Thermal-Wave Fields in Spherical Coordinates

  • Andreas Mandelis


This chapter begins with spherical thermal-wave fields generated by a point source, spatially spherically asymmetric distributions, as well as azimuthally symmetric sources. The experimentally important Gaussian photothermal source distribution is then examined in some detail in cases of optically opaque and absorbing spheres. Spherically symmetric sources and hollow spheres are then treated in the spirit of Theorem 7.1. Finally, the chapter closes with the derivation of thermal-wave fields in spherical cones.


Heat Transfer Coefficient Green Function Spherical Coordinate Thermophysical Property Hollow Sphere 
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. M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions (National Bureau of Standards Appl. Math. Ser. 55, Washington, DC, 1964).zbMATHGoogle Scholar
  2. P. S. Belton, R. H. Wilson, and A. M. Saffa, Anal. Chem. 59, 2378 (1987).CrossRefGoogle Scholar
  3. R. Bracewell, The Fourier Transform and its Applications (McGraw-Hill, New York, 1965).zbMATHGoogle Scholar
  4. J. J. Freedman, R. M. Friedman, and H. R. Reichard, J. Phys. Chem. 84, 315 (1980).CrossRefGoogle Scholar
  5. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (English Translation) (A. Jeffrey, ed.) (Academic, Orlando, FL, 1980).Google Scholar
  6. R. N. Hall, J. Appl. Phys. 20, 925 (1949).MathSciNetADSzbMATHCrossRefGoogle Scholar
  7. J. D. Jackson, Classical Electrodynamics, 2nd Ed. (Wiley, New York, 1975).zbMATHGoogle Scholar
  8. J.-P. Monchalin, L. Bertrand, G. Rousset, and F. Lepoutre, J. Appl. Phys. 56, 190 (1984).ADSCrossRefGoogle Scholar
  9. P. M. Morse and H. Feshbach, Methods of Theoretical Physics, Vol. I (McGraw-Hill, New York, 1953).zbMATHGoogle Scholar
  10. H. K. Wickramasinghe, Sci. Am. (Oct. 1989), p. 98.Google Scholar
  11. H. K. Wicramasinghe, J. Vac. Sci. Technol. A 8, 383 (1990).ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Andreas Mandelis
    • 1
  1. 1.Department of Mechanical and Industrial Engineering, Photothermal and Optoelectronic Diagnostics LaboratoryUniversity of TorontoTorontoCanada

Personalised recommendations