## THERMAL SCIENCE

International Scientific Journal

### Thermal Science - Online First

online first only
### Analyze two-dimensional heat transfer of ultrafast laser heated thin films under siz effects

**ABSTRACT**

An improved dual-phase-lagging (DPL) model which reflects size effects caused by nanostructures is utilized to investigate the two-dimensional thermal conduction of nano silicon films irradiated by ultrafast laser. The integral transformation method is used to solve the conduction governing equation based on the improved DPL model. The variation of the internal temperature along the thickness direction and the radial direction of the thin film is analyzed. We find that the temperature increases rapidly in the heated region of the film, and as time goes by, the energy travels from the heated end to another end in a form of wave. Although both the improved DPL model and the DPL model can obtain similar thermal wave temperature fields, the temperature distribution in the film obtained by the improved DPL model is relatively flat, especially for high Knudsen number. Under the same Knudsen number, the temperature obtained by the two-dimensional improved DPL model is higher than that obtained by the one-dimensional model, and the temperature difference becomes larger and larger as time elapses.

**KEYWORDS**

PAPER SUBMITTED: 2022-08-19

PAPER REVISED: 2022-12-28

PAPER ACCEPTED: 2023-01-13

PUBLISHED ONLINE: 2023-03-11

- Guo, H., Yan, J. F., Li, X., Patterned graphene oxide by spatially shaped femtosecond laser(in Chinese language), Chinese Journal of Lasers, 48(2021), 2, pp.292 300
- Li, Y. L., Wu, L. Y., Shen, H. H., et al., Patterning of graphene by light field modulated nanosecond laser(in Chinese language), High Power Laser and Particle Beams, 30(2018), 12, pp. 148 151
- Ehsan, K. D., Afrasiab, R., Behzad, G., Numerical study of 3 D microscale heat transfer of a thin diamond slab under fix and moving laser heating, Thermal Science, 23(2019), pp. 3035 3045
- Ghai, S. S., Kim, W. T., Jhon, M. S., A novel heat transfer model and its application to information storage systems, Journal of Applied Physics, 97(2005), 10, p703 0.
- Li, F. J., Coherent synthesis of ultrashort pulse fiber laser based on balanced difference method, Thermal Science, 21(2021), pp.4027 4034
- Mo, G. K., Liu, J. H., Zou, Z. L., et al., Preparation of low resistivity GZO thin films using pulsed laser deposition and investigation of optoelectronic properties(in Chinese language), Chinese Journal of Lasers, 46(2019), 10, pp.204 210
- Nenad, D. M., Application of the laser pulse method of measuring thermal diffusivity to thin alumina silicon samples in a wide temperature range, Thermal Science, 14(2014), pp. 417 423
- Wang, C. D., Bao, Z. L., Ma, J. P., et al., Powder separation and its suppression during laser cladding of medical Ti/HA(in Chinese language), Chinese Journal of Lasers, 47(2020), 12, pp.57 68
- Tzou, D. Y., Chiu, K. S., Temperature dependent thermal lagging in ultrafast laser heating, International Journal of Heat and Mass Transfer, 44(2001), pp.1725 1732
- Tzou, D. Y., Chen, J. K., Beraun, J. E., Hot electron blast induced by ultrashort pulsed lasers in layered media, International Journal of Heat and Mass Transfer, 45(2002), pp.3369 3382
- Cattaneo, C., A form of heat conduction equation which eliminates the paradox of instantaneous propagation, Compte-- Rendus, 247(1958), pp.431--435
- Vernotte, P., Some possible complications in the phenomena of thermal conduction, Compte--Rendus, 252(1961), pp.2190--2193
- Guo, S. L., Zhang, Y. X., Wang, K. F., et al., Effects of non--Fourier heat conduction and surface heating rate on thermoelastic waves in semi--infinite ceramics subject to thermal shock, Ceramics International, 47(2021), pp.17494--17501
- Tzou, D. Y., The generalized lagging response in small--scale and high--rate heating, International Journal of Heat and Mass Transfer, 38(1995), 17, pp.3231--3234
- Wang, L., Xu, M., Well--posedness and solution structure of dual--phase--lagging heat conduction, International Journal of Heat and Mass Transfer, 48(2005), pp.1165--1171
- Xu, M., Wang, L., Thermal oscillation and resonance in dual--phase--lagging heat conduction, International Journal of Heat and Mass Transfer, 45(2002), pp.1055--1061
- Joshi, A. A., Majumdar, A., Transient ballistic and diffusive phonon heat transport in thin films, Journal of Applied Physics, 74(1993), pp.31--39
- Torii, S. C., Yang, W. J., Heat transfer mechanisms in thin film with laser heat source, International Journal of Heat and Mass Transfer, 48(2005), pp.537--544
- Hua, Y. C., Cao, B. Y., Phonon ballistic--diffusive heat conduction in silicon nanofilms by Monte Carlo simulations, International Journal of Heat and Mass Transfer, 78(2014), pp.755--759
- Peng, Y., Yan, Z., Characterization of laser--induced local heating in a substrate, International Journal of Heat and Mass Transfer, 106(2017), pp.989--996
- Yang, L. L., Wei, J. T., Ma, Z., et al., The fabrication of micro/nano structures by laser machining, Nanomaterials, 9(2019), 12, pp.1789(1--69)
- Alvarez, F. X., Jou, D., Size and frequency dependence of effective thermal conductivity in nano systems, Journal of Applied Physics, 103(2008), 9, pp. 094321(1--8)
- Al--Nimr, M. A., Kiwan, S., Effect of thermal losses on the microscopic two--step heat conduction model, International Journal of Heat and Mass Transfer, 44(2001), pp.1013--1018
- Alvarez, F. X., Jou, D., Memory and nonlocal effects in heat transport: From diffusive to ballistic regimes, Applied Physics Letters, 90(2007), 8, pp. 083109(1--3)
- Alvarez, F. X., Jou, D., Boundary conditions and evolution of ballistic heat transport, ASME Journal of Heat Transfer, 132(2010), pp. 012404(1--6)
- Mao, Y. D., Xu, M. T., Non--Fourier heat conduction in a thin gold film heated by an ultra--fast--laser, Science China (Technological Sciences), 58(2015), 04, pp. 638--649
- Cheng, L., Xu, M. T.., Wang, L. Q., Single-- and dual--phase--lagging heat conduction models in moving media, ASME Journal of Heat Transfer, 130(2008), pp.1--6
- Choudhuri, S. R., On a thermoelastic three--phase--lag model, Journal of Thermal Stresses, 30(2007), pp.231--238
- Mondal, S., Mallik, S. H., Kanoria, M., Fractional order two--temperature dual--phase--lag thermoelasticity with variable thermal conductivity, International Scholarly Research Notices, 2014, pp.646049(1--13)
- Mao, Y. D., Xu, M. T., Lattice Boltzmann numerical analysis of heat transfer in nano--scale silicon films induced by ultra--fast laser heating, International Journal of Thermal Sciences, 89(2015), pp.210--221