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Transient heat conduction in a medium with multiple spherical cavities
Author(s) -
Gordeliy Elizaveta,
Crouch Steven L.,
Mogilevskaya Sofia G.
Publication year - 2008
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2430
Subject(s) - laplace transform , thermal conduction , superposition principle , mathematics , mathematical analysis , neumann boundary condition , transient (computer programming) , boundary value problem , heat equation , robin boundary condition , physics , thermodynamics , computer science , operating system
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. Copyright © 2008 John Wiley & Sons, Ltd.