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Research Papers: Melting and Solidification

Uncertainty Analysis of Melting and Resolidification of Gold Film Irradiated by Nano- to Femtosecond Lasers Using Stochastic Method

[+] Author and Article Information
Nazia Afrin

Department of Mechanical and
Aerospace Engineering,
University of Missouri,
Columbia, MO 65211

Yuwen Zhang

Fellow ASME
Department of Mechanical and
Aerospace Engineering,
University of Missouri,
Columbia, MO 65211
e-mail: zhangyu@missouri.edu

J. K. Chen

Fellow ASME
Department of Mechanical and
Aerospace Engineering,
University of Missouri,
Columbia, MO 65211

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received July 16, 2015; final manuscript received February 18, 2016; published online March 30, 2016. Assoc. Editor: Alan McGaughey.

J. Heat Transfer 138(6), 062301 (Mar 30, 2016) (12 pages) Paper No: HT-15-1481; doi: 10.1115/1.4032962 History: Received July 16, 2015; Revised February 18, 2016

A sample-based stochastic model is presented to investigate the effects of uncertainties of various input parameters, including laser fluence, laser pulse duration, thermal conductivity constants for electron, and electron–lattice coupling factor, on solid–liquid phase change of gold film under nano- to femtosecond laser irradiation. Rapid melting and resolidification of a free-standing gold film subject to nano- to femtosecond laser are simulated using a two-temperature model incorporated with the interfacial tracking method. The interfacial velocity and temperature are obtained by solving the energy equation in terms of volumetric enthalpy for control volume (CV). The convergence of variance (COV) is used to characterize the variability of the input parameters, and the interquartile range (IQR) is used to calculate the uncertainty of the output parameters. The IQR analysis shows that the laser fluence and the electron–lattice coupling factor have the strongest influences on the interfacial location, velocity, and temperatures.

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Figures

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Fig. 1

Sample-based stochastic model

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Fig. 2

Stochastic convergence analysis of mean value of the input parameters (a) GRT, (b) λ, (c) η, (d) J, and (e) tp

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Fig. 3

Stochastic convergence analysis of standard deviation of the input parameters (a) GRT, (b) λ, (c) η, (d) J, and (e) tp

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Fig. 4

Stochastic convergence analysis of mean value of the output parameters (a) s, (b) us, (c) Tl,I, and (d) Te

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Fig. 5

Stochastic convergence analysis of standard deviation of the input parameters (a) s, (b) us, (c) Tl,I, and (d) Te

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Fig. 6

Typical distributions of the input parameters (a) GRT, (b) λ, (c) η, (d) J, and (e) tp

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Fig. 7

Typical distributions of the output parameters (a) s, (b) us, (c) Tl,I, and (d) Te

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Fig. 8

The IQRs of the output parameters with different COVs of the input parameters (a) s, (b) us, (c) Tl,I, and (d) Te

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Fig. 9

The IQRs of the output parameters with different values and COVs of J (a) s, (b) us, (c) Tl,I, and (d) Te

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Fig. 10

The IQRs of the output parameters with different values and COVs of GRT (a) s, (b) us, (c) Tl,I, and (d) Te

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