Transient heat conduction in a medium with two circular cavities: Semi-analytical solution

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

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

This paper considers a transient heat conduction problem for an infinite medium with two non-overlapping circular cavities. Suddenly applied, steady Dirichlet type boundary conditions are assumed. The approach is based on superposition and the use of the general solution to the problem of a single cavity. Application of the Laplace transform results in a semi-analytical solution for the temperature in the form of a truncated Fourier series. The large-time asymptotic formulae for the solution are obtained by using the analytical solution in the Laplace domain. The method can be extended to problems with multiple cavities and inhomogeneities.

Original languageEnglish (US)
Pages (from-to)3556-3570
Number of pages15
JournalInternational Journal of Heat and Mass Transfer
Volume51
Issue number13-14
DOIs
StatePublished - Jul 1 2008

Keywords

  • Addition theorem
  • Asymptotic series
  • Fourier series
  • Laplace transform
  • Modified Helmholtz equation
  • Transient heat conduction

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