no. 12, 1614–1622.10.1139/cjp-2013-0710Search in Google Scholar

[12] B. S. Yilbas and S. B. Mansoor, Phonon transport in two-dimensional silicon-diamond film pair, J. Thermophys. Heat Transf. 27 (2013), no. 3, 465–473.10.2514/1.T3954Search in Google Scholar

[13] S. B. Mansoor and B. S. Yilbas, Three-dimensional ballistic-diffusive heat transport in silicon: transient response and thermal conductivity, J. Non-Equilib. Thermodyn. 45 (2020), no. 4, 431–441. 10.1515/jnet-2020-0043.Search in Google Scholar

[14] B. S. Yilbas, S. B. Mansoor and H. Ali, Heat Transport in Micro- and Nanoscale Thin Films, Elsevier, New York, 2018.Search in Google Scholar

[15] J. F. Thompson, Z. U. A. Warsi and C. W. Mastin, Numerical Grid Generation: Foundations and Applications, North-Holland, 1985.Search in Google Scholar

[16] S. B. Mansoor, Computational aspects of radiative transfer equation in non-orthogonal coordinates, J. Therm. Eng. 5 (2019), no. 6, 162–170.10.18186/thermal.654191Search in Google Scholar

[17] G. Peckham, The phonon dispersion relation for diamond, Solid State Commun. 5 (1967), 311–313.10.1016/0038-1098(67)90280-3Search in Google Scholar

Received: 2021-08-29

Revised: 2021-11-12

Accepted: 2021-12-07

Published Online: 2022-01-04

Published in Print: 2022-01-31

You are currently not able to access this content.

Articles in the same Issue

https://doi.org/10.1515/jnet-2021-0065

Keywords for this article

phonon transfer; non-orthogonal; ballistic-diffusive; low-dimensional film