@Article{cmc.2005.002.001,
AUTHOR = {Julieta António, António  Tadeu, Luís  Godinho, Nuno Simões},
TITLE = {Benchmark Solutions for Three-Dimensional Transient Heat Transfer in Two-Dimensional Environments Via the Time Fourier Transform},
JOURNAL = {Computers, Materials \& Continua},
VOLUME = {2},
YEAR = {2005},
NUMBER = {1},
PAGES = {1--12},
URL = {http://www.techscience.com/cmc/v2n1/22357},
ISSN = {1546-2226},
ABSTRACT = {The evaluation of heat propagation in the time domain generated by transient heat sources placed in the presence of three-dimensional media requires the use of computationally demanding numerical schemes. The implementation of numerical 3D solutions may benefit from the existence of benchmark solutions to test the accuracy of approximate schemes.<br/>
With this purpose inmind, this article presents analyticalnumerical
solutions to evaluate the heat-field elicited by
monopole heat sources in the presence of three different
inclusions, namely, a cylindrical circular solid inclusion,
a cylindrical circular cavity with null fluxes and a
cavity with null temperatures prescribed along its boundary,
buried in an unbounded medium. The problem is
first subjected to a time and space Fourier Transform,
which allows the solution to be obtained in the frequency
domain as summation of 2D solutions for different spatial
wavenumbers. Then, using the inverse Fourier transforms
in the wavenumber and frequency domains, the 3D
time responses are synthesized. Complex frequencies are
used to avoid the aliasing phenomena.<br/>
This methodology is first validated calculating the fundamental
time solutions for one, two and three dimensions
in an unbounded medium. Simulation analyses of these
idealized models are then used to study the patterns of
heat propagation in the vicinity of the inclusions.},
DOI = {10.3970/cmc.2005.002.001}
}