### Abstract

The spectral boundary element method for solving two-dimensional transient heat conduction problems is developed. This method is combined with the fast Fourier transform (FFT) to convert the solution between the time and frequency domains. The fundamental solutions in the frequency domain, required for the present method, are discussed. The resulting line integrations in the frequency domain are discretized using constant boundary elements and used in a Fortran boundary element program. Three examples are used to illustrate the accuracy and effectiveness of the method in both the frequency and time domains. First, the frequency domain solution procedure is verified using the steady-state example of a semi-infinite half space with a heat flux applied to a patch of the surface. This spectral boundary element method is then applied to the problem of a circular hole in an infinite solid subjected to a time-varying heat flux, and solutions in both the frequency and time domains are presented. Finally, the method is used to solve the circular hole problem with a convection boundary condition. The accurary of these results leads to the conclusion that the spectral boundary element method in conjunction with the FFT is a viable option for transient problems. In addition, this spectral approach naturally produces frequence domain information which is itself of interest.

Original language | English (US) |
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Pages (from-to) | 813-827 |

Number of pages | 15 |

Journal | International Journal of Numerical Methods for Heat & Fluid Flow |

Volume | 5 |

Issue number | 9 |

DOIs | |

State | Published - Sep 1 1995 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Mechanics of Materials
- Mechanical Engineering
- Computer Science Applications
- Applied Mathematics

### Keywords

- Fast Fourier transform
- Spectral boundary elements