科研之友
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摘要
This article considers the dual-phase-lagging (DPL) heat conduction equation in a double-layered nanoscale thin film with the temperature-jump boundary condition (i.e., Robin's boundary condition) and proposes a new thermal lagging effect interfacial condition between layers. A second-order accurate finite difference scheme for solving the heat conduction problem is then presented. In particular, at all inner grid points the scheme has the second-order temporal and spatial truncation errors, while at the boundary points and at the interfacial point the scheme has the second-order temporal truncation error and the first-order spatial truncation error. The obtained scheme is proved to be unconditionally stable and convergent, where the convergence order in -norm is two in both space and time. A numerical example which has an exact solution is given to verify the accuracy of the scheme. The obtained scheme is finally applied to the thermal analysis for a gold layer on a chromium padding layer at nanoscale, which is irradiated by an ultrashort-pulsed laser.
