INTEGRAL TRANSFORM SOLUTION OF HEAT CONDUCTION IN ANISOTROPIC HETEROGENEOUS MEDIA - Institut de Thermique, Mécanique, Matériaux Accéder directement au contenu
Article Dans Une Revue Computational Thermal Sciences: An International Journal Année : 2023

INTEGRAL TRANSFORM SOLUTION OF HEAT CONDUCTION IN ANISOTROPIC HETEROGENEOUS MEDIA

Résumé

The generalized integral transform technique (GITT) is advanced to deal with conduction heat transfer in anisotropic heterogeneous media. A formal solution for exact integral transformation of conduction in anisotropic media is extended to account for heterogeneities expressed as space variable equation coefficients and source terms. The proposed eigenfunction expansion is based on biorthogonal eigenvalue problems, which results in an exact integral transformation for a class of linear problems and in a coupled transformed ordinary differential system for nonlinear situations. An algorithm is proposed for the associated eigenvalue problems, also handled through the GITT, by considering simpler biorthogonal eigenvalue problems of known analytical solution, leading to transformed algebraic eigenvalue problems. A single domain reformulation strategy is adopted to merge the information from multiple regions and materials, either isotropic or anisotropic, into one single diffusion equation. A two-dimensional transient test case is considered that presents an abrupt transition between isotropic and anisotropic materials yielding a marked change in thermal behavior in a defined region of interest formed by the anisotropic inclusion. Convergence behavior of the integral transform solution is illustrated, and the fully converged results are employed as a benchmark to inspect the accuracy of a commercial finite element code for automatically defined mesh refinement levels.
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hal-04595064 , version 1 (30-05-2024)

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Renato Cotta, Mohammed Lachi, Carolina Palma Naveira-Cotta, Arthur E.H. Bruno. INTEGRAL TRANSFORM SOLUTION OF HEAT CONDUCTION IN ANISOTROPIC HETEROGENEOUS MEDIA. Computational Thermal Sciences: An International Journal, 2023, Computational Thermal Sciences: An International Journal, 16 (2), pp.65-90. ⟨10.1615/ComputThermalScien.2023049260⟩. ⟨hal-04595064⟩

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