Micro/Nano Scale Energy Transport in Metallic Films and Stress Analysis: Analytical Approaches

B. S. Yilbas*, A. Y. Al-Dweik, S. B. Mansour

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


Micro/nano scale energy transport takes place in thin films with fine sizes and the time durations less than the thermalization time of the substrate material. In this case, the classical formulation of the energy transport, such as the Fourier law, fails to predict the correct properties, such as temperature, across the thin films within the short periods. In order to find the solution to the transport problem, physical fundamentals of the transport phenomena need to be revisited and the conservation equation for the energy should be reformulated to account for the micro/nano scale and the short durations. Therefore, in the present chapter, formulation of the energy transport pertinent to the micro/nano scale is revisited and the resulting equations are analytically tackled with appropriate boundary conditions as in line with the previous studies. The electron kinetic theory approach is incorporated to derive a hyperbolic form of the heat equation while the Boltzmann equation is reduced to the equation for the radiative phonon transport to account for the micro/nano scale heat transfer. The analytical solution of thermal stress equation is provided and material response, in terms of thermal stresses, to the surface heat source is demonstrated.

Original languageEnglish
Title of host publicationNano- and Microscale Processing - Modeling
PublisherElsevier Ltd.
Number of pages17
ISBN (Print)9780080965338
StatePublished - May 2014

Bibliographical note

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


  • Analytical solution
  • Boltzmann equation
  • Electron kinetic theory
  • Energy transport
  • Micro/nano scale
  • Phonon transport
  • Short-pulse
  • Temperature
  • Thermal stress
  • Thin films

ASJC Scopus subject areas

  • General Materials Science
  • General Engineering


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