Phonons are the main contributors to thermal energy transfer in thin films. The size dependence of the thermal transport characteristics alters the film properties such as thermal conductivity. Hence, in the present study, three-dimensional, transient phonon transport in dielectric material is studied through the Equation of Phonon Radiative Transport (EPRT) to assess the size dependence of thermal conductivity. The numerical scheme is introduced solving the EPRT in three dimensions and the governing algorithm is described in detail. A parametric study is carried out examining the effect of the number on the thermal energy transport characteristics in three-dimensional thermally excited film. The formulation and estimation of the effective thermal conductivity tensor is presented and discussed, thereby extending, to some extent, the one-dimensional results obtained earlier. We demonstrate that thermal conductivity changes in all directions, depending on the size effect. In addition, the directions of the temperature gradient and heat flux vectors differ as the number approaches unity.
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, 153–181.10.1080/00411450.2011.603403)| false
S. Bin Mansoor and B. S. Yilbas, Phonon transport in silicon–silicon and silicon–diamond thin films: Consideration of thermal boundary resistance at interface, Transp. Theory Stat. Phys.406 (2011), 2186–2195.
B. S. Yilbas, R. S. M. Alassar, A. Y. Al-Dweik and S. B. Mansoor, A new approach for semi-analytical solution of cross-plane phonon transport in silicon–diamond thin films, J. Non-Equilib. Thermodyn.43 (2018), no. 4, 359–372.
B. S. Yilbas, R. S. M. Alassar, A. Y. Al-Dweik and S. B. Mansoor, A new approach for semi-analytical solution of cross-plane phonon transport in silicon–diamond thin films, J. Non-Equilib. Thermodyn.43 (2018), no. 4, 359–372.10.1515/jnet-2018-0014)| false
R. G. Yang and G. Chen, Two-dimensional nanoscale heat conduction using ballistic-diffusive equations, in: Proc. of Int. Mechanical Engineering Conference and Exhibition, New York369 (2001), 363–366.
R. G. Yang, G. Chen and Y. Taur, Ballistic-dIFFUSIVE eQUATIONS FOR mULTIDIMENSIONAL nANOSCALE hEAT cONDUction, in: Proc. of International Heat Transfer Conference, Grenoble, France, Elsevier, Paris1 (2002), 579–584.
R. Yang, G. Chen, M. Laroche and Y. Taur, Simulation of nanoscale multidimensional transient heat conduction problems using ballistic-diffusive equations and phonon Boltzmann equation, Trans. Am. Soc. Mech. Eng.127 (2005), 298–306.
B. S. Yilbas and S. Bin Mansoor, Phonon transport in two-dimensional silicon thin film: influence of film width and boundary conditions on temperature distribution, Eur. Phys. J. B (2012), 85. 243.
B. S. Yilbas and S. Bin Mansoor, Frequency dependent phonon transport in two-dimensional Silicon and Diamond thin films, Mod. Phys. Lett. B26 (2012), 17.
Saad B. Mansoor and Bekir S. Yilbas, Phonon transport across nano-scale curved thin films, Physica B503 (2016), 130–140.
D. E. Khalili, R. Afrasiab and G. Behzad, Numerical study of 3-D microscale heat transfer of a thin diamond slab under fix and moving laser heating, Therm. Sci.23 (2019), no. 5B, 3035–3045.10.2298/TSCI171120088D)| false
Journal of Non-Equilibrium Thermodynamics serves as an international publication organ for new ideas, insights and results on non-equilibrium phenomena in science, engineering and related natural systems. The central aim of the journal is to provide a bridge between science and engineering and to promote scientific exchange on non-equilibrium phenomena and on analytic or numeric modeling for their interpretation.