Femtosecond laser heating of multi-layer metals—II. Experiments

Qiu, Tony Z.; Juhász, Tibor; Suárez, C.; Bron, W. E.; Tien, C. L.

doi:10.1016/0017-9310(94)90397-2

Cited by 182 publications

(83 citation statements)

References 30 publications

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“…More recently, it has been shown that in certain situations HHCEs violate the second law of thermodynamics resulting in physically unrealistic temperature distributions such as temperature overshoot phenomena observed in a slab subject to a sudden temperature rise on its boundaries (see, e.g., Taitel [4]). Also, since the classical Fourier and hyperbolic models neglect thermalization time (time for electrons and lattice to reach thermal equilibrium) and relaxation time of the electrons, their applicability to very short-pulse laser heating becomes questionable, as noted by Qiu and Tien [5,6] and Qiu et al [7].…”

Section: Introductionmentioning

confidence: 99%

An alternative discretization and solution procedure for the dual phase-lag equation

McDonough¹,

Kunadian²,

Kumar³

et al. 2006

Journal of Computational Physics

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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 in contrast to the usual practice of decomposing this equation into a system of two equations, we utilize this formulation directly. Truncation error analysis is performed to show consistency and first-order temporal accuracy of the discretized 1-D DPL equation, and it is shown by von Neumann stability analysis and numerical results that the proposed numerical technique is unconditionally stable. The overall approach is then extended to three dimensions via Douglas-Gunn time-splitting, and a simple argument for stability is given for the time-split formulation. Based on a straightforward arithmetic operation count, qualitative comparisons are made with explicit and iterative methods with the expected result that the current approach is generally significantly more efficient, and this is demonstrated with CPU-time results. Application of Richardson extrapolation in time is then investigated to improve the first-order temporal accuracy, and finally, it is shown that numerical predictions agree with available experimental data during sub-picosecond laser heating of a thin film.

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Section: Introductionmentioning

confidence: 99%

An alternative discretization and solution procedure for the dual phase-lag equation

McDonough¹,

Kunadian²,

Kumar³

et al. 2006

Journal of Computational Physics

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“…This figure is similar to that obtained in Reference [8] except that the temperature rise starts at t = 0 (see in Reference [8, p. 143, Figure 5.18]). This is because in Reference [8] it appears that the initial time was set equal to 2t p in Equation (7). To test for the effect of grid size, we used three different meshes of 20 × 20 × 100, 20 × 20 × 200, and 20 × 20 × 400.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…Among these, Qiu and Tien [6,7] employed a semi-implicit Crank-Nicholson scheme to solve Equations (1) and (2) in one dimension in a gold thin film and a double-layered gold and chromium film. However, the stability of the scheme was not investigated.…”

Section: Introductionmentioning

confidence: 99%

An unconditionally stable three level finite difference scheme for solving parabolic two‐step micro heat transport equations in a three‐dimensional double‐layered thin film

Dai

Nassar

et al. 2003

Numerical Meth Engineering

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SUMMARYHeat transport at the microscale is of vital importance in microtechnology applications. The heat transport equations are parabolic two-step equations, which are different from the traditional heat diffusion equation. In this study, we develop a three-level finite difference scheme for solving the micro heat transport equations in a three-dimensional double-layered thin film. It is shown by the discrete energy method that the scheme is unconditionally stable. Numerical results for thermal analysis of a gold layer on a chromium padding layer are obtained.

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“…The total amount of energy is estimated from distribution (by integrating), (16) where N f and N r are the fractions of heat deposited in the front and the rear sections, respectively such that (17) Therefore, the fraction due to no-symmetrical heat deposited in the front section of the ellipsoid is expressed as (18) Total heat input (Q) is also estimated from the effective heat energy transferred to the workpiece from any heat source. Therefore, it is mathematically expressed as (19) where, P is the laser power and the constant term α is introduced to account the over-estimation of heat energy due to discretized geometry (β ~ 1.1).…”

Section: Heat Source Representationmentioning

confidence: 99%

Microscale heat transfer in fusion welding of glass by ultra-short pulse laser using dual phase lag effects

Bag

2018

IOP Conf. Ser.: Mater. Sci. Eng.

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Abstract. The heat transfer in microscale has very different physical basis than macroscale where energy transport depends on collisions among energy carriers (electron and phonon), mean free path for the lattice (~ 10 -100 nm) and mean free time between energy carriers. The heat transport is described on the basis of different types of energy carriers averaging over the grain scale in space and collations between them in time scale. The physical bases of heat transfer are developed by phonon-electron interaction for metals and alloys and phonon scattering for insulators and dielectrics. The non-Fourier effects in heating become more and more predominant as the duration of heating pulse becomes extremely small that is comparable with mean free time of the energy carriers. The mean free time for electron -phonon and phonon-phonon interaction is of the order of 1 and 10 picoseconds, respectively. In the present study, the mathematical formulation of the problem is defined considering dual phase lag i.e. two relaxation times in heat transport assuming a volumetric heat generation for ultra-short pulse laser interaction with dielectrics. The relaxation times are estimated based on phonon scattering model. A three dimensional finite element model is developed to find transient temperature distribution using quadruple ellipsoidal heat source model. The analysis is performed for single and multiple pulses to generate the time temperature history at different location and at different instant of time. The simulated results are validated with experiments reported in independent literature. The effect of two relaxation times and pulse width on the temperature profile is studied through numerical simulation.

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Femtosecond laser heating of multi-layer metals—II. Experiments

Cited by 182 publications

References 30 publications

An alternative discretization and solution procedure for the dual phase-lag equation

An alternative discretization and solution procedure for the dual phase-lag equation

An unconditionally stable three level finite difference scheme for solving parabolic two‐step micro heat transport equations in a three‐dimensional double‐layered thin film

Microscale heat transfer in fusion welding of glass by ultra-short pulse laser using dual phase lag effects

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