Journal of Scientific Computing

, Volume 81, Issue 3, pp 1767–1800 | Cite as

Numerical Schemes for Solving the Time-Fractional Dual-Phase-Lagging Heat Conduction Model in a Double-Layered Nanoscale Thin Film

  • Cui-cui Ji
  • Weizhong Dai
  • Zhi-zhong SunEmail author


This article proposes a time fractional dual-phase-lagging (DPL) heat conduction model in a double-layered nanoscale thin film with the temperature-jump boundary condition and a thermal lagging effect interfacial condition between layers. The model is proved to be well-posed. A finite difference scheme with second-order spatial convergence accuracy in maximum norm is then presented for solving the fractional DPL model. Unconditional stability and convergence of the scheme are proved by using the discrete energy method. A numerical example without exact solution is given to verify the accuracy of the scheme. Finally, we show the applicability of the time fractional DPL model by predicting the temperature rise in a double-layered nanoscale thin film, where a gold layer is on a chromium padding layer exposed to an ultrashort-pulsed laser heating.


Nanoscale heat transfer Fractional dual-phase-lagging model Temperature-jump boundary condition Interfacial condition Finite difference scheme Stability Convergence 



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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsQingdao UniversityQingdaoPeople’s Republic of China
  2. 2.Mathematics and StatisticsLouisiana Tech UniversityRustonUSA
  3. 3.School of MathematicsSoutheast UniversityNanjingPeople’s Republic of China

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