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Integral Transform Solutions for Diffusion in Heterogeneous Media

[+] Author Affiliations
Carolina P. Naveira, Renato M. Cotta, Helcio R. B. Orlande

Universidade Federal do Rio de Janeiro, Rio de Janeiro, RJ, Brazil

Olivier Fudym

École de Mines d’Albi-Carmaux, Albi, Carmaux, France

Paper No. IMECE2008-69114, pp. 949-958; 10 pages
doi:10.1115/IMECE2008-69114
From:
  • ASME 2008 International Mechanical Engineering Congress and Exposition
  • Volume 10: Heat Transfer, Fluid Flows, and Thermal Systems, Parts A, B, and C
  • Boston, Massachusetts, USA, October 31–November 6, 2008
  • Conference Sponsors: ASME
  • ISBN: 978-0-7918-4871-5 | eISBN: 978-0-7918-3840-2
  • Copyright © 2008 by ASME

abstract

The Generalized Integral Transform Technique is employed in the hybrid numerical-analytical solution of heat diffusion problems in heterogeneous media. The GITT is utilized to handle the associated eigenvalue problem with aribitrarily space variable coefficients, defining an eigenfunction expansion in terms of a Sturm-Liouville problem of known solution. The formal solution is first applied in solving an example of space variable thermophysical properties found in heat transfer analysis of functionally graded materials (FGM), validated by the exact solution obtained through classical integral transforms in the specific situation of exponentially varying coefficients. Then, it is challenged in handling a double-layered system with abrupt variation of properties, and critically compared against the exact solution obtained by the classical integral transform method with the adequate discontinuous multi-region eigenvalue problem. The convergence behavior of the proposed expansions is then critically inspected and numerical results are presented to demonstrate the applicability of the general approach.

Copyright © 2008 by ASME

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