James M. McDonough

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Alternative discretization and solution procedures are developed for the 1-D dual phase-lag (DPL) equation, a partial differential equation for very short time, microscale heat transfer obtained from a delay partial differential equation that is transformed to the usual non-delay form via Taylor expansions with respect to each of the two time delays. Then(More)
ly providing a mapping from the space of functions corresponding to the right-hand side, that is, C2(Ω) in the present case, to those of the left-hand side, C1(0,∞), and denote this as u(t) ∈ C(0,∞;C(Ω)) . (1.16) This notation will be widely used in the sequel, so it is worthwhile to understand what it implies. In words, it says that u(t) is a function that(More)
An alternative discretization and solution procedure is developed for implicitly solving a microscale heat transport equation during femtosecond laser heating of nanoscale metal films. The proposed numerical technique directly solves a single partial differential equation, unlike other techniques available in the literature which split the equation into a(More)
In the present work we investigate femtosecond laser heating of nanoscale metal films irradiated by a pulsating laser in three dimensions using the Dual Phase Lag (DPL) model and consider laser heating at different locations on the metal film. A numerical solution based on an explicit finite-difference method has been employed to solve the DPL heat(More)