Heat and Mass Transfer

, Volume 44, Issue 3, pp 331–341 | Cite as

Entropy generation in laser heating in relation to machining

  • B. S. YilbasEmail author
  • S. BinMansoor


Entropy generation during laser evaporative heating of solid substrate in relation to machining is considered and entropy generation rate due to different pulse intensities is computed. Energy method is used when simulating the phase change process and mushy zone formation across solid–liquid and liquid–vapor interfaces are accommodated. Since the heating duration is greater than the electron relaxation time, the Fourier heating model based on the equilibrium transport is employed in the simulations. Entropy generation in the substrate material is formulated during laser heating pulse. It is found that entropy generation rate in the surface region of the substrate material attains high values. Increasing power intensity ratio enhances the total entropy generation rate in a non-linear fashion.


Substrate Material Entropy Generation Mushy Zone Thermodynamic Irreversibility Power Intensity 
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List of symbols


Gaussian parameter (m)


specific heat capacity (J/kg K)


heat transfer coefficient (W/m2 K)


laser peak power intensity (W/m2)


thermal conductivity (W/m K)


latent heat of evaporation (J/kg)


latent heat of melting (J/kg)


temperature (°C)


radial distance (m)


reflection coefficient


entropy ratio


entropy per unit mass (J/kg K)


volumetric entropy generation rate (W/m3 K)


volumetric entropy change in the mushy cell (J/kg K)

\({\dot{S} _{{\rm{in}}} - \dot{S} _{{\rm{out}}}}\)

volumetric entropy generation rate due to mass and heat diffusion (W/m3 K)


entropy change due to melting (J/kg K)


entropy change due to evaporation (J/kg K)


source term (W)


boiling temperature (°C)


melting temperature (°C)


initial temperature (°C)


time (s)


energy content of differential volume (J)


energy content per unit volume (J/m3)


differential volume (m3)


mass fraction of vapour


mass fraction of melt phase


axial distance (m)

Greek symbols


thermal diffusivity (m2/s)


absorption depth (m− 1)



The authors acknowledge the support of King Fahd University of Petroleum and Minerals. Dhahran, Saudi Arabia for this work.


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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.ME Department KFUPMDhahranSaudi Arabia

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