Numerical Computation of Transient and Steady-State Periodic Thermal Wave Distribution in Homogeneous Media

  • P. M. Patel
  • S. K. Lau
  • D. P. Almond
Part of the Review of Progress in Quantitative Nondestructive Evaluation book series


Thermal wave inspection techniques utilise controlled heat diffusion to probe the surface and subsurface structure of a component [1–3]. Various techniques have been developed which use localised intensity or spatially modulated laser heating for thermal wave generation [2] and a variety sensors, acoustic, optical, and thermal, for their detection [3,4]. The quantitative application of these techniques rely on the computation of the surface temperature and its relation to the internal or surface thermal structure. Analytical solutions for the surface temperature are available for the inspection of layered structures, for example, a coating on a substrate. For samples containing defects of a finite geometry (spherical, lens, cylindrical, disc void/inclusion etc) analytical solutions are difficult to obtain. In these cases numerical methods are employed to solve the heat diffusion equation for the surface temperature. In this paper we discuss the application and limitations of finite difference method for periodic and transient heat diffusion.


Boundary Element Method Thermal Wave Rear Face Defect Width Thermal Diffusion Length 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Physical Acoustics 18; Ed W.P Mason and Thruston. ( Academic Press, New York, 1989 )Google Scholar
  2. 2.
    Review of Progress in Ouantitative NDE. 8A and 8B; ed., D.P Thompson and D.E. Chimenti, ( Plenum Press, 1989 )Google Scholar
  3. 3.
    Photothermal Investigations in Solid and Fluids. ed., J.A. Sell, ( Academic Press, New YorK, 1989 )Google Scholar
  4. 4.
    Photoacoustics and thermal wave phenomena in semiconductors. ed., A. Mandelis, (North Holland Press, 1987 )Google Scholar
  5. 5.
    Y. Jaluria and K.E. Torrance, Computational Heat Transfer. (Hemisphere Pub. Company, 1986 )Google Scholar
  6. 6.
    O. C. Zienkiewicz, The Finite Element Method, 3rd Edition. (McGraw-Hill, 1986 )Google Scholar
  7. 7.
    Boundary Element Methods. X. ed.,C.A. Brebbia, ( Comput. Mech. Pub, 1988 )Google Scholar
  8. 8.
    K. J. Baumeister, Heat Transfer: Research and application, AIChE Symp. Ser. 74 (174) p243–249 (1978)Google Scholar
  9. 9.
    Mathsoft Int. One Kendall Sq., Cambridge, MA 02139, USA.Google Scholar
  10. 10.
    NAG Ltd, Wilkinson House, Jorden Hill Road, Oxford, OX2 8DR. EnglandGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • P. M. Patel
    • 1
  • S. K. Lau
    • 1
  • D. P. Almond
    • 1
  1. 1.School of Materials ScienceUniversity of BathBath, AvonEngland

Personalised recommendations