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An approach for analytical solution pertinent to lattice temperature variation due to laser short-pulse heating

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Abstract

Non-equilibrium energy transport in the surface region of the metallic substrate occurs due to a laser irradiation, which in turn results in thermal separation of electron and lattice sub-systems. As the heating period exceeds the thermal relaxation time, both sub-systems become thermally in equilibrium having the identical temperatures. When electron and lattice temperatures become identical the corresponding instant can be called thermal equilibrium time. In the present study, an analytical formulation of lattice site temperature distribution in the domain of thermal equilibrium time is obtained. Temperature differences and temperature distributions in electron and lattice sub-systems are computed for gold. It is found that electron and lattice temperatures become identical for the heating period beyond the thermal equilibrium time. Temperature distribution obtained from the analytical solution and numerical predictions agree well.

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Abbreviations

C e :

Electron heat capacity (J/m3 K)

C l :

Lattice heat capacity (J/m3 K)

G :

Electron–phonon coupling factor (W/m3 K)

I 1 :

Peak amplitude of power intensity (W/m2)

I 0 :

Exponentially decaying laser pulse intensity (W/m2)

T e :

Electron temperature (K)

T l :

Lattice site temperature (K)

T 0 :

Reference temperature (300 K)

k :

Thermal conductivity (W/m K)

t :

Time (s)

x :

Distance (m)

α, β:

Exponentially decaying laser pulse intensity parameters (1.s)

δ:

Absorption length (1/m)

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Acknowledgements

Acknowledgements are due to King Fahd University of Petroleum and Minerals for the support of the work.

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Authors and Affiliations

  1. Department of Energy Systems Engineering, Gebze Institute of Technology, Kocaeli, Turkey

    M. Kalyon

  2. ME Department, KFUPM, Dhahran, 31261, Saudi Arabia

    M. Kalyon & B. S. Yilbas

Authors
  1. M. Kalyon
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  2. B. S. Yilbas
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Correspondence to B. S. Yilbas.

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Kalyon, M., Yilbas, B.S. An approach for analytical solution pertinent to lattice temperature variation due to laser short-pulse heating. Heat Mass Transfer 42, 1111–1117 (2006). https://doi.org/10.1007/s00231-005-0071-9

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  • DOI: https://doi.org/10.1007/s00231-005-0071-9

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