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Optics and Laser Technology
journal homepage: www.elsevier.com/locate/optlastec
Analytical solution of dual-phase-lag based heat transfer model in ultrashort
pulse laser heating of A6061 and Cu
3
Zn
2
nano flm
Jaideep Dutta
a,b
, Ranjib Biswas
b
, Balaram Kundu
a,
⁎
a
Department of Mechanical Engineering, Jadavpur University, Raja S. C. Mallick Road, Kolkata 700032, West Bengal, India
b
Department of Mechanical Engineering, MCKV Institute of Engineering, 243, G. T. Road (N), Liluah, Howrah 711204, West Bengal, India
HIGHLIGHTS
•
Exact solution of dual-phase-lag heat conduction model developed for ultrashort pulse laser irradiation.
•
Inclusion of optical properties in Gaussian form of pulsed laser source.
•
Diference in temperature variation of 38.86% and 57.70% observed for A6061 and Cu
3
Zn
2
nanoflm.
•
Femtosecond pulse laser irradiation penetrates the flm thickness and peak temperature falls.
•
Observation of diference in magnitude of peak temperature between DPL and Fourier’s models.
ARTICLEINFO
Keywords:
Ultrafast pulsed laser
Dual-phase-lag model
Analytical solution
Thermal response
Optical properties
ABSTRACT
The dual-phase-lag model provides the best performance among many existing non-Fourier models and it is
particularly more suitable for a short duration of heating. The present literature survey certifes the availability
of very few research papers specifcally on the development of an exact analytical solution of the dual-phase-lag
model illustrating the thermal analysis of ultrashort pulsed laser heating. To address such issues, the present
work is intended to develop an exact solution of the thermal response based on the dual-phase-lag heat con-
duction model utilized for the femtosecond laser heating of nanoflm. The corresponding solution has been
derived by a hybrid application of the Duhamel’s theorem and the fnite integral transform approach. A com-
parative thermal analysis has been depicted for the laser heating of 5 nm thin A6061 and Cu
3
Zn
2
nanoflm and
the necessity of non-Fourier analysis over the Fourier’s model has been justifed. Existing research works are
mostly based on gold and chromium nanoflm. As multi-component microstructures of Cu and Al are scientif-
cally proved to be excellent metallic properties (magnetic and optical) and exhibit strong response during energy
driven-chemical reactions, the present analysis is focused on these two materials for the femtosecond laser
irradiation. In the present analysis, optical properties (absorptivity and refectivity) of substrate material have
been taken into account to develop a better and realistic analytical model than the existing models. The research
output notifes that at 0.1 ps of the laser pulse and 100 J m
−2
of the laser intensity, developed temperature
history reaches the melting point temperature of both the materials in combination with other thermophysical
properties. The mathematical modeling also provides the appropriate information about the selection of thermal
relaxation time lags for respective materials and this also justifes the experimental observation of relaxation
time lags as reported in the literature. The thermal response has been captured for both A6061 and Cu
3
Zn
2
material along the various depths of the nanoflm to evolve the irradiation capacity of the pulsed femtosecond
laser source. The present research output is well validated through numerical and experimental research works
of existing literature with a negligible variation. The inclusion of optical properties of materials in the present
research work plays an important role as it is noticed that the maximum deviation of the temperature diference
between with and without optical properties is evidenced as 38.86% and 57.70% for A6061 and Cu
3
Zn
2
na-
noflms, respectively.
https://doi.org/10.1016/j.optlastec.2020.106207
Received 18 November 2019; Received in revised form 14 February 2020; Accepted 7 March 2020
⁎
Corresponding author.
E-mail addresses: jdutta.mech@gmail.com (J. Dutta), bkundu@mech.net.in (B. Kundu).
Optics and Laser Technology 128 (2020) 106207
0030-3992/ © 2020 Elsevier Ltd. All rights reserved.
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