Eigenfunction expansions for transient diffusion in heterogeneous media |
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Authors: | Carolina P Naveira-Cotta Renato M Cotta Helcio RB Orlande Olivier Fudym |
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Affiliation: | aLTTC – Laboratory of Transmission and Technology of Heat Mechanical Engineering Department, POLI/COPPE, Universidade Federal do Rio de Janeiro, UFRJ Cx. Postal 68503, Cidade Universitária, 21945-970, Rio de Janeiro, RJ, Brazil;bRAPSODEE UMR 2392 CNRS École des Mines d’Albi, Albi, France |
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Abstract: | The Generalized Integral Transform Technique (GITT) is employed in the analytical solution of transient linear heat or mass diffusion problems in heterogeneous media. The GITT is utilized to handle the associated eigenvalue problem with arbitrarily space variable coefficients, defining an eigenfunction expansion in terms of a simpler Sturm-Liouville problem of known solution. In addition, the representation of the variable coefficients as eigenfunction expansions themselves has been proposed, considerably simplifying and accelerating the integral transformation process, while permitting the analytical evaluation of the coefficients matrices that form the transformed algebraic system. The proposed methodology is challenged in solving three different classes of diffusion problems in heterogeneous media, as illustrated for the cases of thermophysical properties with large scale variations found in heat transfer analysis of functionally graded materials (FGM), of abrupt variations in multiple layer transitions and of randomly variable physical properties in dispersed systems. The convergence behavior of the proposed expansions is then critically inspected and numerical results are presented to demonstrate the applicability of the general approach and to offer a set of reference results for potentials, eigenvalues, and related quantities. |
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Keywords: | Heterogeneous media Diffusion Variable physical properties Heat conduction Sturm-Liouville problems Integral transforms |
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