Numerical Schemes for Solving the Time-Fractional Dual-Phase-Lagging Heat Conduction Model in a Double-Layered Nanoscale Thin Film
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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.
KeywordsNanoscale heat transfer Fractional dual-phase-lagging model Temperature-jump boundary condition Interfacial condition Finite difference scheme Stability Convergence
- 3.Tzou, D.Y.: Macro- To Microscale Heat Transfer: The Lagging Behavior, 2nd edn. Wiley, New York (2015)Google Scholar
- 25.Pillers, M., Lieberman, M.: Rapid thermal processing of DNA origami on silicon creates embedded silicon carbide replicas. In: 13th Annual Conference on Foundations of Nanoscience, Snowbird, Utah, April 11–16 (2016)Google Scholar
- 31.Sun, Z.Z.: The Method of Order Reduction and Its Application to the Numerical Solutions of Partial Differential Equations. Science Press, Beijing (2009)Google Scholar