Numerical Simulation of Thermal Processes in a Domain of Thin Metal Film Subjected to an Ultrashort Laser Pulse
Abstract
:1. Introduction
2. Governing Equations
3. One-Domain Approach
4. Two Forms of the Dual Phase Lag Equation
5. Boundary and Initial Conditions
6. Numerical Algorithm
7. Results of Computations
8. Conclusions
Definition of Symbols
c | volumetric specific heat [W/(m3K)] |
C | substitute thermal capacity [W/(m3K)] |
f | level of time |
fS | volumetric solid-state fraction |
fL | volumetric liquid state fraction |
I0 | laser intensity [J/m2] |
L | volumetric heat of fusion [J/m3] |
q | heat flux vector [W/m2] |
Q | capacity of internal heat sources [W/m3] |
QL | source function resulting from the laser action [W/m3] |
Qph | source function related to melting [W/m3] |
R | reflectivity of the irradiated surface |
R0 | domain radius [m] |
rD | laser beam radius [m] |
T | temperature [K] |
T * | melting temperature [K] |
[T1, T2] | temperature interval in which the melting process takes place |
Tp | initial temperature [K] |
t | time [s] |
tp | characteristic time of laser pulse [s] |
X = {r, z} | geometrical co-ordinates |
Z | domain depth [m] |
Greeks: | |
δ | optical penetration depth [m] |
λ | thermal conductivity [W/(mK)] |
τT | thermalization time [s] |
τq | relaxation time [s] |
Author Contributions
Funding
Conflicts of Interest
References
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Majchrzak, E.; Mochnacki, B. Numerical Simulation of Thermal Processes in a Domain of Thin Metal Film Subjected to an Ultrashort Laser Pulse. Materials 2018, 11, 2116. https://doi.org/10.3390/ma11112116
Majchrzak E, Mochnacki B. Numerical Simulation of Thermal Processes in a Domain of Thin Metal Film Subjected to an Ultrashort Laser Pulse. Materials. 2018; 11(11):2116. https://doi.org/10.3390/ma11112116
Chicago/Turabian StyleMajchrzak, Ewa, and Bohdan Mochnacki. 2018. "Numerical Simulation of Thermal Processes in a Domain of Thin Metal Film Subjected to an Ultrashort Laser Pulse" Materials 11, no. 11: 2116. https://doi.org/10.3390/ma11112116