Analytical solution of dual-phase-lag based heat transfer model in ultrashort pulse laser heating of A6061 and Cu3Zn2 nano film

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 certifies the availability of very few research papers specifically 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 conduction model utilized for the femtosecond laser heating of nanofilm. The corresponding solution has been derived by a hybrid application of the Duhamel’s theorem and the finite integral transform approach. A comparative thermal analysis has been depicted for the laser heating of 5 nm thin A6061 and Cu3Zn2 nanofilm and the necessity of non-Fourier analysis over the Fourier’s model has been justified. Existing research works are mostly based on gold and chromium nanofilm. As multi-component microstructures of Cu and Al are scientifically 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 reflectivity) of substrate material have been taken into account to develop a better and realistic analytical model than the existing models. The research output notifies 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 justifies the experimental observation of relaxation time lags as reported in the literature. The thermal response has been captured for both A6061 and Cu3Zn2 material along the various depths of the nanofilm 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 difference between with and without optical properties is evidenced as 38.86% and 57.70% for A6061 and Cu3Zn2 nanofilms, respectively.