Abstract
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 language | English (US) |
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Pages (from-to) | 751-775 |
Number of pages | 25 |
Journal | International Journal for Numerical Methods in Engineering |
Volume | 77 |
Issue number | 6 |
DOIs | |
State | Published - Feb 5 2009 |
Keywords
- Asymptotic series
- Laplace transform
- Parabolic partial differential equation
- Solids
- Surface spherical harmonics
- Thermal effects