Transient heat conduction in a medium with multiple spherical cavities

Elizaveta Gordeliy, Steven L. Crouch, Sofia G. Mogilevskaya

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14 Scopus citations


This paper considers a transient heat conduction problem for an infinite medium with multiple non-overlapping spherical cavities. Suddenly applied, steady Dirichlet-, Neumann- or Robin-type boundary conditions are assumed. The approach is based on the use of the general solution to the problem of a single cavity and superposition. Application of the Laplace transform and the so-called addition theorem results in a semi-analytical transformed solution for the case of multiple cavities. The solution in the time domain is obtained by performing a numerical inversion of the Laplace transform. A large-time asymptotic series for the temperature is obtained. The limiting case of infinitely large time results in the solution for the corresponding steady-state problem. Several numerical examples that demonstrate the accuracy and the efficiency of the method are presented.

Original languageEnglish (US)
Pages (from-to)751-775
Number of pages25
JournalInternational Journal for Numerical Methods in Engineering
Issue number6
StatePublished - Feb 5 2009


  • Asymptotic series
  • Laplace transform
  • Parabolic partial differential equation
  • Solids
  • Surface spherical harmonics
  • Thermal effects

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