Overcooling Phenomenon by Symmetrical or Asymmetrical Collision of Thermal Waves in Thin Film

  • Shuichi Torii
  • Wen-Jei Yang
Part of the NATO Science Series book series (NAII, volume 99)


A numerical study is performed to investigate wave nature of thermal propagation in a very thin film subjected to asymmetrical or symmetrical temperature change, i.e., cooling, on both sides. The non-Fourier, hyperbolic heat conduction equation is solved using a numerical technique based on MacCormak’s predictorcorrector scheme. Consideration is given to the time history of heat transfer behavior before and after asymmetrical or symmetrical collision of wave fronts from two sides of a filmThe heat conduction in materials in dimension such that Fourier’s law is accurate and appropriate, is usually treated as a diffusion process. In other words, Fourier’s law predicts that conduction is a diffusion phenomenon in which temperature disturbances propagate at an infinite velocity and at time t=0, the heat flux at the wall is infinite while the temperature change is nonzero everywhere except at infinity. Despite such an unacceptable notation pertinent to physical reality, Fourier’s law gives quite reliable results in most practical heat transfer applications. However, the classical Fourier heat conduction equation breaks down at temperatures near absolute zero or at moderate temperatures when the elapsed time during a transient is extremely small. This is because the wave nature of thermal propagation is dominant, that is, a thermal disturbance travels in the medium with a finite speed of propagation (Baumeister and Hamill 1969; Chan et al., 1971; Kazimi and Erdman, 1975; Mourer and Thompson, 1973). Several issues of basic scientific interest arise in cases such as laser penetration and welding, explosive bonding, electrical discharge machining, and heating and cooling of micro-electronic elements involving a duration time of nanosecond or even picosecond in which energy is absorbed within a distance of microns from the surface. For example, the issue of energy transfer into a lattice and resulting temperature in the lattices during such a short period of time and over such a tiny region is of fundamental importance but remains a matter of controversy (Bloembergen et al., 1982).


Heat Transfer Electrical Discharge Machine Thermal Wave Thermal Propagation Thermal Relaxation Time 
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Copyright information

© Springer Science+Business Media Dordrecht 2003

Authors and Affiliations

  • Shuichi Torii
    • 1
  • Wen-Jei Yang
    • 2
  1. 1.Department of Mechanical EngineeringKagoshima UniversityKagoshimaJapan
  2. 2.Mechanical Engineering and Applied MechanicsThe University of MichiganAnn ArborUSA

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